Atomic mean-field

Tike all effective one-electron approaches, the mean-field approximation considerably quickens the calculation of spin-orbit coupling matrix elements. Nevertheless, the fact that the construction of the molecular mean-field necessitates the evaluation of two-electron spin-orbit integrals in the complete AO basis represents a serious bottleneck in large applications. An enormous speedup can be achieved if a further approximation is introduced and the molecular mean field is replaced by a sum of atomic mean fields. In this case, only two-electron integrals for basis functions located at the same center have to be evaluated. This idea is based on two observations first, the spin-orbit Hamiltonian exhibits a 1/r3 radial dependence and falls off much faster... 

The one-center approximation allows for an extremely rapid evaluation of spin-orbit mean-field integrals if the atomic symmetry is fully exploited.64 Even more efficiency may be gained, if also the spin-independent core-valence interactions are replaced by atom-centered effective core potentials (ECPs). In this case, the inner shells do not even emerge in the molecular orbital optimization step, and the size of the atomic orbital basis set can be kept small. A prerequisite for the use of the all-electron atomic mean-field Hamiltonian in ECP calculations is to find a prescription for setting up a correspondence between the valence orbitals of the all-electron and ECP treatments.65-67... 

Computation of the spin-orbit contribution to the electronic g-tensor shift can in principle be carried out using linear density functional response theory, however, one needs to introduce an efficient approximation of the two-electron spin-orbit operator, which formally can not be described in density functional theory. One way to solve this problem is to introduce the atomic mean-field (AMEI) approximation of the spin-orbit operator, which is well known for its accurate description of the spin-orbit interaction in molecules containing heavy atoms. Another two-electron operator appears in the first order diamagnetic two-electron contribution to the g-tensor shift, but in most molecules the contribution of this operator is negligible and can be safely omitted from actual calculations. These approximations have effectively resolved the DET dilemma of dealing with two-electron operators and have so allowed to take a practical approach to evaluate electronic g-tensors in DET. Conventionally, DET calculations of this kind are based on the unrestricted... 

Schimmelpfennig B (1996) AMFI - an atomic mean field integral program. University of Stockholm, Stockholm, Sweden... 

It is better to go one step further and also neglect the multicenter one-electron integrals. The resulting atomic mean-field approximation seems to be good even for molecules composed of light atoms, because it appears that the one- and two-electron multicenter contributions to spin-orbit coupling par-tisdly compensate in a systematic manner. This approxima-... 

Vahtras et al. used the CASSCF(6,6)/DZP and atomic mean-field approximations to calculate the zero-field splitting parameters of benzene, including both spin-spin coupling to the first order and spin-orbit coupling to the second order of... 

Christiansen et al. s tested the coupled-cluster response theory on spin-orbit coupling constants of substituted silylenes (HSiX, X = F, Cl, Br) in the atomic mean-field approximation. Comparison with the full Breit-Pauli showed that the approximation is quite accurate. The calcu-... 

B. Schimmelpfeimig, AMFI, an Atomic Mean-Field Integral program (1996). 

In the previous section we discussed how to calculate the spin-orbit splittings of atomic and molecular states. The effect of spin-orbit coupling was introduced via the restricted active space interaction (RASSI) method with the use of the atomic mean-field AMFI integrals. It appears however, that the discrepancies between the experimental and calculated values of energies can be still quite big. 

State interaction, RASSI [36], method combined with the atomic mean field integrals method, AMFI [37], has been used to take spin-orbit (SO) effects into account. One electron part of AMFI code has been used only. It gives approximate spin-dependent... 

Just as for the Cowan-Griffin operator, the potential is the atomic SCF potential and so includes both one- and two-electron spin-orbit effects. In this respect the integrals over this potential resemble the atomic mean-field spin-orbit integrals of Hess et al. (1996). 

Brownridge S et al (2003) Efficient calculation of electron paramagnetic resonance g-tensors by multireference configuration interaction sum-over-state expansions, using the atomic mean-field spin-orbit method. J Chem Phys 118 9552-9562... 

Results obtained with the Dirac program, taken from Saue [56]. Uncontracted 24s19p12d9f large-component Caussian-type basis. DC = Dirac-Coulomb. AMFI = two-electron SO atomic mean-field integrals. NWChem and Dirac results with the same basis set as used to generate the data of Saue [56]. Vmp = model potential (see text). /ext = external electron-nucleus potential only. 

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