*Case Report* **Dealing with Corticosteroid and High-Dose Cyclosporine Therapy in a Pyoderma Gangrenosum Patient Contracting a COVID-19 Infection**

**Marcella Ricardis May 1 , Albert Rübben 1,2 , Andrea Lennertz 3 , Luk Vanstreels 2 and Marike Leijs 1,2, \***

**Abstract:** Pyoderma gangrenosum (PG) is a rare and chronic neutrophil inflammation belonging to the spectrum of autoinflammatory disorders. Immunosuppressive therapy is the cornerstone of successful treatment. However, due to the global COVID-19 pandemic, physicians struggle with therapeutic strategies during infection. This paper describes the case of a 58-year-old patient with a very painful, rapidly increasing wound on his right foot, which was diagnosed as pyoderma gangrenosum. Five weeks after the initial treatment with high-dose immunosuppressives (combination therapy with cyclosporine A and systemic methylprednisolone), he became infected with COVID-19. Reduction in the immunosuppressive dosage proved effective, as the patient recovered from COVID-19 without any complication and showed rapid wound healing.

**Keywords:** COVID-19; pyoderma gangrenosum; immunosuppression; cyclosporine; corticosteroids; autoinflammatory disease


3. Introduction of electronic phenomenological spectroscopy

The method of electronic phenomenological spectroscopy (EPS) was first proposed by Mikhail Dolomatov [2, 3]. In recent years, this science direction has been intensively developed by the Dolomatov group at the Oil Technical State University and Bashkir State University (Ufa) in Russia. There are the following approaches and physical phenomena in the basis of EPS:

Unlike conventional spectroscopic methods, the EPS studies substances as a comprehensive quantum quasicontinuum without separating the spectrum of the substance into characteristic spectral bands by certain resonance frequencies or wavelengths of individual functional groups or components. The spectrum is

studied as a single system (broadband signal) from a set of electronic states. Therefore, at this system integral level, there are new physical effects, not previously known. For example, the effects of the relationship of integral optical characteristics with different macroscopic and quantum properties of the substance as a whole by quantum quasicontinuum "spectrum-properties" and "color-properties" are observed. Qualitatively new physical phenomena appear when considering systems interacting with radiation in a wide optical spectrum. According to these laws, changes in the physical and chemical properties of substances cause a change in the integral characteristics of absorbed, reflected, or emitted radiation in the ultraviolet (UV), visible, and near-infrared (IR) regions of the electromagnetic spectrum. This allows the use of EPS methods for the study of individual and complex multicomponent substances.

For example, there may be a relationship between the integral force of the oscillator and some physical and chemical properties Z:

$$
\Delta Z = \mathbf{c} \cdot \Delta \Theta \tag{9}
$$

Obviously, a special case of Eq. (10) is the effect of "color-properties" (1) (we found with the coauthors O. Kydyrgychova, L. Dolomatova and V. Kartasheva in 1999 [5]). Phenomenological spectroscopy methods have been developed for identification and simultaneous determination of a set of different physical and chemical properties of natural and technical multicomponent organic systems, as well as properties of individual substances. For example, in a few minutes, it is possible to determine such properties of formation oils as the average molecular weight, viscosity, density, thermal stability index, index of reactivity of fractions in the processes of coking and thermal cracking, etc. EPS methods were adopted in the oil and petrochemical industry [2–4], environmental monitoring [3], biophysics and medicine [24, 25], nanotechnology and molecular electronics [15–18], and space

For science and technology, of interest are laws of the relationship of the integral characteristics of the spectrum and the electronic properties of matter. The knowledge of the electron structure of the molecular substances and materials has the fundamental importance for solving real problems in many fields of science and technology (physic of solid state, chemistry, electronics, electrical engineering). Despite progress in the experimental and quantum methods in some cases, there are significant discrepancies between the predicted values and experimental results of electron structure determination of complex materials and compounds. Many compounds and some materials for nanotechnology are characterized by complex structure and chemical and phase instabilities. Therefore, it is necessary to create new methods for assessing electronic structures, for example, ionization potentials,

