11institutetext:  Instituto de Física Fundamental, CSIC, C/ Serrano 123, 28006
Madrid, Spain
11email<EMAIL_ADDRESS><EMAIL_ADDRESS>22institutetext:
Observatorio Astronómico Nacional, IGN, Calle Alfonso XII 3, 28014 Madrid,
Spain 33institutetext: Observatorio de Yebes, IGN, Cerro de la Palera s/n,
19141 Yebes, Guadalajara, Spain

# The chemistry of H2NC in the interstellar medium and
the role of the C + NH3 reaction††thanks: Based on observations carried out
with the IRAM 30m Telescope. IRAM is supported by INSU/CNRS (France), MPG
(Germany) and IGN (Spain).

M. Agúndez 11 O. Roncero 11 N. Marcelino 2233 C. Cabezas 11 B. Tercero 2233 J.
Cernicharo 11

(Received; accepted)

We carried out an observational search for the recently discovered molecule
H2NC, and its more stable isomer H2CN, toward eight cold dense clouds (L1544,
L134N, TMC-2, Lupus-1A, L1489, TMC-1 NH3, L1498, and L1641N) and two diffuse
clouds (B0415+379 and B0355+508) in an attempt to constrain its abundance in
different types of interstellar regions and shed light on its formation
mechanism. We detected H2NC in most of the cold dense clouds targeted, 7 out
of 8, while H2CN was only detected in 5 out of 8 clouds. The column densities
derived for both H2NC and H2CN are in the range 1011-1012 cm-2 and the
abundance ratio H2NC/H2CN varies between 0.51 and $>$ 2.7. The metastable
isomer H2NC is therefore widespread in cold dense clouds where it is present
with an abundance similar to that of H2CN. We did not detect either H2NC or
H2CN in any of the two diffuse clouds targeted, which does not allow to shed
light on how the chemistry of H2NC and H2CN varies between dense and diffuse
clouds. We found that the column density of H2NC is correlated with that of
NH3, which strongly suggests that these two molecules are chemically linked,
most likely ammonia being a precursor of H2NC through the C + NH3 reaction. We
performed electronic structure and statistical calculations which show that
both H2CN and H2NC can be formed in the C + NH3 reaction through two different
channels involving two different transition states which lie very close in
energy. The predicted product branching ratio H2NC/H2CN is very method
dependent but values between 0.5 and 0.8 are the most likely ones. Therefore,
both the astronomical observations and the theoretical calculations support
that the reaction C + NH3 is the main source of H2NC in interstellar clouds.

###### Key Words.:

astrochemistry – line: identification – molecular processes – ISM: molecules –
radio lines: ISM

##  1 Introduction

The detection of H2NC in the interstellar medium by Cabezas et al. (2021) came
as a surprise. The observation of several groups of unidentified lines in the
cold dense clouds L483 and B1-b motivated the search for potential carriers,
among which H2NC was not initially considered. Only after many plausible
candidates were ruled out, H2NC was found to confidently reproduce the complex
spectral pattern of astronomical lines. H2NC was not initially considered as a
plausible carrier because it is a high-energy isomer of H2CN, which lies
$\sim$ 30 kcal mol-1 above in energy (Puzzarini, 2010; Cabezas et al., 2021).
Moreover, there are two isomers not yet detected in space which are
substantially more stable than H2NC. These are the trans and cis forms of
HCNH, which lie $\sim$ 8 and $\sim$ 13 kcal mol-1, respectively, above the
most stable isomer H2CN (Puzzarini, 2010; Cabezas et al., 2021). It is worth
to note that although H2NC is the least stable member of this family of four
isomers, it is the one showing the most intense lines in L483 and B1-b.

The discovery of interstellar H2NC came with several interesting implications.
In addition to L483 and B1-b, H2NC was also detected toward the $z$ = 0.89
galaxy in front of the quasar PKS 1830$-$211, which is a high-redshift source
exceptionally rich in molecules (Muller et al., 2011; Tercero et al., 2020).
The fact that the abundance ratio H2NC/H2CN is $\sim$ 1 in L483 and B1-b and
0.27 toward PKS 1830$-$211 suggests that this ratio behaves as the HNC/HCN
ratio, with values close to one in cold dense clouds and below one in diffuse
clouds (Hirota et al., 1998; Sarrasin et al., 2010; Liszt & Lucas, 2001).
Surprisingly, neither H2NC nor H2CN were detected toward the cyanopolyyne peak
of TMC-1 (hereafter TMC-1 CP) in spite of a previous claim of detection of
H2CN in this cloud by Ohishi et al. (1994). While TMC-1 CP is a young starless
core rich in carbon chains, L483 and B1-b are more evolved sources rich in
molecules such as ammonia. The detection of H2NC in L483 and B1-b and its non
detection in TMC-1 CP suggests that this species is more favored in NH3-rich
sources. This would be in line with the suspected chemical origin of H2NC due
to the reaction C + NH3 (see discussion in Cabezas et al. 2021).

In order to shed light on the issues raised by the discovery of H2NC, that is,
whether or not the H2NC/H2CN ratio behaves differently in dense and diffuse
clouds, as occurs for the HNC/HCN ratio, and whether or not there is a
correlation between the abundances of H2NC and NH3, which would reflect a
chemical link between the two species, we carried out an observational survey
to search for H2NC, and simultaneously for H2CN, toward a sample of dense and
diffuse clouds with the IRAM 30m telescope. Here we report the results of this
survey. We also present a computational study of the reaction between C and
NH3 aimed at investigating whether or not H2NC can be formed in this reaction
at the low temperatures of cold interstellar clouds.

##  2 Astronomical observations

Table 1: Sources coordinates. Source | RA(J2000.0) | Dec(J2000.0)
---|---|---
L1544 | 05:04:18.10 |  $+$25:10:48.0
L134N | 15:54:06.55 |  $-$02:52:19.1
TMC-2 | 04:32:44.74 |  $+$24:24:33.5
Lupus-1A | 15:42:52.40 |  $-$34:07:53.5
L1489 | 04:04:50.60 |  $+$26:18:29.4
TMC-1 NH3 | 04:41:23.02 |  $+$25:48:13.3
L1498 | 04:10:51.46 |  $+$25:09:58.2
L1641N | 05:36:19.01 |  $-$06:22:13.3
B0415+379 | 04:18:21.28 |  $+$38:01:35.8
B0355+508 | 03:59:29.75 |  $+$50:57:50.2
Table 2: Line parameters of the strongest hyperfine components of H2NC and
H2CN.

Source | Molecule | Transition | $\nu_{calc}$ | $V_{\rm LSR}$ | $\Delta v$ |  $T_{A}^{*}$ peak | $\int T_{A}^{*}dv$
---|---|---|---|---|---|---|---
|  |  | (MHz) |  (km s-1) |  (km s-1) | (mK) |  (mK km s-1)
L1544 |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 72194.211 | 7.10(2) | 0.49(4) | 31.7(2) | 16.5(10)
L1544 |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 72210.940 | 7.13(3) | 0.48(6) | 26.4(2) | 13.4(14)
L134N |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 72194.211 | 2.40(2) | 0.47(3) | 39.4(3) | 19.6(10)
L134N |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 72210.940 | 2.40(3) | 0.43(6) | 25.7(3) | 11.8(15)
TMC-2 |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 72194.211 | 6.19(5) | 0.45(13) | 19.4(5) | 9.3(21)
TMC-2 |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 72210.940 | 6.25(4) | 0.20(10) | 16.8(5) |  3.6(16) a
Lupus-1A |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 72194.211 | 5.00(8) | 0.40(19) | 18.9(5) | 8.0(27)
Lupus-1A |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 72210.940 | 5.11(5) | 0.34(10) | 17.7(5) | 6.4(17)
L1489 |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 72194.211 | 6.66(4) | 0.50(9) | 14.1(3) | 7.4(12)
L1489 |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 72210.940 | 6.71(5) | 0.39(10) | 14.2(3) | 5.9(14)
TMC-1 NH3 |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 72194.211 | 5.89(3) | 0.54(8) | 22.8(2) | 13.0(17)
TMC-1 NH3 |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 72210.940 | 5.86(4) | 0.54(9) | 22.4(2) | 12.7(18)
L1498 |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 72194.211 | 7.71(5) | 0.57(14) | 16.7(4) | 10.2(20)
L1498 |  H2NC |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 72210.940 | 7.80(2) | 0.20(10) | 20.2(4) | 4.4(13)
L1544 |  H2CN |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 73345.486 | 7.19(3) | 0.39(7) | 14.9(2) | 6.2(9)
L1544 |  H2CN |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 73349.648 | 7.23(3) | 0.40(5) | 17.8(2) | 7.6(9)
L134N |  H2CN |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 73345.486 | 2.53(7) | 0.40(15) | 6.6(2) |  2.8(9) a
L134N |  H2CN |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 73349.648 | 2.45(5) | 0.50(15) | 11.8(2) | 6.3(14)
TMC-2 |  H2CN |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 73345.486 | 6.40(11) | 0.67(22) | 10.5(4) | 7.5(23)
TMC-2 |  H2CN |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 73349.648 | 6.47(7) | 0.46(20) | 17.0(4) | 8.2(25)
Lupus-1A |  H2CN |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 73345.486 | 4.97(9) | 0.31(16) | 9.9(4) |  3.3(16) a
Lupus-1A |  H2CN |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 73349.648 | 5.10(2) | 0.20(10) | 28.9(4) | 6.1(16)
L1489 |  H2CN |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 2.5-1.5 | 73345.486 | 6.49(5) | 0.49(13) | 7.8(2) | 4.1(9)
L1489 |  H2CN |  10,1-00,0 $J$ = 1.5-0.5 $F_{1}$ = 2.5-1.5 $F$ = 3.5-2.5 | 73349.648 | 6.86(5) | 0.33(8) | 9.1(2) | 3.2(8)

The line parameters $V_{\rm LSR}$, $\Delta v$ (full width at half maximum),
$T_{A}^{*}$ peak, and $\int T_{A}^{*}dv$ were derived from a Gaussian fit to
the line profile. Numbers in parentheses are 1$\sigma$ uncertainties in units
of the last digits. a Marginal detection.

