Mpller-Plesset second-order perturbation electron correlation

Specifies the calculation of electron correlation energy using the Mpller-Plesset second order perturbation theory (MP2). This option can only be applied to Single Point calculations. 

We have above discussed the CASSCF method and how we can choose the active space. We noted that this choice was closely connected to the method we use to compute the effects of dynamic correlation, in this case the CASPT2 method. The development of this approach was inspired by the success of the Mpller-Plesset second order perturbation theory (MP2), which has been used for a long time to treat electron correlation for ground states, where the reference function is a single determinant. It was assumed that such an approach would be even more effective with the more accurate CASSCF reference function. A first attempt was made soon... 

Chalasinski and Szczesniak have provided a means of decomposing the correlation contribution to the interaction energy into four separate terms. Their philosophy takes the electron exchange operator as a second perturbation in the spirit of many-body perturbation theory, with molecular interaction as the first perturbation in their intermolecular Mpller-Plesset perturbation theory (IMPPT). At the level of second order of the correlation operator, they obtain a number of separate terms. The first is the dispersion energy, e... 

MC approaches [30] involve the optimization of molecular orbitals within a restricted subspace of electronic occupations provided such active space is appropriately chosen, they allow for an accurate description of static electron correlation effects. Dynamical correlation effects can also be introduced either at the perturbation theory level [complete active space with second-order perturbation theory (CASPT2), and multireference Mpller-Plesset (MR-MP2) methods] [31] or via configuration interaction (MR-CI). 

There is also a hierarchy of electron correlation procedures. The Hartree-Fock (HF) approximation neglects correlation of electrons with antiparallel spins. Increasing levels of accuracy of electron correlation treatment are achieved by Mpller-Plesset perturbation theory truncated at the second (MP2), third (MP3), or fourth (MP4) order. Further inclusion of electron correlation is achieved by methods such as quadratic configuration interaction with single, double, and (perturbatively calculated) triple excitations [QCISD(T)], and by the analogous coupled cluster theory [CCSD(T)] [8],... 

Prior to stretching C-S bond, we optimized the geometry of the anionic Me-S-Me molecule and parent neutral molecule at the unrestricted second-order Mpller-Plesset (UMP2) perturbation level of theory (in order to take into account the effect of electron correlation) with aug-cc-pVDZ basis sets [9]. We also... 

In ab initio methods the HER approximation is used for build-up of initial estimate for and which have to be further improved by methods of configurational interaction in the complete active space (CAS) [39], or by Mpller-Plesset perturbation theory (MPn) of order n, or by the coupled clusters [40,41] methods. In fact, any reasonable result within the ab initio QC requires at least minimal involvement of electron correlation. All the technical tricks invented to go beyond the HFR calculation scheme in terms of different forms of the trial wave function or various perturbative procedures represent in fact attempts to estimate somehow the second term of Eq. (5) - the cumulant % of the two-particle density matrix. 

In this section, we briefly discuss some of the electronic structure methods which have been used in the calculations of the PE functions which are discussed in the following sections. There are variety of ab initio electronic structure methods which can be used for the calculation of the PE surface of the electronic ground state. Most widely used are Hartree-Fock (HF) based methods. In this approach, the electronic wavefunction of a closed-shell system is described by a determinant composed of restricted one-electron spin orbitals. The unrestricted HF (UHF) method can handle also open-shell electronic systems. The limitation of HF based methods is that they do not account for electron correlation effects. For the electronic ground state of closed-shell systems, electron correlation effects can be accounted for relatively easily by second-order Mpller-Plesset perturbation theory (MP2). In modern implementations of MP2, linear scaling with the size of the system has been achieved. It is thus possible to treat quite large molecules and clusters at this level of theory. 

The first such method has been explored by Foresman et al. [1], who have called the method CIS-MP2 as it adds electron correlation effects to CIS in a similar way as the second-order Mpller-Plesset perturbation (MP2) theory [56] does in the ground state. The MP2 correlation correction to the HF total energy is evaluated by using the formula... 

SM calculations are broadly based on either the (i) Hartree-Fock method (ii) Post-Hartree-Fock methods like the Mpller-Plesset level of theory (MP), configuration interaction (Cl), complete active space self-consistent field (CASSCF), coupled cluster singles and doubles (CCSD) or (iii) methods based on DFT [24-27]. Since the inclusion of electron correlation is vital to obtain an accurate description of nearly all the calculated properties, it is desirable that SM calculations are carried out at either the second-order Mpller-Plesset (MP2) or the coupled cluster with single, double, and perturbative triple substitutions (CCSD(T)) levels using basis sets composed of both diffuse and polarization functions. 

Several post-HF models have been developed to give more accurate results based on better treatment of electron correlation. Mpller-Plesset (MP) models include an approximation of electron correlation by adding further terms to the HF approach. The first-order solution calculates ground and excited states separately without interacting as in HF methods but the addition of second- and higher-order terms introduces perturbation. The second-order calculation, or MP2, therefore explicitly includes electron-electron interactions through the effects of electron promotion. ... 

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