Hence the difficulty of determining the first ionization potentials (IP), the affinity of electrons (EA) and other characteristics of the energies of electronic

an atom or molecule. The unit of measurement of this physical quantity is the amount of energy required to remove one electron from one atom or molecule, expressed in electronic volts. The ionization potential (IP) is the electrical potential at which an electron leaves an atom or molecule, overcoming the forces of attrac-

As known, ionization energy is the energy required to remove an electron from

If during the electronic transition the geometry of the molecule changes minimally, it is said about the vertical IP. Next, we will consider the vertical potential only. According to the theorem of Koopmans, the first vertical ionization energy of a molecular system is equal to the negative of the orbital energy of the highest

The electron affinity (EA) of an atom or molecule is defined as the amount of energy released or spent when an electron is added to a neutral atom or molecule

In the chemistry IP and EA are the characteristics for ability of molecules to donor-acceptor properties [27]. These physical values may be used for the determination of the indexes of reactivity of molecules (a characteristic of its chemical

In previous works [2, 14, 20, 21], we established new physical effects between spectral densities (integral absorption, reflection, and transmission characteristics)

X � e� ! Xþ þ energy (11)

X þ e� ! X� þ energy (12)

exploration.

states for such systems.

affinities to electron, and some other properties.

New Results in the Theory and Practical Application of Color

DOI: http://dx.doi.org/10.5772/intechopen.84832

tion. This process forms a positive ion [27, 28].

occupied molecular orbital (HOMO).

activity).

15

with the formation of a negative ion [28].

Here θ is the integral absorption—integral oscillator force (IOF), which has a simple physical explanation, namely, the area under the radiation absorption curve for the visible and UV regions of the spectrum, l nm mole�1 cm�1 ;

c is the constant depending on the method of measuring the spectrum, the nature of the substance, and individual for each property.

Therefore, it can be assumed that there is a relationship between any integral optical characteristic of a wide-spectrum signal (Figure 4) and properties having the form.

$$
\Delta Z = \mathbf{c} \cdot \Delta P \tag{10}
$$

Here, P is the integral spectral parameter, for example, integrated oscillator power, color characteristics, integral autocorrelation function, or relative imperial parameter and others into Figure 1.

### Figure 1.

Integral phenomenological characteristics of electronic spectra.

New Results in the Theory and Practical Application of Color DOI: http://dx.doi.org/10.5772/intechopen.84832

studied as a single system (broadband signal) from a set of electronic states. Therefore, at this system integral level, there are new physical effects, not previously known. For example, the effects of the relationship of integral optical characteristics with different macroscopic and quantum properties of the substance as a whole by quantum quasicontinuum "spectrum-properties" and "color-properties" are

observed. Qualitatively new physical phenomena appear when considering systems interacting with radiation in a wide optical spectrum. According to these laws, changes in the physical and chemical properties of substances cause a change in the integral characteristics of absorbed, reflected, or emitted radiation in the ultraviolet (UV), visible, and near-infrared (IR) regions of the electromagnetic spectrum. This allows the use of EPS methods for the study of individual and complex

For example, there may be a relationship between the integral force of the

Here θ is the integral absorption—integral oscillator force (IOF), which has a simple physical explanation, namely, the area under the radiation absorption curve

c is the constant depending on the method of measuring the spectrum, the

Therefore, it can be assumed that there is a relationship between any integral optical characteristic of a wide-spectrum signal (Figure 4) and properties having

Here, P is the integral spectral parameter, for example, integrated oscillator power, color characteristics, integral autocorrelation function, or relative imperial

ΔZ ¼ c � ΔΘ (9)

ΔZ ¼ c � ΔP (10)

;

oscillator and some physical and chemical properties Z:

for the visible and UV regions of the spectrum, l nm mole�1 cm�1

nature of the substance, and individual for each property.

multicomponent substances.

Color Detection

parameter and others into Figure 1.

Integral phenomenological characteristics of electronic spectra.

the form.

Figure 1.

14

Obviously, a special case of Eq. (10) is the effect of "color-properties" (1) (we found with the coauthors O. Kydyrgychova, L. Dolomatova and V. Kartasheva in 1999 [5]). Phenomenological spectroscopy methods have been developed for identification and simultaneous determination of a set of different physical and chemical properties of natural and technical multicomponent organic systems, as well as properties of individual substances. For example, in a few minutes, it is possible to determine such properties of formation oils as the average molecular weight, viscosity, density, thermal stability index, index of reactivity of fractions in the processes of coking and thermal cracking, etc. EPS methods were adopted in the oil and petrochemical industry [2–4], environmental monitoring [3], biophysics and medicine [24, 25], nanotechnology and molecular electronics [15–18], and space exploration.