The astronomical observations were carried out with the IRAM 30m telescope
during December 2021, April 2022, and June 2022. The weather conditions ranged
from very good to moderate, with levels of precipitable water vapor in the
range 1-10 mm. We used the EMIR E090 receiver connected to a fast Fourier
transform spectrometer providing a spectral resolution of 48.8 kHz. We
targeted the 10,1-00,0 rotational transition of ortho H2NC, which consists of
multiples hyperfine components around 72.2 GHz, and the 10,1-00,0 transition
of ortho H2CN, which has the strongest hyperfine components around 73.3 GHz.
For both H2NC and H2CN, ortho levels have $K_{a}$ even, while para levels have
$K_{a}$ odd.

We searched for H2NC toward the cold dense clouds L1544, L134N, TMC-2,
Lupus-1A, L1489, TMC-1 at the peak position of NH3 (hereafter TMC-1 NH3),
L1498, and L1641N, and toward the diffuse clouds B0355+508 and B0415+379. The
source coordinates are given in Table 1. The criteria to select these sources
were bright emission of HNC, based on the expected analogy of the H2NC/H2CN
and HNC/HCN ratios, and bright emission of NH3, because of the potential
correlation between H2NC and NH3. We used the studies of cold dense clouds by
Suzuki et al. (1992) for ammonia data and by Hirota et al. (1998) for HNC
data. We also included the dense core Lupus-1A because of its similarity to
TMC-1 CP (Sakai et al., 2010). Regarding diffuse clouds, we included the two
clouds among the sample of Liszt & Lucas (2001) with the deepest absorption of
HNC, B0415+379 and B0355+508, both of which show also deep absorption by NH3
(Liszt et al., 2006).

For the cold dense clouds the observations were carried out in the frequency-
switching observing mode with a frequency throw of 7.2 MHz, while for the
diffuse clouds we used the wobbler-switching observing mode with the secondary
mirror nutating by 3′ at a rate of 0.5 Hz. Focus was checked at the beginning
of each observing session and after sunrise and sunset and pointing was
regularly checked every 1 h. The intensity scale is expressed in terms of
$T_{A}^{*}$, the antenna temperature corrected for atmospheric absorption and
for antenna ohmic and spillover losses. The uncertainty in $T_{A}^{*}$ is
estimated to be around 10 %. All data were reduced using the program CLASS
from the software GILDAS111https://www.iram.fr/IRAMFR/GILDAS/.

Figure 1: Spectra of L1544, L134N, TMC-2, Lupus-1A, L1489, TMC-1 NH3, and
L1498 in the region covering the two most intense hyperfine components of the
10,1-00,0 transition of H2NC, at 72194.211 MHz and 72210.940 MHz. In red we
show the calculated synthetic spectra for H2NC adopting the column densities
given in Table 3, an ortho-to-para ratio of 3, a rotational temperature of 4.0
K, a line width consistent with the values derived from the observations (see
Table 2), and an emission size that fills the IRAM 30m main beam. The bright
line around 72198 MHz corresponds to C2D (see Cabezas et al. 2021). Figure 2:
Spectra of L1544, L134N, TMC-2, Lupus-1A, and L1489 in the region covering two
of the brightest hyperfine components of the 10,1-00,0 transition of H2CN,
lying at 73345.486 MHz and 73349.648 MHz. In red we superimpose the computed
synthetic spectra for H2CN adopting the column densities given in Table 3, an
ortho-to-para ratio of 3, a rotational temperature of 4.0 K, a line width
consistent with the values derived from the observations (see Table 2), and an
emission size that fills the IRAM 30m main beam. Figure 3: Spectra of
B0415+379 and B0355+508 at the frequencies of H2CO 10,1-00,0 (72837.949 MHz)
and of the strongest hyperfine component of H2NC and H2CN (72194.211 MHz and
73349.648 MHz, respectively). The $y$ axis is expressed as line/continuum. The
position of the deepest absorption of H2CO, $V_{\rm LSR}$ = $-$0.9 km s-1 in
B0415+379 and $V_{\rm LSR}$ = $-$10.4 km s-1 in B0355+508, is indicated by a
blue dotted vertical line.

##  3 Astronomical results

###  3.1 Detections and non-detections of H2NC and H2CN

The high-energy isomer H2NC turned out to be easier to detect than its more
stable isomer H2CN. We detected H2NC in 7 out of the 8 cold dense clouds
targeted (L1544, L134N, TMC-2, Lupus-1A, L1489, TMC-1 NH3, and L1498; that is,
in all but L1641N), while H2CN was only detected in 5 of these sources (L1544,
L134N, TMC-2, Lupus-1A, and L1489). On the other hand, neither H2NC nor H2CN
were detected in the two diffuse clouds observed, B0415+379 and B0355+508.

We searched for H2NC through the 10,1-00,0 transition, which lies around 72.2
GHz and spreads over $\sim$ 50 MHz due to fine and hyperfine splitting (see
Cabezas et al. 2021). In Fig. 1 we show the part of the spectrum covering the
two brightest hyperfine components for the 7 cold dense clouds where H2NC was
detected. The strongest component at 72194.211 MHz is well detected in the 7
sources, while the second strongest one at 72210.940 MHz is well seen in all
sources except TMC-2, where it is only marginally detected. In addition, there
are various weaker hyperfine components for which there is a good match
between observed and calculated spectra. The line parameters for the two
strongest components of H2NC 10,1-00,0 are given in Table 2. In the case of
H2CN, we targeted the 10,1-00,0 transition, which lies around 73.3 GHz and has
also a complex hyperfine pattern with components spread over almost 200 MHz.
We show the observed spectra around the most intense component, lying at
73349.648 MHz, for the 5 cold dense clouds where H2CN was detected in Fig. 2.
In some of the sources the weaker component at 73345.486 MHz is also clearly
seen. The line parameters for these two components are given in Table 2.

The two isomers H2NC and H2CN were also searched for toward the diffuse clouds
B0415+379 and B0355+508, although none of them were detected in these two
sources. In Fig. 3 we show the observed spectra around the strongest hyperfine
component of H2NC and H2CN, at 72194.211 MHz and 73349.648 MHz, respectively,
for the two clouds. In addition we show the observed spectra around the
10,1-00,0 transition of H2CO, lying at 72837.949 MHz, which shows absorption
at different velocities, in agreement with previous observations of other
transitions of H2CO toward these two sources (Liszt & Lucas, 1995). The
ordinate scale is expressed as line/continuum, following the convention by
Liszt et al. (2006), where by ’line’ we mean the $T_{A}^{*}$ of the observed
spectrum after baseline (or continuum) subtraction and by ’continuum’ we mean
the $T_{A}^{*}$ of the continuum level. We find that the deepest H2CO
absorption in B0415+379 occurs at $V_{\rm LSR}$ = $-$0.9 km s-1, while in
B0355+508 it is located at a velocity of $V_{\rm LSR}$ = $-$10.4 km s-1, in
agreement with previous observations of simple molecules toward these two
sources (e.g., Liszt & Lucas 1995, 2001; Liszt et al. 2006). As shown in Fig.
3, there is not hint of absorption by H2NC or H2CN toward either B0415+379 or
B0355+508.

###  3.2 Calculation of column densities

We calculated column densities for H2NC and H2CN in those sources where the
molecule was detected. When the molecule was not detected, we computed an
upper limit to the column density.

Table 3: Column densities of H2NC and H2CN.

Source |  $N$(H2NC) |  $N$(H2CN) |  H2NC/H2CN | Reference |  |  $N$(NH3) | Reference
---|---|---|---|---|---|---|---
|  (cm-2) |  (cm-2) |  |  |  |  (cm-2) |
cold dense clouds
L483 |  1.0 $\times$ 1012 |  8.0 $\times$ 1011 | 1.25 | (1) |  |  14 $\times$ 1014 | (3)
B1-b |  1.0 $\times$ 1012 |  1.0 $\times$ 1012 | 1.00 | (1) |  |  11.2 $\times$ 1014 | (4)
TMC-1 CP |  $<$ 3.2 $\times$ 1011 |  $<$ 4.8 $\times$ 1011 | – | (1) |  |  1.9 $\times$ 1014 | (4)
L1544 |  3.9 $\times$ 1011 |  4.3 $\times$ 1011 | 0.91 | (2) |  |  2.7 $\times$ 1014 | (4)
L134N |  4.0 $\times$ 1011 |  2.5 $\times$ 1011 | 1.60 | (2) |  |  7.8 $\times$ 1014 | (4)
TMC-2 |  2.1 $\times$ 1011 |  4.1 $\times$ 1011 | 0.51 | (2) |  |  6.1 $\times$ 1014 | (4)
Lupus-1A |  1.9 $\times$ 1011 |  2.8 $\times$ 1011 | 0.68 | (2) |  |  1.1 $\times$ 1014 | (5)
L1489 |  1.7 $\times$ 1011 |  2.1 $\times$ 1011 | 0.81 | (2) |  |  6.3 $\times$ 1014 | (4)
TMC-1 NH3 |  3.3 $\times$ 1011 |  $<$ 1.2 $\times$ 1011 |  $>$ 2.7 | (2) |  |  5.2 $\times$ 1014 | (4)
L1498 |  1.9 $\times$ 1011 |  $<$ 1.4 $\times$ 1011 |  $>$ 1.4 | (2) |  |  4.1 $\times$ 1014 | (4)
L1641N |  $<$ 3.1 $\times$ 1011 |  $<$ 4.6 $\times$ 1011 | – | (2) |  |  11.0 $\times$ 1014 | (4)
diffuse-like clouds
PKS 1830$-$211 |  5.3 $\times$ 1011 |  2.0 $\times$ 1012 | 0.27 | (1) |  |  (5-10) $\times$ 1014 | (6)
B0415+379 |  $<$ 3.1 $\times$ 1011 |  $<$ 5.5 $\times$ 1011 | – | (2) |  |  10.53 $\times$ 1012 | (7)
B0355+508 |  $<$ 9.2 $\times$ 1010 |  $<$ 2.0 $\times$ 1011 | – | (2) |  |  2.54 $\times$ 1012 | (7)

References: (1) Cabezas et al. (2021). (2) This work. (3) Anglada et al.
(1997). (4) Suzuki et al. (1992). (5) Value at position Lup1 C4, $\sim$ 2
arcmin off from Lupus-1A (Benedettini et al., 2012). (6) Henkel et al. (2008).
(7) Values at the velocity components $V_{\rm LSR}$ = $-$0.9 km s-1 for
B0415+379 and $V_{\rm LSR}$ = $-$10.4 km s-1 for B0355+508 (Liszt et al.,
2006).

