Basis sets moment gradient

The calculated dipole moment is remarkably insensitive to the size of the basis set. Note that the SVWN value in this case is substantially better than BLYP and BPW91, i.e. this is a case where the theoretically poorer method provides better results than the more advanced gradient methods. Inclusion of exact exchange again improves the performance, and provides results very close to the experimental value, even with quite small basis sets. 

Due to the electric quadrupole interaction, the Mi = 1/2 and Mi = 3/2 components of the 7 = 3/2 state of 57Fe split up, giving rise to the quadrupole splitting. Derived from the interaction of the nuclear quadrupole moment with the electric field gradient at the iron nuclei, AEq provides information about the asymmetry of the electron density around the iron nucleus. The electric field gradient at the iron nucleus can be calculated to obtain AEq (97). Since both 6 and AEq are related to the electron density at the nucleus, basis sets with an enlarged flexibility at the core region... 

Table 7.8 compares with experiment dipole moments calculated by B3LYP/6-31G, M06/6-31G, AMI (as a check on this fast method), and MP2(fc)/6-31G, for ten molecules. The two DFT methods give the same mean unsigned error, 0.11 D, three times smaller than the error of 0.31 D from the slowest method, MP2 (at least for this small selection of molecules), and the very fast AMI moments lie in-between, 0.22 D. None of these methods consistently gives values accurate to within 0.1 D. Very accurate dipole moments (mean absolute deviation 0.06-0.07 D) can be obtained with gradient-corrected DFT and very large basis sets [74]. 

The ground state force field, vibrational normal modes and frequencies have been obtained with MCSCF analytic gradient and hessian calculations [176]. Frequencies computed with the DZ basis set are compared with experimental ones in Table 16. The T - So transition moments were obtained using distorted benzene geometries with atomic displacements along the normal modes, and with the derivatives in Eq. 97 obtained by numerical differentiation. The normal modes active for phosphorescence in benzene are depicted in Fig. 12. The final formula for the radiative lifetime of the k spin sublevel produced by radiation in all (i/f) bands is (ZFS representation x,y,z is used [49]) ... 

Table 3.20 Changes of electric field gradient and dipole moment caused by H-bonding (atomic units) and rms HCl Ubrational angle (degs) calculated with [642/531/31] basis set for [C1,P/N/H]. ...

Moments and polarizabilities can also be obtained by the fixed-charge method [76]. This technique allows for the single-step incorporation of the nonuniform electric field contributions due to gradients and higher order field derivatives. One or more charges are placed around the molecule in regions where the molecular wavefunctions are negligible. It is important that the basis set used for the field-free molecule be the same as that used in the presence of the field and that the molecule basis be adequate to describe any... 

Results for dipole moments are shown in Table 29. ° Clearly, coupled with good basis sets, correlated methods can do quite well for this property. Elsewhere, we have used relaxed density-based CC and MBPT methods to study spin densities and the related hyperfine coupling constants to evaluate relativistic corrections (Darwin and mass-velocity term) when impor-tant and to evaluate highly accurate electric field gradients to extract nuclear quadruple moments. 

Ab initio SCF-MO calculations have been performed on BFg, and alterations in predicted geometries with different gaussian-orbital basis sets noted. Further non-empirical SCF calculations on this molecule have been reported by Rothenberg and Schaeffer. Values of the dipole moment, quadrupole moment, octupole moment, second and third moments of the electronic charge distribution, diamagnetic susceptibility, and electric field gradient were calculated. 

The evaluation of the matrix elements uses the molecular parameter eqQ for the coupling strength, where e is the elementary Charge, q the electric field gradient of the electron distribution at the nucleus averaged over the electron distribution, and Q the nuclear quadrupole moment. The matrix elements as functions of the quantum numbers of the angular momenta involved ean be found in different references. For Z states with two nuclei of spin / > 1 two different basis sets are in use ... 

All the reviewed programs carry out fundamental tasks of a computational chemist or a computational molecular physicist calculation of energy for various hamUtonians evaluation of gradients of energy (needed to locate stationary points on the potential energy surface) evaluation of the energy hessian (required to analyze the character of the located stationary point, identify local minima and saddle points, and perform vibrational frequency calculation) and evaluation of basic properties (population analysis, dipole moments). The components of the programs include basis set libraries and pseudopotentials. 

The changes in the response density distribution of CS are parallel to calculated changes in other one-electron properties of CS. Most properties oscillate dependent upon the order of PT applied where HF and MP2 results often represent the upper and lower bounds of computed values. Oscillations in calculated one-electron properties are observed in many cases (charges, dipole moments, quadrupole moments, electric field gradients, nuclear quadrupole moments, etc.) and are largely independent of the basis set used. In general, one can draw the following conclusions ... 

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