For science and technology, of interest are laws of the relationship of the integral characteristics of the spectrum and the electronic properties of matter. The knowledge of the electron structure of the molecular substances and materials has the fundamental importance for solving real problems in many fields of science and technology (physic of solid state, chemistry, electronics, electrical engineering). Despite progress in the experimental and quantum methods in some cases, there are significant discrepancies between the predicted values and experimental results of electron structure determination of complex materials and compounds. Many compounds and some materials for nanotechnology are characterized by complex structure and chemical and phase instabilities. Therefore, it is necessary to create new methods for assessing electronic structures, for example, ionization potentials, affinities to electron, and some other properties.

Hence the difficulty of determining the first ionization potentials (IP), the affinity of electrons (EA) and other characteristics of the energies of electronic states for such systems.

As known, ionization energy is the energy required to remove an electron from an atom or molecule. The unit of measurement of this physical quantity is the amount of energy required to remove one electron from one atom or molecule, expressed in electronic volts. The ionization potential (IP) is the electrical potential at which an electron leaves an atom or molecule, overcoming the forces of attraction. This process forms a positive ion [27, 28].

$$\mathbf{X} - \mathbf{e}^- \to \mathbf{X}^+ + \mathbf{e} \text{energy} \tag{11}$$

If during the electronic transition the geometry of the molecule changes minimally, it is said about the vertical IP. Next, we will consider the vertical potential only. According to the theorem of Koopmans, the first vertical ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital (HOMO).

The electron affinity (EA) of an atom or molecule is defined as the amount of energy released or spent when an electron is added to a neutral atom or molecule with the formation of a negative ion [28].

$$\mathbf{X} + \mathbf{e}^- \to \mathbf{X}^- + \mathbf{energy} \tag{12}$$

In the chemistry IP and EA are the characteristics for ability of molecules to donor-acceptor properties [27]. These physical values may be used for the determination of the indexes of reactivity of molecules (a characteristic of its chemical activity).

In previous works [2, 14, 20, 21], we established new physical effects between spectral densities (integral absorption, reflection, and transmission characteristics) with IP and EA. We propose to use these effects in determining the energies of electronic states. Methods for determination of IP and EA for molecules and organic semiconductors have been developed. We propose to use these effects in determining the energies of electronic states.

The IP and the EA of materials were estimated from the empirical dependencies linking these characteristics with the integral parameter of UV and/or vis spectrum:

$$E = a\_0 + a\_1 P \tag{13}$$

where Е is effective ionization potential or effective electron affinity, eV; α1 and α2 are empirically determined coefficients, and P is the integral spectral parameter. For example, integrated oscillator force (IOF), color characteristics, integral autocorrelation function or relative empirical parameter, and others (Figure 1).

The first experiments in the detection of the phenomenon (2) were carried out in 1988–1992 together with the Dr. G. Mukaeva [14]. The dependence of IP and EA on the integral oscillator force (IOF) was established by the results of the study of about 200 optical spectra of atoms and organic molecules:

$$E = a\_1 + a\_2 \cdot \theta,\tag{14}$$

IP ¼ γ1þγ2�ACv, (18) EA ¼ χ 1þχ 2�ACv, (19) IP ¼ φ1þφ2�μ, (20) EA ¼ η1þη2�μ, (21)

> Constants by (18) and (19), 10�17 eV s

γ1 χ1 γ2 χ2 IP EA

5.43 1.68 1.88 �1.36 0.88 0.87

Determination coefficient, R2

coefficient, R2

Statistic characteristics

Mean-square deviation, eV

Variation coefficient, %

IP is the effective ionization potential; EA is the effective electron affinity; Acv is

