and bending [@Dragan], macromolecular docking [@Jackson], enzyme catalysis [@LiCata], drug classification [@Bergstrom], and solvation energies [@Raschke]. The SES model also plays a crucial role in implicit solvent models [@Baker:2005; @DuanChen:2011a], molecular dynamics simulations [@Geng:2011] and ion channel transports [@DuanChen:2011a; @QZheng:2011a; @QZheng:2011b]. Computationally, efficient algorithms for computing SES are developed or introduced, such as alpha-shapes [@WYChen:2010] and marching tetrahedra [@SLChan:1998]. A popular software for the Lagrangian representation of SESs, called MSMS, has been developed [@Sanner:1996]. Recently, a software package, called Eulerian solvent excluded surface (ESES), for the Eulerian representation of SESs [@ESES:2015], has also been developed. However SAS and SES are still not differentiable and have geometric singularities, i.e., cusps and tips. To construct smooth surface representation of macromolecules, Gaussian surface (GS) has been proposed to represent each atom by a C$^{\infty}$ Gaussian function, while accounting their overlapping properties [@Grant:1995]. Differential geometry theory of surfaces provides a natural approach to describe biomolecular surfaces and boundaries. Utilizing the Euler-Lagrange variation, a differential geometry based surface model, the minimal molecular surface (MMS), has been introduced for biomolecular geometric modeling [@Bates:2006; @Bates:2008]. Differential geometry based variational approach has been widely applied to biophysical modeling of solvation [@Wei:2009; @ZhanChen:2010a; @ZhanChen:2010b; @BaoWang:2015a], ion channel [@Wei:2012; @DuanChen:2012a; 