For the cold dense clouds L1544, L134N, TMC-2, Lupus-1A, L1489, TMC-1 NH3,
L1498, and L1641N we computed H2NC and H2CN column densities assuming local
thermodynamic equilibrium (LTE). Since the hyperfine components of H2NC and
H2CN observed belong to the same rotational transition, the 10,1-00,0 for both
molecules, the detected lines have very similar upper level energies and thus
it is not possible to determine the rotational temperature. In L483 Cabezas et
al. (2021) derive a rotational temperature of 4.0 K for both H2NC and H2CN
from the observation of various rotational transitions with different upper
level energies.This value is lower than the gas kinetic temperature (around 10
K in L483; Anglada et al. 1997; Agúndez et al. 2019), which indicates
subthermal excitation, in line with the fact that these two molecules have
high dipole moments (3.83 D for H2NC and 2.54 D for H2CN; Cabezas et al. 2021;
Cowles et al. 1991). Since cold dense clouds typically have kinetic
temperatures around 10 K and H2 volume densities of a few 104 cm-3 (Benson &
Myers, 1989), in the absence of better constraints we adopted the rotational
temperature derived in L483 for both H2NC and H2CN, 4.0 K, in all the cold
dense clouds. We however note that the excitation of H2NC and H2CN could be
different, as found for other isomer such as HCN and HNC (Hernández Vera et
al., 2017) or the family of isomers of cyanoacetylene (Bop et al., 2019). In
the case of H2NC and H2CN, collision rate coefficients are not available and
thus we cannot investigate this point, although we acknowledge that this
introduces an uncertainty in the calculation of the column densities. Cabezas
et al. (2021) also showed that the ortho-to-para ratio of H2NC in L483 is
consistent with the statistical value of three. We adopt this value here for
both H2NC and H2CN, although we note that this is an additional source of
uncertainty in the calculation of the column densities. With these
assumptions, we computed synthetic spectra for H2NC and H2CN adopting as line
width a value consistent with that observed in each source (see Table 2). The
synthetic spectra calculated for H2NC and H2CN are compared with the observed
ones in Fig. 1 and Fig. 2, respectively, while the corresponding column
densities derived are given in Table 3.

In the case of non-detections of either H2NC or H2CN in cold dense clouds we
derived 3 $\sigma$ upper limits to the column density, which are also given in
Table 3. The only reported detection of H2NC or H2CN in the sources observed
here is that of H2CN in L1544 by Vastel et al. (2019). The column density
derived here, 3.9 $\times$ 1011 cm-2 (see Table 3), is in agreement with the
range of values found by Vastel et al. (2019), (3-6) $\times$ 1011 cm-2.

In the case of the diffuse clouds B0415+379 and B0355+508 we derived upper
limits to the column densities of H2NC and H2CN in the following way. We first
computed the line opacity $\tau$ using the equation (e.g., Linke et al. 1981;
Nyman 1984; Greaves et al. 1992; Corby et al. 2018)

$\tau=\rm-Ln\bigg{(}1+\frac{line}{continuum}\bigg{)}.$ (1)

The velocity-integrated opacity $\int\tau dv$ is then related to the column
density $N$ through the expression (Nyman, 1984; Greaves & Nyman, 1996; Corby
et al., 2018)

$\int\tau
dv=\frac{N}{Q(T_{rot})}\frac{8\pi^{3}S\mu^{2}}{3h}\bigg{(}e^{-E_{l}/kT_{rot}}-e^{-E_{u}/kT_{rot}}\bigg{)},$
(2)

where $T_{rot}$ is the rotational temperature, $Q(T_{rot})$ is the partition
function, $S$ is the line strength, $\mu$ is the dipole moment, $E_{l}$ and
$E_{u}$ are the energies of the lower and upper level, respectively, and $h$
and $k$ are the Planck and Boltzmann constants, respectively. For convenience,
Eq. (2) can be expressed as

$\int\tau dv=\frac{N}{Q(T_{rot})}\frac{S\mu^{2}}{8.0\times
10^{12}}\bigg{(}e^{-E_{l}/T_{rot}}-e^{-E_{u}/T_{rot}}\bigg{)},$ (3)

where $\int\tau dv$ is in units of km s-1, $N$ in cm-2, $\mu$ in Debye, and
$E_{l}$, $E_{u}$, and $T_{rot}$ are in units of K. We assumed a rotational
temperature equal to that of the cosmic microwave background, i.e., 2.725 K.
To derive upper limits to the column densities of H2NC and H2CN we used the
line parameters of the strongest hyperfine component, lying at 72194.211 MHz
and 73349.648 MHz, respectively. For H2NC, $\mu$ = 3.83 D, $Q(2.725K)$ =
35.075, $S$ = 2.67, $E_{l}$ = 0.012 K, and $E_{u}$ = 3.477 K, while for H2CN,
$\mu$ = 2.54 D, $Q(2.725K)$ = 34.597, $S$ = 2.67, $E_{l}$ = 0.018 K, and
$E_{u}$ = 3.538 K. The 3 $\sigma$ upper limits to the column densities of H2NC
and H2CN in B0415+379 and B0355+508 are given in Table 3. As a reference, the
column densities derived for para-H2CO are 4.0 $\times$ 1012 cm-2 in B0415+379
at $V_{\rm LSR}$ = $-$0.9 km s-1 and 1.1 $\times$ 1012 cm-2 in B0355+508 at
$V_{\rm LSR}$ = $-$10.4 km s-1, values which are very similar to those derived
by Liszt & Lucas (1995).

##  4 Astrophysical lessons on H2NC and H2CN

The column densities derived for H2NC and H2CN are typically in the range
1011-1012 cm-2, where the largest values are found for the cold dense clouds
L483 and B1-b and the $z$ = 0.89 galaxy in front of PKS 1830$-$211, which
happen to be the three sources where H2NC was initially discovered by Cabezas
et al. (2021). On the other hand, the H2NC/H2CN abundance ratio is relatively
uniform around unity, with the lowest value of 0.27 found toward PKS
1830$-$211 and the largest one, $>$ 2.7, occurring in the cold dense cloud
TMC-1 NH3. We aim to understand whether the abundances of H2NC and H2CN, or
the abundance ratio H2NC/H2CN, depend on some physical or chemical
characteristic of the host cloud.

Figure 4: The column density of H2NC is represented as a function of the
column density of NH3 for the sources where H2NC has been searched for. Cold
dense clouds are plotted in blue and diffuse-like clouds in magenta. The
values of the column densities and the corresponding references are given in
Table 3.

Cabezas et al. (2021) proposed that the H2NC/H2CN ratio could behave as the
HNC/HCN ratio, with values close to one in cold dense clouds and below one in
diffuse clouds. This idea was suggested by the fact that the H2NC/H2CN ratio
derived in the cold dense clouds L483 and B1-b was $\sim$ 1, while in the
redshifted galaxy in front of the quasar PKS 1830$-$211, which has a chemical
composition characteristic of a diffuse or translucent cloud, the H2NC/H2CN
ratio was found to be 0.27. With this idea in mind, in this study we searched
for H2NC and H2CN in various cold dense clouds and in the two most promising
diffuse clouds known to contain a relatively rich molecular content, based on
the series of studies by Liszt and Lucas (e.g., Liszt & Lucas 2001; Liszt et
al. 2006). The observations of cold dense clouds carried out here confirm that
the H2NC/H2CN ratio is close to one in this type of sources, with the largest
deviation occurring for TMC-1 NH3, where the detection of H2NC and the non
detection of H2CN set a lower limit to the H2NC/H2CN of 2.7. However, we did
not detect H2NC or H2CN toward the diffuse clouds B0415+379 and B0355+508,
making impossible to constrain the H2NC/H2CN ratio in galactic diffuse clouds.
The non detection of H2NC and H2CN in these two diffuse clouds is probably
related to a too low column density of NH3, in comparison with the typical
column densities of NH3 in cold dense clouds, which are 1-2 orders of
magnitude higher (see discussion on this point below). The sensitivity
achieved in the IRAM 30m observations of these two diffuse clouds, in
particular for B0415+379 where the $T_{A}^{*}$ rms noise level reached is
$\sim$ 4 mK, suggests that it would be challenging to detect either H2NC or
H2CN in a galactic diffuse cloud. It seems therefore difficult to confirm
whether or not the H2NC/H2CN ratio is significantly lower in diffuse clouds
than in cold dense clouds.