In the calculation of integral parameters using the autocorrelation function of the signal, we have used the techniques adopted in statistical physics and spectroscopy [29]. We presented the energy spectrum of the molecule in the form of the integral of the autocorrelation function (IACF), frequency-dependent transitions. The integral autocorrelation function (ACF) is defined by the following formula:

and (19)eV

Complex oxy-compounds 9.35 0.08 �1.96 1.24 0.90 0.88 Ketones and aldehydes 10.65 �0.02 �2.98 1.76 0.85 0.81 Constants by (20) and (21), eV Determination

Polycyclic aromatic hydrocarbons φ1 φ2 η1 η2 IP EA

integral autocorrelation function of the electron spectrum (IAFS) (23); μ is the relative empirical autocorrelation parameter (μ, parameter) (24); ε (v) is the density distribution function of the radiation absorption; v is the spectral frequency; γ0, γ1, χ1, χ2, η1, η2, φ0, and φ1 are empirically defined coefficients (Table 4); and m is

Dependence E ¼ α1 þ α2 � θlg

New Results in the Theory and Practical Application of Color

α1, eV

Coefficient of correlation equations

> α2, 10�7 eV nm�1

Correlation coefficient

IP 8.074 �0.0010256 0.76 0.22 3.07

EA 0.290 0.00064502 0.71 0.16 2.22

IP 10.11 �0.00250000 0.88 0.26 2.46

IP 11.03 �0.00347000 0.82 0.32 2.54

EA

DOI: http://dx.doi.org/10.5772/intechopen.84832

Coefficients of dependence (16) for homologous series.

Homologous series IP or

Polycyclic aromatic compounds

Polycyclic aromatic compounds

Nitrogen-containing compounds [35]

Oxygen-containing compounds [35]

Table 3.

Table 4.

17

the number of spectrum bands.

Group of organic semiconductor Constants by (18)

Constants and determination coefficients for dependencies (14–16).

Integral spectral characteristic can be any physical value of general absorption or emission of electromagnetic radiation, such as integral oscillator force (IOF):

$$\theta = \int\_{\delta} \left[ f(\xi) d\xi d\delta \right] \tag{15}$$

where θ is a reflection of quantum continuum as the sum of different states of electron, for example, all vibration states and electron states of transition among different levels, f(ξ) is spectral function of absorption or emission of radiation, and δ is a range of resonance wavelengths or frequencies.

Let us consider the method, which was proved in our previous works [14, 15]. The IP and EA are estimated according to empirical dependencies which link these characteristics with logarithmic integral index of absorption (1).

$$E = a\_1 + a\_2 \theta\_{\lg} \tag{16}$$

Here Е is the ionization potential or an electron affinity, eV; α1 and α2 are empirically determined coefficients, eV and eV �nm�1 , respectively.

$$\int\_{\omega\_1}^{\lambda\_2} \lg \varepsilon\_\lambda d\lambda = \theta\_{\lg} \tag{17}$$

where ε(λ) is the molar extinction coefficient, l mol�1 cm�1 ; θ1g is the integral logarithmic index of absorption (logarithmic IOS), �nm; λ1 and λ2 are borders of the spectrum in UV and (or) visible region, nm; and λ1 and λ2 are the borders of wavelength of the spectrum in UV and (or) visible region.

Table 3 shows the corresponding coefficients for the dependencies (16) in different classes of organic molecules.

Breakthrough research in this area was done in collaboration with Dr. D. Shulyakovskii, Dr. E. Kovaleva, Dr. G. Yarmuhamedova, N. Paimurzina, and K. Latypov [20, 21]. We established the following regularities, which connected the integral parameters of the spectrum with IP and EA (18)–(21).

New Results in the Theory and Practical Application of Color DOI: http://dx.doi.org/10.5772/intechopen.84832

## Table 3.

with IP and EA. We propose to use these effects in determining the energies of electronic states. Methods for determination of IP and EA for molecules and organic semiconductors have been developed. We propose to use these effects in determin-

The IP and the EA of materials were estimated from the empirical dependencies linking these characteristics with the integral parameter of UV and/or vis spectrum:

where Е is effective ionization potential or effective electron affinity, eV; α1 and α2 are empirically determined coefficients, and P is the integral spectral parameter. For example, integrated oscillator force (IOF), color characteristics, integral autocorrelation function or relative empirical parameter, and others (Figure 1).

