Dipole-moment gaussian density

The width rj 1 of the gaussian is chosen to be of the order of the lattice step, so that the two series, in the real and reciprocal spaces, converge rapidly. For the whole lattice, including the origin 0, and for a wave vector K, the dipole-moment gaussian density is... 

Accordingly, dipole moment and polarizability calculations are sensitive to both the quantum chemistry method and the basis set used. Accurate calculations typically require the use of D FTor Hartree-Fock methods with the inclusion of M P2 treatment of electron correlation [53, 54]. Furthermore, Gaussian basis sets should be augmented with diffuse polarization functions to provide an adequate description of the tail regions of density (the most easily polarized regions of the molecule). 

Sim, F., Salahub, D.R., and Chin, S. (1992) The accurate calculation of dipole moments and dipole polarizabilities using Gaussian-based density functional methods. Int. J. Quantum Chem., 43 (4), 463-479. 

Figure 1.1. Scheme of dipole-moment densities utilized in the method of Ewald (A) Distribution of point dipoles whose field is calculated at the origin 0. (B) distribution of gaussians centered at each point, point 0 included. (C) distribution of dipoles plus gaussians ... 

The dipole-moment density of the gaussian centered at each point x is... 

Calculation of Dipole Moments and Dipole Polarizabilities Using Gaussian-Based Density Functional Methods. 

For Hartree-Fock calculations of cyclopropane, benzene and adamantane, we used the Gaussian valence-shell dou-ble-zeta-and-polarization 9s5plAs p)l[ is2p dl2s p] basis set of Dunning and Hay [8]. The geometries of the three molecules were optimized with this DZP basis set and then used for analytical evaluation of normal modes, harmonic frequencies, dipole moment and its derivatives, and density matrix and its derivatives with respect to atomic coordinates. 

If experimental values of the polarizability and/or the dipole moment of the neutral molecule are unavailable, as is the case for many molecules, then these quantities can be calculated from ab initio or density functional theory (DFT) quantum chemical calculations. Zhao and Zhang have provided a comprehensive evaluation of this approach by carrying out calculations on 78 hydrocarbons and 58 non-hydrocarbons [31], A quite modest level of theory (DFT with the B3LYP functional and a 6-31G(d,p) Gaussian basis set) gave polarizabilities and dipole moments which yielded good agreement with experiment (where such values were available). The calculated dipole moments and polarizabilities were then employed in ADO calculations to obtain thermal rate coefficients. For most molecules, the predicted proton transfer rate coefficient was within 25% of the value determined from SIFT measurements. 

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