Wavefunction perturbation methods

The idea of coupling variational and perturbational methods is nowadays gaining wider and wider acceptance in the quantum chemistry community. The background philosophy is to realize the best blend of a well-defined theoretical plateau provided by the application of the variational principle coupled to the computational efficiency of the perturbation techniques. [29-34]. In that sense, the aim of these approaches is to improve a limited Configuration Interaction (Cl) wavefunction by a perturbation treatment. 

However, if this is not the case, the perturbations are large and perturbation theory is no longer appropriate. In other words, perturbation methods based on single-determinant wavefunctions cannot be used to recover non-dynamic correlation effects in cases where more than one configuration is needed to obtain a reasonable approximation to the true many-electron wavefunction. This represents a serious impediment to the calculation of well-correlated wavefunctions for excited states which is only possible by means of cumbersome and computationally expensive multi-reference Cl methods. 

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... 

Nice introduction to the basics of quantum chemistry, then a focus on semiem-pirical calculations and perturbation methods. Although published more than 40 years ago, the fundamentals, like the Schrodinger equation and wavefunctions, remain true, and the engagingly assertive style of the doyen of modem semiempiri-cal methods makes this book worth reading. 

Such second-order molecular properties as spin-spin coupling depend upon distortion of electron clouds by additional external perturbations that is, in the NMR experiment they depend upon the electronic motion induced by an applied magnetic field. Theories for such second-order molecular properties require a study of the change in the molecular-orbital wavefunctions, which may be found by using a perturbation method to describe the effects occurring when a magnetic field is applied.8-1065-67... 

Linear electric polarizabilities of atoms and polarizability anisotropies of molecules have been rather extensively evaluated by using more or less approximate wavefunctions and various perturbation methods. Note-... 

The connection with the perturbation method may be made by assuming the exact eigenfunctions //q and ij/o to be available. Using ji/iI/qiPo as a zeroth-order dimer wavefunction the dimer energy is obtained as... 

Ab initio MP2/6-311++G(d,p) calculations were performed to obtain geometries and electron densities. The perturbative MP2 approach is one of the wavefunction-based methods most frequently used to include electron correlation and its well-gained reputation needs no further comments. The basis set... 

Our multireference M0Uer-Plesset (MRMP) perturbation method [1-4] and MC-QDPT quasi-degenerate perturbation theory (QDPT) with multiconfiguration self-consistent field reference functions (MC-QDPT) [5,6] are perturbation methods of such a type. Using these perturbation methods, we have clarified electronic stmctures of various systems and demonstrated that they are powerful tools for investigating excitation spectra and potential energy surfaces of chemical reactions [7-10]. In the present section, we review these multireference perturbation methods as well as a method for interpreting the electronic structure in terms of valence-bond resonance structure based on the CASSCF wavefunction. 

The MRMP method [1-4] and MC-QDPT [5,6] are perturbation methods in this category. In these methods, the CASSCF wavefiinction(s) is(are) first determined, and the perturbation calculation is done with those wavefunctions used as reference (zeroth-order wavefiinction) based on Rayleigh-Schrodinger PT in MRMP and van Vleck PT in MC-QDPT. 

To demonstrate how such perturbative methods lead to so-callcd direct Cl techniques, let us consider a simple application of Eqs. (2.109) and (2.110) to a Cl wavefunction consisting of a dominant HF configuration I Aih > plus all pair excitations of the form The elements of... 

How does dynamical correlation stabilize electronic states This is explained by considering the energy of the M0ller-Plesset perturbation method, which is a perturbation method based on the Hartree-Fock wavefunction (McWeeny 1992). In this method, by assuming the sum of the Fock operators as the nonperturbative operator, the Hamiltonian is defined as... 

Within the so-called wavefunction-based methods, Eq. (5) is most often solved by first approximating Wg as a single Slater determinant. Thereby correlation effects are by definition ignored. (Parts of) these may, however, be added subsequently either directly or via perturbation theory. The N single-particle functions 0i, 02, , of the Slater determinant are calculated by solving the Hartree-Fock single-particle equations... 

The various EDA techniques discussed so far were based on the variational principle. Another route to partition the INT is by employing the perturbation method. " Among the various perturbational tools used to analyze the individual energy components contributing to the stabilization of intermolecular complexes, many-body SAPT has received widespread attention.Jeziorski et al. have reviewed various aspects of wavefunction-based SAPT theory. 

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