The first experiments in the detection of the phenomenon (2) were carried out in 1988–1992 together with the Dr. G. Mukaeva [14]. The dependence of IP and EA on the integral oscillator force (IOF) was established by the results of the study of

Integral spectral characteristic can be any physical value of general absorption or

emission of electromagnetic radiation, such as integral oscillator force (IOF):

δ

ð

ξ

where θ is a reflection of quantum continuum as the sum of different states of electron, for example, all vibration states and electron states of transition among different levels, f(ξ) is spectral function of absorption or emission of radiation, and

Let us consider the method, which was proved in our previous works [14, 15]. The IP and EA are estimated according to empirical dependencies which link these

Here Е is the ionization potential or an electron affinity, eV; α1 and α2 are

logarithmic index of absorption (logarithmic IOS), �nm; λ1 and λ2 are borders of the spectrum in UV and (or) visible region, nm; and λ1 and λ2 are the borders of

Table 3 shows the corresponding coefficients for the dependencies (16) in

Dr. D. Shulyakovskii, Dr. E. Kovaleva, Dr. G. Yarmuhamedova, N. Paimurzina, and K. Latypov [20, 21]. We established the following regularities, which connected

λ ð2

λ1

Breakthrough research in this area was done in collaboration with

the integral parameters of the spectrum with IP and EA (18)–(21).

where ε(λ) is the molar extinction coefficient, l mol�1 cm�1

wavelength of the spectrum in UV and (or) visible region.

different classes of organic molecules.

16

θ ¼ ð

about 200 optical spectra of atoms and organic molecules:

δ is a range of resonance wavelengths or frequencies.

empirically determined coefficients, eV and eV �nm�1

characteristics with logarithmic integral index of absorption (1).

E ¼ α0þα1P (13)

E ¼ α1 þ α2 � θ, (14)

E ¼ α1 þ α2θlg, (16)

, respectively.

; θ1g is the integral

lg ελdλ ¼ θlg (17)

fð Þξ dξdδ (15)

ing the energies of electronic states.

Color Detection

Coefficients of dependence (16) for homologous series.

$$\text{IP} = \gamma\_1 + \gamma\_2 \mathbf{A}\_{\text{C}\text{ov}} \tag{18}$$

$$\mathbf{E}\mathbf{A} = \boldsymbol{\chi}\_1 + \boldsymbol{\chi}\_2 \mathbf{A}\_{\mathrm{C\boldsymbol{\eta}}},\tag{19}$$

$$\text{IP} = \varphi\_1 + \varphi\_2 \mu,\tag{20}$$

$$EA = \eta\_1 + \eta\_2 \mu,\tag{21}$$

IP is the effective ionization potential; EA is the effective electron affinity; Acv is integral autocorrelation function of the electron spectrum (IAFS) (23); μ is the relative empirical autocorrelation parameter (μ, parameter) (24); ε (v) is the density distribution function of the radiation absorption; v is the spectral frequency; γ0, γ1, χ1, χ2, η1, η2, φ0, and φ1 are empirically defined coefficients (Table 4); and m is the number of spectrum bands.

In the calculation of integral parameters using the autocorrelation function of the signal, we have used the techniques adopted in statistical physics and spectroscopy [29]. We presented the energy spectrum of the molecule in the form of the integral of the autocorrelation function (IACF), frequency-dependent transitions. The integral autocorrelation function (ACF) is defined by the following formula:

## Table 4.

Constants and determination coefficients for dependencies (14–16).

$$\mathbf{A}(\Delta o) = \int\_{\omega\_0}^{\omega\_2} f(o)f(o + \Delta o)dou\tag{22}$$

where ω ¼ 2πυ, cyclical frequency, s �1 .

