Wave function, calculation

Luce T A and Bennemann K H 1998 Nonlinear optical response of noble metals determined from first-principles electronic structures and wave functions calculation of transition matrix elements P/rys. Rev. B 58 15 821-6... 

View the contour map m several planes to see the general Torm of the distiibiiiioii. As long as you don t alter the molecular coordinates, you don t need to repeat th e wave function calculation. Use the left mouse button and the IlyperChem Rotation or Translation tools (or Tool icons ) to change the view of amolecnle without changing its atomic coordinates. 

If a covalent bond is broken, as in the simple case of dissociation of the hydrogen molecule into atoms, then theRHFwave function without the Configuration Interaction option (see Extending the Wave Function Calculation on page 37) is inappropriate. This is because the doubly occupied RHFmolecular orbital includes spurious terms that place both electrons on the same hydrogen atom, even when they are separated by an infinite distance. 

See also Extending the Wave Function Calculation on page 37. 

The quantity, V(R), the sum of the electronic energy Egjg. computed in a wave function calculation and the nuclear-nuclear coulomb interaction V(R,R), constitutes a potential energy surface having 3N independent variables (the coordinates R). The independent variables are the coordinates of the nuclei but having made the Born-Oppenheimer approximation, we can think of them as the coordinates of the atoms in a molecule. 

Table 1.10. Coefficients of Wave Functions Calculated for Methyl Cation by the CNDO/2...

As noted above, in the reference model the dependence of the electron wave functions A and B on the nuclear coordinates was entirely neglected and the wave functions A and B for the isolated ions or the wave functions calculated for corresponding equilibrium nuclear configurations Qk0i and Qkof according to Eqs. (8) were usually used in the calculations. 

It is not possible to use normal AO basis sets in relativistic calculations The relativistic contraction of the inner shells makes it necessary to design new basis sets to account for this effect. Specially designed basis sets have therefore been constructed using the DKH Flamiltonian. These basis sets are of the atomic natural orbital (ANO) type and are constructed such that semi-core electrons can also be correlated. They have been given the name ANO-RCC (relativistic with core correlation) and cover all atoms of the Periodic Table.36-38 They have been used in most applications presented in this review. ANO-RCC are all-electron basis sets. Deep core orbitals are described by a minimal basis set and are kept frozen in the wave function calculations. The extra cost compared with using effective core potentials (ECPs) is therefore limited. ECPs, however, have been used in some studies, and more details will be given in connection with the specific application. The ANO-RCC basis sets can be downloaded from the home page of the MOLCAS quantum chemistry software (http //www.teokem.lu.se/molcas). 

Non-Bom-Oppenheimer wave functions calculated in this way look more like their Born-Oppenheimer counterparts in the smaller basis set limits, and thus a good starting guess for these may be taken from Bom-Oppenheimer calculations in the same basis. Thus we calculate the electronic part first (this requires much fewer basis functions than does a full non-Bom-Oppenhimer calculation) and then form the total basis function by multiplying each electronic portion by a guess for the nuclear portion ... 

By calculating A.U (R) and Al/ (i ) separately, we can straightforwardly calculate the total adiabatic correction V (R) for any isotopes of A and B. The adiabatic corrections are calculated by numerical differentiation of the multi-configurational self-consistent field (MCSCF) wave functions calculated with Dalton [23]. The nurnerical differentiation was performed with the Westa program developed 1986 by Agren, Flores-Riveros and Jensen [22],... 

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