Another interesting feature discussed by Cabezas et al. (2021) concerns the
chemical origin of H2NC. The reactions N + CH3 and C + NH3 are two potentially
important sources of H2NC. Chemical routes to H2NC involving ions are also
possible. For example, the dissociative recombination of cations, such as
CH3N+, CH2NH${}_{2}^{+}$, CH3NH${}_{2}^{+}$, or CH3NH${}_{3}^{+}$, with
electrons could produce as fragments H2NC and H2CN, although experimental or
theoretical information on these reactions is scarce (Yuen et al., 2019). A
similar mechanism operates in cold dense clouds for HCN and HNC, with the two
isomers being formed with nearly equal yields upon dissociative recombination
of HCNH+ with electrons (Mendes et al., 2012). The reaction C + NH3 is a more
likely source of H2NC than N + CH3 because it involves a smaller rearrangement
of atoms. If the reaction C + NH3 is the main pathway to H2NC we could expect
a relation between the abundance of H2NC and that of NH3. To investigate this
point we represented in Fig. 4 the column density of H2NC versus that of NH3.
Some interesting features emerge from this plot. First, the two sources with
the largest column densities of H2NC, which are L483 and B1-b, have also the
highest column densities of NH3. Second, among the cold dense clouds, the
sources with the lowest column densities of NH3, Lupus-1A and TMC-1 CP, have
also low column densities of H2NC. These two findings are very suggestive of a
relation between H2NC and NH3, and thus of NH3 being a precursor of H2NC. Cold
dense clouds with NH3 column densities in between those of Lupus-1A and TMC-1
CP, on one side, and L483 and B1-b, on the other, show a less clear relation
between H2NC and NH3. In particular, there are sources, such as L1498, L1489,
TMC-2, and L1641N, which have a moderately high column density of NH3 but a
low H2NC column density. This fact suggests that NH3 may not be the only
species that regulates the abundance of H2NC. Indeed, if H2NC is mainly formed
by the reaction C + NH3, the abundance of atomic carbon would also be a
relevant parameter setting the abundance of H2NC. However, it is very
difficult to constrain the abundance of atomic carbon inside cold dense clouds
(Schilke et al., 1995; Stark et al., 1996). Diffuse clouds have a markedly
different chemistry compared to cold dense clouds, with a lower chemical
complexity (e.g., Liszt et al. 2008). This may be the reason why H2NC and H2CN
were not detected toward B0415+379 or B0355+508. However, if the relation
between H2NC and NH3 found for cold dense clouds holds down to the diffuse
stage, the reason of the non detection of H2NC and H2CN toward B0415+379 or
B0355+508 could be the low NH3 column density in these two sources, 1-2 orders
of magnitude smaller than in cold dense clouds (see Fig. 4).

##  5 The reaction C + NH3 as a source of H2NC

The suspected chemical link between H2NC and NH3 in interstellar clouds may be
attributed to the fact that the reaction C + NH3 is the main formation
mechanism of H2NC in these environments. Here we revisit this reaction and
investigate whether H2NC can be produced this way.

###  5.1 Previous studies

Figure 5: Energies (in kcal mol-1) of the stationary points describing the C +
NH3 reaction on the triplet state obtained at RCCSD(T)-F12 with the VQZ-F12
basis set, including the ZPE. All energies are referred to the C(${}^{3}P$) +
NH3(${}^{1}A^{\prime}$) reactants.

The reaction C + NH3 has been found to be fast at low temperature, with a
measured rate coefficient of (1.8 $\pm$ 0.2) $\times$ 10-10 cm3 s-1 at 50 K
(Hickson et al., 2015). The reaction products,

$\displaystyle\rm C(^{3}P)+NH_{3}(^{1}A^{\prime})$
$\displaystyle\rightarrow\rm H(^{2}S)+H_{2}CN(^{2}B_{2})$ (4a)
$\displaystyle\rightarrow\rm H(^{2}S)+\textit{trans-}HCNH(^{2}A^{\prime})$
(4b) $\displaystyle\rightarrow\rm H(^{2}S)+\textit{cis-}HCNH(^{2}A^{\prime})$
(4c) $\displaystyle\rightarrow\rm H(^{2}S)+H_{2}NC(^{2}B_{2}),$ (4d)

were investigated by Bourgalais et al. (2015). These authors measured the H
atom yield to be 0.99 $\pm$ 0.08, independent of temperature, over the 50-296
K range. On the other hand, they also used tunable vacuum-ultraviolet
photoionization coupled with time of flight mass spectrometry in a gas flow
tube experiment at 330 K, which indicated that H2CN, and not cis or trans
HCNH, is likely the main isomer produced. Bourgalais et al. (2015) also
performed electronic structure calculations, which indicated that the
reactants approach each other in an attractive potential without barrier to
form the intermediate CNH3 (hereafter I4; see Fig. 5). From I4 the dynamics
can proceed overpassing two barriers. The lower is TSI3I4, that connects I4 to
I3, giving access to the statistical reaction mechanism that is expected to
majoritarily lead to H2CN. The second barrier, TSI4P4, connects I4 directly
with the H2NC product, and according to Bourgalais et al. (2015) has an energy
slightly above the reactants (although this is very method dependent), which
implies that this pathway is closed at a temperature of 10 K. As a
consequence, Bourgalais et al. (2015) assigned a branching ratio of 100 % for
channel (4a).

It is also interesting to discuss the reaction N + CH3 because it occurs on
the same triplet potential energy surface (PES) than C + NH3. This reaction
has been studied experimentally (Stief et al., 1988; Marston et al., 1989a, b)
and theoretically (González & Schlegel, 1992; Sadygov & Yarkony, 1997; Cimas &
Largo, 2006; Alves et al., 2008; Chiba et al., 2015). The rate coefficient has
been measured to be (0.64-1.7) $\times$ 10-10 cm3 s-1 in the temperature range
200-423 K (Marston et al., 1989a). The major reaction products have been
experimentally inferred to be H2CN + H, with about 10 % of the reaction
leading to HCN + H2 (Marston et al., 1989b), which has been theoretically
explained in terms of an intersystem crossing from the triplet to the singlet
PES (González & Schlegel, 1992; Sadygov & Yarkony, 1997; Chiba et al., 2015).
The mechanism of the reaction has been discussed in detail by Cimas & Largo
(2006). The reactants approach each other in an attractive potential to form
the intermediate NCH3 (hereafter I1; see Fig. 5), which is connected to two
saddle points: the lower is TSI1P1, which yields H2CN as product, while the
higher TSI1I2 connects to the HCNH2 intermediate (I2). The two barriers are
submerged, i.e., have energies below the reactants N + CH3, but since TSI1P1
$<$ TSI1I2, according to RRKM arguments most of the flux will go through
TSI1P1 to form H2CN. The I2 intermediate in turn is connected to I3 (H2NCH).
The path along these intermediates I1 $\rightarrow$ I2 $\rightarrow$ I3, in
which successive H atom migrations take place, is expected to behave
statistically, and therefore the main product along this second statistical
reaction mechanism is also expected to be H2CN. Thus, Cimas & Largo (2006)
conclude that the main products should be H + H2CN.

###  5.2 Stationary points of the triplet electronic state

We carried out a progressive optimization of the stationary points of the
triplet PES using several methods, M06-2X, RCCSD(T), and RCCSD(T)-F12, and
different basis sets, VTZ-F12 and VQZ-F12 (Peterson & Werner, 2008), using the
MOLPRO package (Werner et al., 2012). The relative energies of the stationary
points varied considerably depending on the method and basis set, specially
for the transition states, which indicates that electronic correlation is very
important. For every transition state we calculated the intrinsic reaction
coordinate to check the two minima connected to it.

Table 4: Electronic energies $E_{el}$ calculated at RCCSD(T)-F12/VQZ-F12
level, zero point energies (ZPE), and the sum of both for the stationary
points involved in the C + NH3 reaction on the triplet state. Energies are
referred to C + NH3 (R2). All values in kcal mol-1.

Name | System |  $E_{el}$ | ZPE |  $E_{el}$ \+ ZPE
---|---|---|---|---
R2 |  C(3P)+NH3(${}^{1}A^{\prime}$) | 0.0 | 21.599 | 0.0
R1 |  N(4S)+CH3(${}^{2}A_{2}^{\prime\prime}$) |  $-$9.153 | 18.718 |  $-$12.033
I4 |  C-NH3 |  $-$26.884 | 24.580 |  $-$23.902
I3 |  HC-NH2 |  $-$68.771 | 23.487 |  $-$66.882
I2 |  H2C-NH |  $-$71.036 | 22.392 |  $-$70.235
I1 |  H3C-N |  $-$84.210 | 23.353 |  $-$82.455
P4 |  H + H2NC |  $-$14.745 | 16.664 |  $-$19.680
P3 |  H + cis-HCNH |  $-$31.780 | 15.651 |  $-$37.727
P2 |  H + trans-HCNH |  $-$36.775 | 16.244 |  $-$42.129
P1 |  H + H2CN |  $-$44.274 | 15.780 |  $-$50.092
TSI3I4 |  CHNH2 |  $-$1.750 | 20.420 |  $-$2.929
TSI2I3 | HCHNH |  $-$26.836 | 20.007 |  $-$28.427
TSI1I2 |  H2CHN |  $-$37.337 | 19.825 |  $-$39.111
TSI4P4 |  CNH2-H | 1.547 | 19.306 |  $-$0.745
TSI1P1 |  H-H2CN |  $-$41.726 | 17.062 |  $-$46.262

The calculation of $E_{el}$ for N + CH3 (R1) was done independently for each
subsystem and their energies were added. The imaginary frequencies at the
saddle points TSI3I4, TSI2I3, TSI1I2, TSI4P4, TSI1P1 are 4.837, 5.719, 5.578,
5.154, and 2.283 kcal mol-1, respectively.