In [20] we proposed numerical parameter from IACP in the optical spectra was determined with the logarithmic function. The parameters of the ACF are because numbers are calculated using definite integral.

$$\mathbf{A}\_{\nu} = \bigcap\_{m\_1=1}^{m\_2 \cdot \nu 2} \mathbf{e}(\nu)\mathbf{e}(\nu + \Delta\nu)d\nu \,\mathrm{dm} \tag{23}$$

where lgε νð Þ and lgε νð Þ þ Δν are logarithms of molar extinction coefficient on frequency ν, ν þ Δν; ν1, ν2, and νn are the spectrum boundary, Hz; Δν is the argument increment (step), Hz; and m is the number of spectrum bands.

$$\mu = \frac{\int\_{m\_1}^{m\_2} \int\_{\nu\_1}^{\nu\_2} \lg \varepsilon(\nu) \cdot \lg \varepsilon(\nu + \Delta \nu) d\nu dm}{\int\_{m\_0}^{m\_2} \int\_{\nu\_0}^{\nu\_2} \lg \varepsilon(\nu) \cdot \lg \varepsilon(\nu + \Delta \nu) d\nu dm} \tag{24}$$

where the numerator of fraction is the integral autocorrelation function (IACF) in the UV spectral region; the denominator is IACF in the UV-vis spectral region; ν, ν þ Δν; ν1, ν2, and νn are the spectrum boundary 1014 Hz; Δv is small increment of the argument (the analysis step of 1.5 � 1016 Hz); lgε(v) and lgε(v + Δv) are molar absorption coefficients at certain frequencies; and m is the number of spectrum bands.

The dependencies of IP and EA on the μ-factor for polycyclic aromatic hydrocarbons (PAH) of various classes (Figures 2 and 3) are established [20]. In addition, the dependencies of IP and EA on IACP for oxygen-containing compounds (alcohols, aldehydes, ketones) (Figures 4 and 5) are established [21].

IP and EA of organic molecules and PAH of different origin are presented in Tables 5 and 6.

EA and IP of organic molecules and semiconductors of different origins are presented in Tables 2 and 3.

Thus it is established that IP and EA of PAH, calculated by RHF 6-31G\*\* and DFT methods, have the IACF dependence and μ-factor. These dependencies allow

simplification of the estimations of IP and EA of organic molecules and PAH of

different molecules and organic semiconductors are developed.

Relationship of EA from IACF of organic oxygen groups containing molecules.

Relationship of EA with the relative empirical autocorrelation parameter μ for PAH.

New Results in the Theory and Practical Application of Color

DOI: http://dx.doi.org/10.5772/intechopen.84832

Relationship of IP from IACF of organic oxygen groups containing molecules.

Thus, new methods for determining characteristics of electronic structure of

Subsequently, dependence (14) was confirmed by the study of IP and EA for various classes of sulfur and nitrogen organic compounds, organic dyes, amino

In studies [2–4] for very complex multicomponent systems, the problem of determining the electronic structure and, consequently, chemical activity was

different origin (Tables 5 and 6).

acids, and biological fluids [24].

solved.

19

Figure 5.

Figure 3.

Figure 4.

Figure 2. Relationship of IP with the relative empirical autocorrelation parameter μ for PAH.

New Results in the Theory and Practical Application of Color DOI: http://dx.doi.org/10.5772/intechopen.84832

Að Þ¼ Δω

Aν ¼

ðm2 m1

ðm2 m0

μ ¼

bands.

Figure 2.

18

Tables 5 and 6.

presented in Tables 2 and 3.

mð2

ν ð 2

ν1

m1

ment increment (step), Hz; and m is the number of spectrum bands.

ðν2 ν1

ðν2 ν0

where ω ¼ 2πυ, cyclical frequency, s

Color Detection

numbers are calculated using definite integral.

ωð2

fð Þ ω fð Þ ω þ Δω dω (22)

ε νð Þε νð Þ þ Δν dνdm (23)

(24)

ω0

�1 . In [20] we proposed numerical parameter from IACP in the optical spectra was determined with the logarithmic function. The parameters of the ACF are because

where lgε νð Þ and lgε νð Þ þ Δν are logarithms of molar extinction coefficient on frequency ν, ν þ Δν; ν1, ν2, and νn are the spectrum boundary, Hz; Δν is the argu-

lgε νð Þ� lgε νð Þ þ Δν dvdm

lgε νð Þ� lgε νð Þ þ Δν dvdm

where the numerator of fraction is the integral autocorrelation function (IACF) in the UV spectral region; the denominator is IACF in the UV-vis spectral region; ν, ν þ Δν; ν1, ν2, and νn are the spectrum boundary 1014 Hz; Δv is small increment of the argument (the analysis step of 1.5 � 1016 Hz); lgε(v) and lgε(v + Δv) are molar absorption coefficients at certain frequencies; and m is the number of spectrum

