Hartree-Fock finite perturbation method

Since 1993 considerable effort has been taken to reproduce Se chemical shifts by ab initio calculations. Japanese authors reported a study describing the calculation of Se chemical shifts of various selenides R-Se-R by the Hartree-Fock finite perturbation method they found that the shielding is dominated by the contribution of the 4p orbital of Se to the paramagnetic... 

We have previously defined the one-electron spin-density matrix in the context of standard HF methodology (Eq. (6.9)), which includes semiempirical methods and both the UHF and ROHF implementations of Hartree-Fock for open-shell systems. In addition, it is well defined at the MP2, CISD, and DFT levels of theory, which permits straightforward computation of h.f.s. values at many levels of theory. Note that if the one-electron density matrix is not readily calculable, the finite-field methodology outlined in the last section allows evaluation of the Fermi contact integral by an appropriate perturbation of the quantum mechanical Hamiltonian. 

A Consequence of the Instability in First-order Properties.—Suppose a first-order property which is stable to small changes in the wavefunction (though is not necessarily close to the experimental value) is calculated to, say, three decimal places does an error in the fourth matter To provide a concrete example for discussion, a method described in the next section will be anticipated, namely the finite field method for calculating electric polarizability a. In this method a perturbation term Ai—— fix(F)Fa is added to the Hartree-Fock hamiltonian and an SCF wave-function calculated as usual. For small uniform fields,... 

In practice, calculations of xHF are based on the uncoupled Hartree-Fock, the finite field, and the self-consistent perturbation methods. Some workers use gauge-invariant atomic orbitals (GIAOs). A full review of the gauge invariance of SCF wavefunctions has been given by Epstein. 6... 

There exist two main methods for implementing nonlinear optical calculations into a given computational technique coupled methods and uncoupled methods. Coupled methods [sometimes called finite field (FF) or coupled-perturbed Hartree-Fock (CPHF) methods] include the effect of the perturbing field into the Hamiltonian. The energy (e) of the system in the field E... 

An extensive study of the BH molecule has been presented by Ingamells et a/.107 The static a, / and tensors are computed by finite field and perturbation methods using Hartree-Fock, MP2, MP4 (including single, double, triple and quadruple substitutions), the Brueckner variant of the CCSD(T) method and DFT with the B3LYP functional. Contributions from vibration at MP2 level and rotation at Hartree-Fock level are calculated. The frequency dependence of the vibrational contribution is analysed. 

N(C2H2)bNH2 with respect to the number of units n. The DFT (LC-BOP, BOP, and B3LYP) results were obtained by the coupled-pertuibed Kohn-Sham method (see Sect. 4.7), the HF result was given by the coupled-perturbed Hartree-Fock method, and the ab initio results were provided by the finite-field method (see Sect. 4.7). The aug-cc-pVDZ basis functions tire used. See Kamiya et al. (2005)... 

Wavefunction derivatives involved in Eq. [12] and [17] comprise the major part of the evaluations of AATs. In earlier days, a finite difference method was used to obtain these derivatives. The implementation of analytical coupled perturbed Hartree-Fock (CPHF) methods 3- 6 has permitted these derivatives to be obtained more efficiently. In the MFP approach, two sets of CPHF calculations are required to obtain re-... 

Maroulis and Haskopoulos calculated the interaction electric dipole moment and polarizability for the C02-Rg systems, Rg = He, Ne, Ar, Kr and Xe. The potential minimum is very well defined for all these systems. In Fig. 19 is shown the potential energy surface for the C02-He interaction calculated at the MP2 level of theory. The most stable configuration corresponds to a T-shaped structure. The two local minima for the linear configuration of C02-He are also clearly visible. All interaction induced properties were extracted from finite-filed Moller-Plesset perturbation theory and coupled-cluster calculations with purpose-oriented basis sets. CCSD(T) values were calculated for the dipole moment pim of C02-He and C02-Ne the corresponding results are 0.0063 and 0.0107 eao, respectively. All post-Hartree-Fock methods yield stable values for this important property. For C02-He, = 0.0070 (SCF), 0.0063 (MP2), 0.0063 (MP4),... 

With ab initio methods there are two distinct approaches to calculating time dependent properties. One is the analytic derivative approach, where explicit expressions are obtained for the derivatives of the dipole moment or of the pseudoenergy. The other approach, known as response theory calculates the response function directly by time dependent perturbation theory. In general finite field methods are not applicable for dynamit properties except that, e.g., j8(ru 0, ru) could be calculated by the finite difference of a ay,a)) calculated at two different field strengths. Consider first methods based on Hartree-Fock theory, known collectively as TDHF. 

In principle, density functional theory calculations should be able to give answers that are more reliable than Hartree-Fock but at similar cost. Static a and can be calculated by finite field methods or by coupled perturbed Kohn-Sham theory (CPKS) and give answers that are broadly comparable with MP2. In 1986 Sennatore and Subbaswamy did some calculations of the dynamic polarizability and second hyperpolarizability of rare gas atoms, but there have been no calculations of frequency dependent polarizabilities or hyperpolarizabilities of molecules until very recently. 

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