The RCCSD(T)-F12/VQZ-F12 results are listed in Table 4 and represented in Fig.
5. The height of TSI4P4 is critical since it connects the CNH3 well, I4, with
the H2NC product, P4. With the RCCSD(T)-F12/VQZ-F12 method the electronic
energy of TSI4P4 is above that of the reactants C + NH3, but when the zero
point energy (ZPE) is included the energy at the TSI4P4 point becomes
negative, and therefore the H2NC product becomes accessible in the C + NH3
reaction even at low temperatures.

The computational effort of geometry optimization increases dramatically with
the size of the basis set, specially when the gradients and hessians need to
be calculated numerically, as it happens when using RCCSD(T)-F12 methods. An
alternative is to extrapolate the energies obtained with two or more
electronic correlation-consistent basis sets to the complete basis set (CBS)
limit. There are many extrapolation methods, and some of them were reviewed
and applied to H${}_{3}^{+}$ by Velilla et al. (2010), who found that the best
option is the two points extrapolation method (Lee & Park, 2000; Huh & Lee,
2003):

$E_{X}=E_{CBS}+A(X+k)^{-3},$ (5)

where $X$ refers to the basis ($X$ = 3 and 4 for VTZ and VQZ, respectively)
and $k$ = $-$1 is the best choice when using RCCSD(T) methods. The results are
listed in Table 5. In the CBS limit, the transition states TSI4P4 and TSI3I4
have similar energies, both lying below the reactants C + NH3, as found with
the RCCSD(T)-F12/VQZ-F12 method.

Table 5: Electronic energies calculated at the complete basis set (CBS) limit
$E_{CBS}$ using the RCCSD(T)-F12, MRCI-F12, and MRCI-F12+Q methods plus the
ZPE. Energies are referred to C + NH3 (R2). All values in kcal mol-1

Name |  $E_{CBS}$ \+ ZPE
---|---
| RCCSD(T)-F12 | MRCI-F12 | MRCI-F12+Q
R2 | 0.0 | 0.0 | 0.0
I4 |  $-$25.395 |  $-$29.574 |  $-$28.455
TSI3I4 |  $-$3.907 |  $-$7.567 |  $-$7.392
TSI4P4 |  $-$1.568 |  $-$7.260 |  $-$6.266

CBS energies obtained using Eq. (5) with the VTZ-F12 and VQZ-F12 basis sets,
where in both cases electronic energies are obtained at the geometries
optimized using RCCSD(T)-F12/VQZ-F12.

Single reference methods like RCCSD(T)-F12 have problems to describe
reactions, specially at the saddle points, which usually present a large
multi-reference character. In the RCCSD(T)-F12 calculations discussed above,
the T1-diagnostic is always below 0.023, as previously found by Bourgalais et
al. (2015). This value usually allows to consider that RCCSD(T)-F12 results
are reasonably good even at saddle points (Lee & Taylor, 1989). Multi
reference methods, such as the multi reference configuration interaction
(MRCI) method (Werner & Knowles, 1988; Shiozaki & Werner, 2013) are considered
more accurate to describe reactions, specially at saddle points. Since MRCI
calculations are more computationally demanding, here we performed single
point calculations at the geometries optimized with the RCCSD(T)-F12/VQZ-F12
method, with and without the Davidson correction (Davidson, 1975), which we
denote as MRCI-F12 and MRCI-F12+Q, respectively. The results obtained with the
VTZ and VQZ basis sets are then used to get the complete basis limit, which
are listed in Table 5. With the MRCI-F12 and MRCI-F12+Q methods the heights of
the reaction barriers TSI3I4 and TSI4P4 are lower than with the RCCSD(T)-F12
method and, interestingly, the energies of these two transitions states become
much more similar.

###  5.3 Reaction rate coefficient and RKKM branching ratios

Figure 6: Capture rate coefficient $k_{c}$ calculated for the reaction C + NH3
according to Eq. (7) is compared with the experimental measurements of the
reactive rate coefficient by Hickson et al. (2015).

At low energies, the two reactants approach each other forming the CNH3
intermediate I4 following a descendent potential energy path with no barrier.
This is a clear example of a capture mechanism, which is governed by long-
range interactions at low temperatures. Long-range forces are due to the
interaction of the electric dipole and quadrupole of NH3 with the quadrupole
of the p state of C(${}^{3}P$), and the long-range potential $V_{LR}$ varies
as a function of $R$ (the distance between the C atom and the center of mass
of NH3) as (Zeimen et al., 2003)

$V_{LR}(R,\theta)=M_{QD}(\theta){Q({\rm C})D({\rm NH_{3}})\over
R^{4}}+M_{QQ}(\theta){Q({\rm C})Q({\rm NH_{3}})\over R^{5}},$ (6)

where $Q$(C) and $Q$(NH3) are the quadrupoles of C and NH3, respectively,
$D$(NH3) is the dipole moment of NH3, and $M_{QD}(\theta)$ and
$M_{QQ}(\theta)$ are 3 $\times$ 3 matrices that account for the quadrupole-
dipole and quadrupole-quadrupole interactions, respectively (Zeimen et al.,
2003). In the present treatment we neglect the quadrupole-quadrupole
contribution and the dependence on the angle $\theta$. We thus consider an
isotropic long range potential $A/R^{4}$, where $A$ = 2 $M_{QD}$ $Q$(C)
$D$(NH3). The parameter $A$ is obtained by fitting to CCSD(T) calculations,
with the aVTZ basis set. The ab initio calculations are done for NH3 in its
equilibrium geometry, with its symmetry axis along the $z$ axis and its center
of mass at origin, varying the $R$ = $z$ coordinate of the C atom. We obtain a
value of $A$ = $-$0.85 hartree bohr4. This is similar to the Langevin case,
and the capture rate coefficient $k_{c}$ is then given by

$k_{c}(T)=2\pi\sqrt{A/\mu}\leavevmode\nobreak\ \leavevmode\nobreak\
q_{e}(T)=3.13\times 10^{-10}{\rm cm^{3}s^{-1}}\leavevmode\nobreak\
\leavevmode\nobreak\ q_{e}(T),$ (7)

where $\mu$ is the reduced mass of the C + NH3 system and $q_{e}$ is the
electronic partition function of C(${}^{3}P$). Assuming that only the 3 lowest
spin-orbit states of C(${}^{3}P$) yield trapping, we get

$q_{e}(T)={1+2\exp(-23.62/T)\over 1+3\exp(-23.62/T)+5\exp(-62.46/T)}.$ (8)

The calculated capture rate coefficient is compared in Fig. 6 with the
experimental reactive rate coefficient measured at different temperatures by
Hickson et al. (2015). We note that the capture rate coefficient is an upper
limit to the reactive rate coefficient because once the complex is formed it
can either come back to the reactants C + NH3 or evolve to form different
products (H2CN, cis-/trans-HCNH, or H2NC).

According to the statistical RRKM theory, the micro-canonical rate coefficient
$K$ leading to any possible product at a fixed collision energy $E$ and total
angular momentum $J$ is expressed as (Marcus, 1952a, b; Miller, 1979, 1987)

$K(E,J)={\sum_{v,K}P(E-\epsilon_{JKv})\over 2\pi\hbar\rho(E,J)},$ (9)

where $\epsilon_{JKv}$ are the energies of the vibrational and rotational
levels at the saddle point yielding each product and $\rho(E,J)$ is the
density of states of the initial system, which in our case is the intermediate
CNH3 (I4). The function $P(E-\epsilon_{JKv})$ in Eq. (9) is the transmission
probability over the $\epsilon_{JKv}$ barrier, and can be calculated
classically or semiclassically by considering tunneling through a
monodimensional Eckart barrier, as proposed by Miller (1979, 1987).

Figure 7: Product branching ratio [H2NC]/[H2CN] obtained for the reaction C +
NH3 using the VQZ-F12 and CBS results according to Eq. (9), with and without
tunneling.

The intermediate CNH3 (I4) will unimolecularly decompose into three channels.
The first one is the redissociation back to the reactants C + NH3 (R2)
overpassing the barrier of the effective $-A/R^{4}+\hbar^{2}\ell(\ell+1)/2\mu
R^{2}$ monodimensional potential (where $\ell$ is the orbital angular momentum
of the C atom with respect to the center of mass of NH3), similarly as it is
done for the capture model. The second channel leads to the products H + H2NC
(P4) overpassing TSI4P4 barrier. The third one consists of a statistical
mechanism in which TSI3I4 is overpassed to reach the I3 intermediate. Along
this mechanism, the system will proceed towards I2 and I1 intermediates. This
complex-forming mechanism is expected to behave statistically, favoring the
exit towards the most stable product, H + H2CN (P1). This was the case
calculated by Cimas & Largo (2006) in the N + CH3 reaction. Here, we shall
assume as a zero-order approximation that once TSI3I4 is overpassed the
reaction mechanism yields only H + H2CN (P1).

The branching ratio between the two products channels leading to H2NC (P4) and
H2CN (P1) is then given as a function of collision energy $E$ as

${\left[{\rm H_{2}NC}\right]\over\left[{\rm
H_{2}CN}\right]}(E)={\sum_{J}(2J+1)K^{{\rm
H_{2}NC}}(E,J)\over\sum_{J}(2J+1)K^{{\rm H_{2}CN}}(E,J)}.$ (10)

The calculated branching ratio [H2NC]/[H2CN] is shown in Fig. 7 as a function
of the collision energy using the CBS limit results with the RCCSD(T)-F12,
MRCI-F12, and MRCI-F12+Q methods. It is seen that the branching ratio is very
dependent on the relative heights of the barriers TSI4P4 and TSI3I4, which in
turn are very dependent on the method, i.e., on how electronic correlation is
included. Saddle points correspond to the configurations where bonds are
formed and destroyed, and hence, multi-reference methods are in principle more
accurate. For this reason, we consider that MRCI-F12 and MRCI-F12+Q results
are the most accurate in the present work. The inclusion of tunneling only
accounts for corrections of about 2 %. It is worth noting that the energy
differences between the barriers TSI4P4 and TSI3I4 involved in this reaction
are probably close to the accuracy of state-of-the-art ab initio methods. For
all explored methods, the [H2NC]/[H2CN] branching ratio is almost constant for
collision energies below $\sim$ 0.3 eV. Above this energy, the ratio increases
because the density of states at TSI4P4 increases faster than at TSI3I4 due to
the smaller rotational constants. Using the MRCI+Q-CBS results, the rotational
constants for TSI4P4 are 5.18 cm-1, 0.98 cm-1, and 0.96 cm-1, while for TSI3I4
they are 6.49 cm-1, 0.87 cm-1, and 0.86 cm-1.