The dependencies of IP and EA on the μ-factor for polycyclic aromatic hydrocarbons (PAH) of various classes (Figures 2 and 3) are established [20]. In addition,

IP and EA of organic molecules and PAH of different origin are presented in

EA and IP of organic molecules and semiconductors of different origins are

Thus it is established that IP and EA of PAH, calculated by RHF 6-31G\*\* and DFT methods, have the IACF dependence and μ-factor. These dependencies allow

the dependencies of IP and EA on IACP for oxygen-containing compounds (alcohols, aldehydes, ketones) (Figures 4 and 5) are established [21].

Relationship of IP with the relative empirical autocorrelation parameter μ for PAH.

Figure 3. Relationship of EA with the relative empirical autocorrelation parameter μ for PAH.

Figure 4. Relationship of IP from IACF of organic oxygen groups containing molecules.

Figure 5. Relationship of EA from IACF of organic oxygen groups containing molecules.

simplification of the estimations of IP and EA of organic molecules and PAH of different origin (Tables 5 and 6).

Thus, new methods for determining characteristics of electronic structure of different molecules and organic semiconductors are developed.

Subsequently, dependence (14) was confirmed by the study of IP and EA for various classes of sulfur and nitrogen organic compounds, organic dyes, amino acids, and biological fluids [24].

In studies [2–4] for very complex multicomponent systems, the problem of determining the electronic structure and, consequently, chemical activity was solved.

The asphaltenes are complex substances that can be found in crude oil, bitumen, and high-boiling hydrocarbon distillates. The asphaltenes are composed mainly of polyaromatic and heterocyclic compounds with traces of vanadium and nickel, which are in porphyrin structures. The electronic structure of asphaltenes has not been researched enough. The aim of research was to define the electronic structure of various asphaltenes. We have used the EPS methods. Some of the results are

Thus for asphaltenes, IP is in the interval from 4.37 up to 6.41 eV and EA differs from 1.82 to 2.66 eV. The size of energy band gap from 1.93 to 3.85 eV indicates that oil asphaltenes belong to amorphous, compensated, wideband semiconductors.

The experiments for band gap estimation of the asphaltene molecules were confirmed by electronic structure computing with ab initio methods. The main deduction from this research is that oil asphaltenes can be used as organic

Asphaltenes EIP, eV EEA, eV Band gap

The characteristics of the electronic structure of asphaltenes by EPS method.

New Results in the Theory and Practical Application of Color

DOI: http://dx.doi.org/10.5772/intechopen.84832

Asphaltenes of Radevski oil 5.70 1.85 3.85 1.92 Asphaltenes of Surgut oil 5.20–5.70 2.10–2.50 3.10–3.20 1.55–1.60 Asphaltenes of distillate fraction 4.37–5.27 2.44–2.50 1.93–2.77 0.96–1.38 Hydrogenation asphaltenes of West Siberia oil 6.41 2.66 3.75 1.85 Asphaltenes and resins of Surgut oil 5.34 1.82 3.52 1.76 Asphaltenes of Kushkul oil 5.2 1.90 3.30 1.65

4. Effects of dependence of ionization potentials and electron affinity

lar orbital, which characterizes the IP and EA, and color properties.

The research [7] (co-author Dr. Shulyakovskaya D. and Dr. Yarmuhametova G.) established the phenomenon of the relationship between the energy of the molecu-

where Е is energy of the boundary molecular orbital (IP or EA), eV; α1 and α2 are empirically determined coefficients eV; q is one of the color characteristics (CCs) for standard light source A, B, C, or D; and CCs can be represented in one of the international color measurement systems (e.g., color coordinates or chromaticity coordinates in XYZ or RGB systems). The color coordinates of polycyclic aromatic hydrocarbons in the XYZ system are shown (Figure 6). These coordinates are calculated in the visible region of the transmission spectra of hydrocarbon solutions

Several classes of compounds, including PAH, were studied by dependence (25). The corresponding coefficients for IP and EA are presented in Tables 8 and 9. As can be seen from the tables, the accuracy of the assessment of ionization potentials and electron affinity is satisfactory. Thus, the effect of the relationship between IP and EA on the color characteristics can be used to simultaneously measure these

E ¼ β1 þ β2 � q, (25)

energy, eV

Quasi Fermi level, eV

shown in Table 7.

Table 7.

semiconductors.

with color characteristics

according to the formulas (2)–(7).

physical quantities.

21

### Table 5.

Calculated values of IP and EA.

### Table 6.

Calculated values of IP and EA.

The characteristics of the chemical activity can be determined from the electron absorption spectra simplification. The authors introduced new values: effective IP and effective electron affinity [30]. The effective IP and EA are the averaged potentials of ionization and the electron affinity of the radiation-absorbing components.

They allow to estimate the electron states of multicomponent and highmolecular substances, such as heavy residual resins of oil processing, highmolecular mixtures, and others.

Determining the electronic structure of materials and nanomaterials is an important problem of molecular electronics. For this, EPS was used. This application of EPS to determine the electronic structure of high-molecular compounds of petroleum (petroleum asphaltenes) was proposed in our previous works (Dolomatov et al.) [2–4, 30].

New Results in the Theory and Practical Application of Color DOI: http://dx.doi.org/10.5772/intechopen.84832

Table 7.

The characteristics of the electronic structure of asphaltenes by EPS method.

The asphaltenes are complex substances that can be found in crude oil, bitumen, and high-boiling hydrocarbon distillates. The asphaltenes are composed mainly of polyaromatic and heterocyclic compounds with traces of vanadium and nickel, which are in porphyrin structures. The electronic structure of asphaltenes has not been researched enough. The aim of research was to define the electronic structure of various asphaltenes. We have used the EPS methods. Some of the results are shown in Table 7.

Thus for asphaltenes, IP is in the interval from 4.37 up to 6.41 eV and EA differs from 1.82 to 2.66 eV. The size of energy band gap from 1.93 to 3.85 eV indicates that oil asphaltenes belong to amorphous, compensated, wideband semiconductors. The experiments for band gap estimation of the asphaltene molecules were confirmed by electronic structure computing with ab initio methods. The main deduction from this research is that oil asphaltenes can be used as organic semiconductors.


**2.1 Familial adenomatous polyposis**

FAP is an inherited disease classically characterized by the development of hundreds to thousands of adenomas in the rectum and colon during the second decade of life (**Figure 1**). A less aggressive variant of FAP is the so-called attenuated FAP (aFAP), where the rectum is frequently spared.

Although FAP is responsible for less than 1% of colorectal malignancies, untreated individuals with FAP carry a 100% risk of colorectal cancer by 40–50 years.

Thus, for patients with FAP, the single way to prevent colorectal cancer is surgery. Nowadays, it is widely accepted that RPC-IPAA is the procedure of choice to treat patients with classical FAP.

We can choose for aFAP, total abdominal colectomy with ileorectal anastomosis (TAC-IRA), or proctocolectomy with stapled ileal pouch distal rectal anastomosis (CP-IPDRA).

FAP highlights:

• young population; absolute indication for surgery; if present rectal involvement, proctocolectomy is required; higher risk of desmoid in some family; RPC-IPAA is the procedure of choice to treat patients with classical FAP; RPC-IPAA easier in FAP than in UC [5].

**Figure 1.** *Familial adenomatous polyposis – colon details.*


*2.7. Statistical Analyses*

Comparative analysis of roughness for the natural leaves was performed by the Student's *t*-test for independent variables (results from *S. molesta* were excluded). Hydrophobicity results were compared using the Kruskal-Wallis H test and post-hoc analysis with the Mann Whitney U test and Bonferroni correction. Comparison of hydrophobicity and bacterial adhesion among transferred plates was performed by the one-factor Anova test and multiple comparisons through the Tukey's HSD test. Roughness results among transferred plates were compared using the Kruskal-Wallis H test and post-hoc analysis with the Mann Whitney U test and Bonferroni correction. Bivariate analysis tests were performed after previous verification of compliance with the assumptions of normality and homoscedasticity of the variances through the statistics of Shapiro Wilk and Levene, respectively. Values of *p* < 0.05 were considered statistically significant. Software SPSS (V. 25) was used for statistical analyses.