We can conclude that the [H2NC]/[H2CN] branching ratio at 10 K should have a
value between 0.5 and 0.8. This value is to be compared with the abundance
ratio H2NC/H2CN observed in cold dense clouds in this work, which lies between
0.51 and $>$ 2.7 (see Table 3). Taking into account the significant variation
of the predicted branching ratio [H2NC]/[H2CN] with the method employed and
the spread of H2NC/H2CN ratios found in the targeted clouds, the reaction C +
NH3 could perfectly be the main source of H2NC in cold dense clouds, and also
in the redshifted galaxy in front of the quasar PKS 1830$-$211, where the
abundance ratio H2NC/H2CN is 0.27.

##  6 Concluding remarks

We carried out an observational survey to search for the metastable isomer
H2NC toward various cold dense and diffuse clouds to determine its abundance
and understand the chemistry of this recently discovered molecule.
Simultaneously the most stable isomer, H2CN, was also searched for in the same
sources. We were mainly interested in exploring two particular hypotheses
suggested by the discovery of H2NC. First, whether or not the H2NC/H2CN
abundance ratio behaves as the HNC/HCN ratio, with values around one in cold
dense clouds and below one in diffuse clouds. And second, whether or not H2NC
is chemically connected to ammonia.

We detected H2NC in most of the cold dense clouds targeted, which indicates
that this species is widespread in this kind of interstellar clouds. On the
other hand, we did not detect neither H2NC nor H2CN toward two diffuse clouds
which seemed among the most favorable for detection, most likely because of
the lower molecular richness of diffuse clouds compared to dense clouds. The
non detection of H2NC toward diffuse clouds did not allowed to confirm the
hypothesis that the H2NC/H2CN abundance ratio behaves similarly to the HNC/HCN
in dense and diffuse clouds. On the other hand, we found that the column
density of H2NC is correlated with that of NH3 because the sources where H2NC
is most abundant are also very abundant in ammonia. This latter fact suggests
that these two molecules are chemically connected, probably because ammonia is
a precursor of H2NC through the C + NH3 reaction.

Previous studies of the C + NH3 reaction favored H2CN as the main product. We
thus revisited this reaction from a theoretical point of view and found that
the two isomers H2CN and H2NC can be formed through two different reaction
pathways which involve two different transition states, the energies of which
are predicted to be very similar and slightly below that of the reactants. The
product branching ratio H2NC/H2CN is predicted to be between 0.5 and 0.8,
which is of the order of the abundance ratios H2NC/H2CN observationally found
in cold dense clouds, which range from 0.51 to $>$ 2.7. We therefore conclude
that the reaction C + NH3 is probably the main formation route to H2NC in
interstellar clouds.

###### Acknowledgements.

We acknowledge funding support from Spanish Ministerio de Ciencia e Innovación
through grants PID2019-106110GB-I00, PID2019-107115GB-C21,
PID2019-106235GB-I00, and PID2021-122549NB-C2. We thank the referee for useful
comments that helped to improve this article.

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# Social Convos: Capturing Agendas and Emotions on Social Media

###### Abstract

Social media platforms are popular tools for disseminating targeted
information during major public events like elections or pandemics. Systematic
analysis of the message traffic can provide valuable insights into prevailing
opinions and social dynamics among different segments of the population. We
are specifically interested in influence spread, and in particular whether
more deliberate influence operations can be detected. However, filtering out
the essential messages with telltale influence indicators from the extensive
and often chaotic social media traffic is a major challenge. In this paper we
present a novel approach to extract influence indicators from messages
circulating among groups of users discussing particular topics. We build upon
the concept of a convo to identify influential authors who are actively
promoting some particular agenda around that topic within the group. We focus
on two influence indicators: the (control of) agenda and the use of emotional
language.

Keywords: agenda, emotions, social networks, campaigns

Social Convos: Capturing Agendas and Emotions on Social Media

Ankita Bhaumik, Ning Sa, Gregorios Katsios, Tomek Strzalkowski
---
Rensselaer Polytechnic Institute
Troy, New York
{bhauma, san2, katsig<EMAIL_ADDRESS>

Abstract content

## 1\. Introduction

Popular social media platforms, such as Twitter (now X), Facebook, Instagram,
and others, have become global, wide reaching communication channels that
remain largely unregulated for access and content. They are an ideal vehicle
for placing precisely targeted commercial advertising and other types of
outreach activities. Social media have also become means of choice for
spreading propaganda, disinformation, and for running influence operations. In
this paper we focus on this last phenomenon; more specifically: how the
presence of deliberate influence operations can be detected among the overall
message traffic.

While at the first glance the social media message traffic may appear random
and chaotic, it is in fact an environment where all kinds of social phenomena
obtain, not unlike in any other forms of human interaction, except at a much
larger scale. Social media is thus as an extensive repository of information
to study group dynamics at scale, including sociolinguistic behaviors such as
agenda control and influence, as well as the methods and techniques deployed
to achieve them (Del Vicario et al., 2017; Bovet and Makse, 2019; Caldarelli
et al., 2020).

At the same time, a crucial challenge for an effective analysis of the message
traffic is separating specific interactions from among many that may be
occurring at the same time, all set against the backdrop of largely unrelated
"noise". If we want to analyze an potential influence operation, we must zero
in on a subset of messages shared between the possible influencers and their
targets, as well as many onlookers. It is within this potentially large group
where the key social behaviors can be observed with sufficient clarity.
Previous work has been done on the representation of such behaviors on social
media as a landscape of convos (Katsios et al., 2019), and this paper builds
upon it.

Katsios et al., 2019 define a convo as an online social phenomenon where
people are engaged around a topic or an activity. A convo can be formed among
users who read, edit, comment or forward an information artifact, which could
be a document, a project, a topic, or an idea. Some examples can be a
repository on GitHub, a subreddit on Reddit or a hashtag group on Twitter. We
hypothesize that convos can be used to detect focused groups of messages
around a particular topic, which can be further used for detecting influence
operations.

One well-documented situation where social media can be used to run influence
operations is during national elections and public emergencies, such as the
recent COVID-19 pandemic (Karlsen and Enjolras, 2016; Jungherr, 2016; Badawy
et al., 2019). These operations are driven by groups of users and
characterized by the specific agendas they aim to promote. We deploy the
concept of a convo to extract the subsets of social media traffic devoted to
popular topics arising within the specified time periods, e.g., during French
national elections in 2022. From the convo traffic, we extract the messages
related to its main topic, as well as a network of influential authors who are
actively promoting a particular viewpoint, or agenda within the convo. We
characterize the convo representation using well-established influence
indicators, specifically, agenda control (Broadwell et al., 2013) and use of
emotional language(Bhaumik et al., 2023). This allows us to identify the most
influential members of the convo, as well as to uncover a network of
relationships between them. Our hypothesis is that a dense network of mutual
connections among the key influencers in the convo indicates a deliberate
influence operation. This may be contrasted with a more organic message
traffic where individual influencers are acting largely independently of one
another.

Existing works on extracting influence indicators from social media has been
performed on a message level (Mather et al., 2022; Bhaumik et al., 2023).
After tagging individual messages with agenda and emotion labels, the
aggregate agendas and emotions in the dataset are typically obtained by
calculating a relative distribution or density of each label. However, this
bottom-up approach has several drawbacks. Firstly, by working on individual
messages, this approach underestimates the semantic and social links between
the messages, thus treating them as independent events. Secondly, by ignoring
duplicate messages and reposts (retweets on Twitter), this approach weighs
each unique message equally and ignores the differences in their popularity.
Thirdly, although there are predefined emotion categories, the set of agendas
germane in each type of event are typically unknown in advance. As a result,
some amount of human annotation may be needed in order to obtain the relevant
agenda labels.

To mitigate the above drawbacks, we propose a novel top-down approach to
detect agendas (and who pushed them) and emotions (and who uses them)
simultaneously from focused groups of messages in a convo. We use instruction
tuned pre-trained large language models (LLMs) that have the ability to
process collections of messages as opposed to fine-tuned models that work at a
message level.

We perform our experiments on the 2022 French Election Twitter dataset to
study popular influence operations, such as #Frexit (Wikipedia, 2023), that
promoted France’s exit from the European Union. We outline the complete
methodology of extracting convos from a social media corpus, identification of
influential authors in a convo and characterizing them using agendas and
emotions in Section 2. Though our experiments have been carried out on a
Twitter dataset, our approach has been generalized for multiple social media
platforms like Reddit or public forums which do not use hashtags.

## 2\. Methodology

Our approach to identify convo networks comprises of three major steps (Fig.
1):

  1. 1.

Identification of a convo using hashtag or topic groups around the keywords of
interest.

  2. 2.

Identification of authors who act as top influential users in a convo.

  3. 3.

Detection of entities, agendas and emotions from the convo.

Figure 1: Overview of our approach to extract and characterize convos.

In the following subsections, we outline every step in detail.

### 2.1. Identification of Convos

As described by Katsios et al., the definition of a convo depends on the type
of social media under examination. For example, on Twitter, convos typically
form around hashtag groups and on Reddit they arise in subreddits discussing
similar topics. Therefore, given a set of terms of interest, the first step in
our approach is to identify these hashtag or topic groups in the input corpus.

Employing a keyword search mechanism to identify the hashtag or topic groups
on social media is a less effective approach due to the inherent complexities
of the medium. Social media messages are often short and may not mention
certain keywords directly. For example, when examining tweets from the 2022
French Elections presidential campaign, its not guaranteed that the terms
France, president, or election will be explicitly mentioned. To address this
challenge, we first identify hashtag groups on Twitter, or topic groups in
other social media platforms, and we use these groups to gather messages
related to keywords of interest, allowing for a more comprehensive and
accurate analysis.

To identify hashtag convos, we create a co-occurrence based distance matrix of
the top 6000 tokens in the hashtag vocabulary of the corpus. Using this as our
feature representation, we perform dimensionality reduction via UMAP (McInnes
et al., 2018) and then use HDBSCAN (Campello et al., 2013) to cluster them
into hashtag groups. Some examples of hashtag groups are listed in Table 1.

For datasets from other social media like Reddit or public forums, we use the
LDA topic modeling algorithm to identify topic distributions in the input
corpus (Blei et al., 2003). Finally, we identify convos around a particular
topic using the hashtag/topic groups containing any of the terms of interest.

Hashtag Groups
---
#frexit, #ue, #asselineau, #reprenonslecontrôle, #schengen
#stopputin, #stoprussia, #standwithukraine, #closetheskyoverukraine,
#noflyzoneoverukraine
#covid19, #covid, #covid_19, #omicron,
#vaccine
#passvaccinal, #passevaccinal, #passsanitaire, #passdelahonte,
#passevaccinaldelahonte
#mckinseygate, #macronmckinsey, #macronassassin, #macronmckinseygate,
#macroncnon
Table 1: Examples of hashtag groups extracted from the French Elections 2022
dataset, showing top 5 hashtags in each group.

### 2.2. Identification of the Top Influencers

As previously discussed, not all messages within a hashtag convo carry equal
significance. The weight of a message is determined by the number of retweets,
reflecting broader agreement among users. Conversely, a collection of messages
from a single user can provide a more comprehensive expression of their ideas
and positions compared to a single message. Therefore, instead of analyzing
all tweets in a convo, we prioritize the examination of tweets from
influential users, who are often retweeted.

To characterize these influential tweets we categorize them by topic, allowing
us to extract the agendas and emotions associated with each topic group. We
use a two-level hierarchical clustering method to identify distinct topics
within bigger groups of messages (Grootendorst, 2022). The agendas and
emotions expressed by these influential users serve as a representative sample
of the entire convo.

Furthermore, we explore the underlying efforts driving these agendas by
scrutinizing the tweeting behavior of influential users and exploring the
connections within the cross-influencer network. We hypothesize that in a
targeted influence operation these authors would be actively retweeting each
other to promote similar ideas.

### 2.3. Agenda and Emotion Detection

In order to effectively perform the tasks of agenda and emotion detection
across a collection of messages, we utilize large language models (LLMs) as
they have a large context window. Existing fine-tuned models are not suitable
for these tasks, primarily due to their limitations in processing single
messages within specific domains. Recent advancements in pre-trained LLMs have
demonstrated remarkable capabilities in zero-shot summarization across diverse
domains (Zhang et al., 2023; Yang et al., 2023). Leveraging these
breakthroughs, we have developed an instruction-tuned model for agenda and
emotion detection.

In our approach, we provide the LLM with a global context that acts as an
instructional guide for its intended task. We adopt a prompt-based template to
extract both the agendas and emotions from a collection of messages.
Additionally, we employ an output template designed to steer the LLM in
generating outputs in a format conducive to visualizing all components within
the convo network. This output template replicates a JSON file structure,
enhancing its utility for seamless downstream processing. We design prompts to
direct the model to answer the questions and accomplish the following tasks:

  * •

Prompt 1: What are the top distinct entities (maximum 5) mentioned in several
messages?

  * •

Prompt 2: What are the authors promoting about each entity? Give me 1 phrase
for each.

  * •

Prompt 3: What are the emotions expressed towards each entity?

  * •

Prompt 4: Combine the entities, promoted actions and emotions in the output
template.

The prompts are used to fill out an output JSON template:

    output = [
    {
    "entity": {entity},
    "promoted_actions": {action},
    "emotions": {emotion}
    },
    ...
    ]

This yields a file that contains information regarding the entities, agendas,
and emotions within the conversation.

## 3\. Experiments

### 3.1. Dataset

We run our experiments on a publicly available dataset from the 2022 French
presidential elections Daignan (2022). It contains 45 million tweets and
retweets from Nov. 12, 2021 to Apr. 03, 2022, around the main actors in the
election. French is the dominant language of the dataset, and there are also
certain amount of tweets written in English. This dataset contains all retweet
information about the tweets which makes it an ideal choice to identify
influential message groups in this corpus. We choose two keywords of interest
that were popular topics during the French election campaign as studied from
news articles and online forums : #frexit and #covid_19 (Wikipedia, 2023).

(a) #Frexit convo

(b) #covid_19 convo

Figure 2: Influencer Networks among top influencers in each convos. Each node
(red point) represents an influencer, with her index marked below the node.
The arrows indicate the direction of the connections and the numbers above
show the weight of the connections. A balloon on top of a node means a self-RT
link.

### 3.2. Implementation

To make a traceable retweet network, we pre-process the original dataset to
link all retweets to the original tweet. We also remove emojis, hyperlinks and
tweets having less than 3 textual tokens. To pick the most influential
messages in a convo we examine at the messages by the top 10 most retweeted
authors in that convo. Alternatively, this value could be determined based on
the proportion of messages contributed by each author in a convo. We use
multilingual BERTopic to separate the convo messages into smaller groups
(Grootendorst, 2022).

To implement the agenda and emotion detection system we use a LLM with a
sufficiently large context window. We perform our experiments using
Llama-2-13b-chat model with a context length of 4096 tokens (Touvron et al.,
2023). We provide the global context in the system prompt and use the prompts
to further probe the LLM. We use nucleus sampling with $p$ as 0.9 for
generating responses and limit the number of new tokens to 500. We also tested
our approach using ChatGPT to achieve comparable performance (Ouyang et al.,
2022). The experiments are performed on 2 NVIDIA A100 GPUs.

### 3.3. Results

To establish a mapping between each tweet and its corresponding retweets, we
preprocess the original corpus, resulting in a dataset comprising of 16.7
million tweets. On further removal of emojis, hyperlinks, tweets without
hashtags, and tweets having less than 3 textual tokens, we arrive at 2.8m
tweets and their associated retweet information.

Our first step to identify all hashtag groups in the corpus results in more
than 40 hashtag groups (Table 1). We select the two that contain our terms of
interest, frexit and covid_19, to extract the hashtag convos around them.
Table 2 lists the total number of authors, tweets and retweets in each of
these convos. We then select the messages by the top 10 retweeted authors. In
the #frexit convo, the top influencers’ messages account for 5% of total
messages in the convo and comprise around 44% of the total retweets (20,135
out of 44,859). Whereas for the larger #covid_19 convo, that has a larger
number of tweets and authors, the top influencers contribute 1% of all tweets
and their retweet number comprise 28% of the total retweets.

To understand the connections among the top 10 influencers, we construct a
network based on their retweet behavior in the whole corpus (Fig. 2). The
nodes in Fig. 2 represent the authors and the weight of the edges represent
the number of retweets between them, balloons on top of the node indicate
instances of self-retweeting by that author. We construct a graph for each
convo and notice that there is no overlap in top influencers between the two,
signifying that these authors are predominantly dedicated to promoting
specific agendas. While the top 10 influencers in the #Frexit convo (Fig.2(a))
are connected by a dense network of retweet or self-retweet, the network for
#covid_19 (Fig. 2(b)) contains only 8 authors.

| #Frexit | #Covid_19
---|---|---
| Inf. | Convo | Inf. | Convo
No. authors | 10 | 3,572 | 10 | 10,239
No. tweets | 902 | 16,406 | 403 | 39,719
No. RT count | 20,135 | 44,859 | 38,144 | 133,457
Table 2: Descriptive results of influencers (Inf.) in the #Frexit and the
#Covid_19 convo

(a) Convos in the #frexit clusters

(b) Convos in the #covid_19 clusters

Figure 4: Different clusters in the convos about #Frexit and #covid_19. They
are characterized by the indicators of top entities, promoted actions, and
emotions. The influencers are the top 10 retweeted authors in that convo. The
expanded network of the influencers are illustrated in Fig. 2(a) and 2(b).
Entities are grey blobs and promoted actions are the grey edge labels. Emotion labels over the edges are colored as negative/positive ones. The model also generates an agenda summary, given in Table 3. Message Cluster |  Agenda Summary
---|---
Fig. 4(a) \- left |  The agenda behind this set of tweets is to promote the candidacy of François Asselineau for the French presidency in 2022 and to advocate for France’s withdrawal from the European Union (#Frexit)
Fig. 4(a) \- right |  The agenda behind this set of tweets is to promote the political movement #LesPatriotes and its leader, Florian Philippot, and to campaign against the current French President Emmanuel Macron and his policies, particularly the controversial vaccine pass
Fig. 4(b) \- left |  The agenda behind this set of tweets is primarily focused on the French government’s handling of the COVID-19 pandemic, specifically the use of vaccination passports, the easing of health constraints, and the perceived political motivations behind these actions
Fig. 4(b) \- right |  The agenda behind this set of tweets is to criticize and scrutinize the actions and words of French President Emmanuel Macron regarding the COVID-19 pandemic and vaccination
Table 3: Summarized agendas of the messages clusters shown in Fig.4

We cluster the influencers’ messages in each convo into smaller topic groups
to be able to analyze the content more effectively. We run our emotion and
agenda detection model over the message clusters to characterize the influence
indicators in each influential convo. Fig 4 visualizes the json outputs we
obtain to depict the top entities, promoted actions and emotions of two
selected message clusters from each convo. The generated agenda summaries,
listed in Table 3, provide us with a concise and informative snapshot of the
convos around the topic of interest.

#### #frexit convo (Fig 4(a)):

In the first message cluster of this convo, the influencers promote the
candidacy of François Asselineau and advocate for France leaving the EU. The
first snapshot also illustrates a similar idea: the influencers support
François Asselineau who advocates for #Frexit, encourage the French people to
take back control of their country, and admire Charles de Gaulle who
represented French independence and greatness. They also accuse Emmanuel
Macron for suppressing the French people’s opinion and are angry about EU for
manipulating the French people and damaging France’s economy and sovereignty.

The second influential message group in the same convo represents another view
of the influencers where they advocate for another candidate in the election:
Florian Philippot and support the LesPatriotes party he leads. They also
criticize president Macron and call for a campaign against his policy on
PassVaccinal.

#### #covid_19 convo (Fig. 4(b)):

In both the influential message clusters of this convo, the influencers feel
concerned about COVID19 and criticize Emmanuel Macron for using the crisis for
electoral gain and the improper policies. In the first message cluster,
Vaccination passport is supported and thought to be able to protect public
health, while the Government is accused for easing the Health constraints for
political purposes. Whereas in the second message cluster, people show desire
for nightclubs, advocate for Ivermectin as a possible treatment for Covid-19,
and think SudRadio is a trustful resource of information and opinion.

### 3.4. Analysis and Discussion

To validate our hypotheses, we manually analyze the generated convo
visualizations and influencer networks. In addition, we verify the generated
agendas by comparing them with news articles and online forums. By this
process we ascertain that they are correct representations of the broader
corpus of data.

The numbers in Table 2 show that in both the convos, the top 10 influencers
generate a very small fraction (5% and 1%) of the tweets in the convo, but
receive a large proportion of retweets (44% and 28%). Therefore, we can
reasonably extract the tweets by the top influencers to represent the
influential or popular messages in the convo. A noticeable difference between
the two convos is that, the number of the influential tweets in the #Frexit
convo is more than twice of the number in the #covid_19 convo. This signifies
that the influencers in the #Frexit convo have been much more active in
generating content to drive their agendas.

We closely examine the network of influencers to analyze their retweet
behavior. The#frexit influencer network (Fig. 2(a)) is strongly connected by a
large number of retweets. Bi-directional retweeting is also found between 4
pairs of authors. On the contrary, in the #covid_19 influencer network, the
connections are notably weaker. All the connections are one-directional and
majority of them originate from one author. We hypothesize that a combination
of the influencers’ efforts in generating the tweets and the density of their
retweet network may serve as an early sign of a potential influence operation
within the convo. Consequently, though the influencers’ receive a substantial
number of retweets in both convos, it is plausible that an influence operation
may be more prominent in the #Frexit convo compared to the #covid_19 convo.

Next, we analyze the agendas and convos snapshots generated by our model. In
the #Frexit convo, both the message clusters in Fig. 2(a) criticize president
Macron but they advocate for different candidates
111https://www.thenationalnews.com/world/europe/2022/04/13/marine-le-pen-
denies-frexit-agenda-as-presidential-rivals-clash-over-europe/. The first
cluster focuses more on France’s withdrawal from the EU, and support François
Asselineau who is a lead character in the #Frexit movement
222https://international.la-croix.com/news/politics/frances-frexit-
presidential-candidate/4821. However, the second cluster advocates for Florian
Philippot and his party, and shows strong opposition against the vaccine pass
333https://www.thelocal.fr/20180219/les-patriotes-florian-philippot-what-you-
need-to-know-france-newest-far-right-party. Influencer I4 and I1 are the top
contributors in the first cluster, while more than 90% of the tweets in the
second cluster come from I6. Fig 2(a) also depicts that I4 and I1 retweet each
other, and I6 is not directly connected to either of them. Hence, we can
deduce that even within the same convo, distinct sub-groups of influencers and
their respective retweeting users tend to agree on specific topics while
disagreeing on others. Similarly, the agendas in the #covid_19 convo discuss
several topics around the vaccine pass in France and criticize Macron for his
handling of the pandemic
444https://www.france24.com/en/europe/20211014-macron-s-covid-health-pass-a-
success-in-overcoming-france-s-vaccine-scepticism.

Therefore, these visualizations of the focused message groups in the convos
provide a concise representation of the ongoing discussions among popular
authors around that topic. Extracting such detailed analysis would require
significant manual effort and time from experienced analysts. Together with
the influencer networks, they provide valuable insights about targeted
operations in a corpus.

## 4\. Related Work

### 4.1. Agenda and Emotion Detection

In previous studies, agenda and emotion detection are usually presented as
individual tasks. Most of the work on agenda theory focus on the agenda
setting process between the media and the audience, between different types of
media, or between different groups of people Ceron et al. (2016); Guo (2019);
McCombs et al. (1997); Vargo et al. (2014). In McCombs et al. (1997), the
authors investigate the images of the election candidates presented by mass
media and shaped among the voters. Document level content analysis is
performed on TV news and newspaper stories, and the voters’ opinions towards
the candidates are collected by surveys.

The agendas in any political campaign are usually candidate names, their
personalities, ideologies, and qualifications, and whether their images are
built to be positive, neutral, or negative. The authors compare the proportion
of each agenda between the media and voters to understand the effects of media
on the general population. With the emergence of social media, similar
research has been performed to explore the agenda-setting dynamics between
mass media and social media, to identify the roles of the agenda setter
between them Su and Borah (2019); Conway et al. (2015).

The use of emotional language has also been an important indicator during any
political campaign (Grüning and Schubert, 2022). With the availability of deep
learning models and annotated datasets, fine-tuning models for emotion
detection in particular domains have become a popular approach for emotion
detecteion (Cai and Hao, 2018; Huang et al., 2019; Chiorrini et al., 2021).
Prompting techniques using pre-trained large larguage models have also been
deployed to perform zero-shot emotion detection in unknown domains (Plaza-del
Arco et al., 2022). Although there has been significant research on emotion
detection over individual messages on social media, our work is dedicated to
detecting emotions expressed in groups of messages towards specific entities
or topics.

All the works mentioned above aim to clarify the phenomena of information flow
from one source to another, and ignore the possible influence operations
behind the information flow. In contrast, our approach addresses this missing
piece by identifying the influencers in the dynamic process and analyzing
their behaviors and their inter-connections. Additionally, our break-down and
summary method works efficiently as it requires lesser human annotation, which
is a necessary step in most of the previous works Guo (2019); Su (2022);
Subbiah et al. (2023).

## 5\. Conclusion

In this work we introduce a novel systematic approach to identify influential
message subsets from social media datasets. We build upon the idea of a convo
to extract concise snapshots of these online discussions around particular
events or topics. We characterize these convos using agendas and emotions to
enable us to detect targeted influence operations by a group of influencers.
We also create a network of these influencers to analyze the retweet behavior
and group dynamics among them. A case study around prominent campaigns during
the 2022 French Elections helps us to evaluate our proposed approach. Future
work would include application of our approach on other types of social media
and definition of concrete metrics to measure degrees of influence and
precisely identify influence operations.

## 6\. Acknowledgements

This paper is based upon work supported by the Defense Advanced Research
Projects Agency (DARPA) under Contract No. HR001121C0186. Any opinions,
findings and conclusions or recommendations expressed in this material are
those of the authors and do not necessarily reflect the views of DARPA or the
U.S. Government.

## 7\. Limitations and Ethical Considerations

Given the nature of the proposed task and the role of LLM in our approach,
this work does have several limitations. Firstly, we analyze our approach on a
publicly available Twitter dataset. The dataset contains retweet information
but does not differentiate between tweets, quotes, and replies. In future, we
plan to extend to other platforms and other datasets with more diverse user
interactions in order to better understand the group dynamics of online
communities. Secondly, it is well known that the current large language models
have a wide range of biases. Consequently, it is possible that our findings
reflect the biased opinions nested in the LLM rather than from the dataset
(Rozado, 2023).

We do not use or analyze any personally identifiable data in our experiments.
The outputs generated are solely based on summaries generated by filtering
popular messages on Twitter and the use of popular LLMs. They may reflect
various political agendas or opinions of particular candidates. They must be
verified by expert analysts before use in any downstream application.

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##  Appendix A Appendices

### A.1. Appendix: Agenda and Emotion Detection Prompts

    [INST] <<SYS>>
    You are a helpful, respectful and honest agenda detection assistant.
    Read the list of messages given and understand the hidden agendas behind them.

    Please do not share false information. If you are unable to understand the agenda,
    simply say "No agenda".
    <</SYS>>

    What is the overall agenda behind this set of messages? Give me a short summary.
    Messages: {input_text}
    [/INST]
    The agenda behind this set of tweets is

---

Table 4: System Prompt use to characterize convos using Llama-2-13b-chat

    What are the top distinct entities (maximum 5) mentioned in several messages?
    What are the authors promoting about each entity? Give me 1 phrase for each.
    Give the emotions expressed towards each entity.
    Combine the entities, promoted actions and emotions in the following format:
    output = [
    {
    "entity": {entity},
    "promoted_actions": {action},
    "emotions": {emotion}
    },
    ...
    ]

---

Table 5: Prompts and output template to extract entities, promoted actions and
emotions