Explicitly correlated second-order

Klopper, W., Samson, C.C.M. Explicitly correlated second-order Moller-Plesset methods with auxiliary basis sets. J. Chem. Phys. 2002,116, 6397-410. 

Ten-no, S. Explicitly correlated second order perturbation theory introduction of a rational generator and numerical quadratures. J. Chem. Phys. 2004, 121, 117-29. 

Werner, H.-J. Eliminating the domain error in local explicitly correlated second-order Moller-Plesset perturbation theory. J. Chem. Phys. 2008, 129, 101103. 

MP2-F12 Explicitly correlated second order Mpller-Plesset perturbation theory... 

Werner HJ, Manby ER (2006) Explicitly correlated second-order perturbation theory using density fitting and local approximations. J Chem Phys 124 12... 

MNDOC has the same functional form as MNDO, however, electron correlation is explicitly calculated by second-order perturbation theory. The derivation of the MNDOC parameters is done by fitting the correlated MNDOC results to experimental data. Electron correlation in MNDO is only included implicitly via the parameters, from fitting to experimental results. Since the training set only includes ground-state stable molecules, MNDO has problems treating systems where the importance of electron comelation is substantially different from normal molecules. MNDOC consequently performs significantly better for systems where this is not the case, such as transition structures and excited states. 

A new treatment for S = 7/2 systems has been undertaken by Rast and coworkers [78, 79]. They assume that in complexes with ligands like DTPA, the crystal field symmetry for Gd3+ produces a static ZFS, and construct a spin Hamiltonian that explicitly considers the random rotational motion of the molecular complex. They identify a magnitude for this static ZFS, called a2, and a correlation time for the rotational motion, called rr. They also construct a dynamic or transient ZFS with a simple correlation function of the form (BT)2 e t/TV. Analyzing the two Hamiltonians (Rast s and HL), it can be shown that at the level of second order, Rast s parameter a2 is exactly equivalent to the parameter A. The method has been applied to the analysis of the frequency dependence of the line width (ABpp) of GdDTPA. These results are compared to a HL treatment by Clarkson et al. in Table 2. 

Bukowski R, Jeziorski B, Szalewicz K (1996) Basis set superposition problem in interaction energy calculations with explicitly correlated bases saturated second- and third-order energies for He2. J Chem Phys 104 3306-3319... 

MNDOC has the same functional form as MNDO, however, electron correlation is explicitly calculated by second-order perturbation theory. The derivation of the MNDQC... 

C. Density functional theory Density functional theory (DFT) is the third alternative quantum mechanics method for obtaining chemical structures and their associated energies.Unlike the other two approaches, however, DFT avoids working with the many-electron wavefunction. DFT focuses on the direct use of electron densities P(r), which are included in the fundamental mathematical formulations, the Kohn-Sham equations, which define the basis for this method. Unlike Hartree-Fock methods of ab initio theory, DFT explicitly takes electron correlation into account. This means that DFT should give results comparable to the standard ab initio correlation models, such as second order M(j)ller-Plesset (MP2) theory. 

Semi-empirical MO methods address electron correlation implicitly they simply adjust parameters until the calculations give the correct answer compared with experiment. EHT does not address electron correlation at all, so quantitative results from such calculations are almost always wrong unless fortuitous. There are, however, several approaches to explicitly account for electron correlation. One approach is to perform post-ab initio (post-H-F) calculations that in effect mix different electronic configurations involving the ground state and several excited states of the molecule. Such calculations are quite computationally intensive and can be performed only on relatively small molecules. Two commonly-seen acronyms associated with the post H-F approach to electron correlation are MP2 and Cl, which stand for Mpller-Plesset theory at the level of second-order and configuration interaction, respectively. 

We present a theoretical formulation of van der Waals (VdW) molecule-substrate attraction in which the second order vdW energy is explicitly exhibited as a correlation/self-energy of the molecular/atomic electrons generated by a dynamic nonlocal image potential due to polarization of... 

Values for many of the parameters in Heff cannot be determined from a spectrum, regardless of the quality or quantity of the spectroscopic data, because of correlation effects. When two parameters enter into the effective Hamiltonian with identical functional forms, only their sum can be determined empirically. Sometimes it is possible to calculate, either ab initio or semiempirically, the value of one second-order parameter, thereby permitting the other correlated parameter to be evaluated from the spectrum. Often, although the parameter definition specifies a summation over an infinite number of states, the largest part or the explicitly vibration-dependent part of the parameter may be evaluated from an empirically determined electronic matrix element times a sum over calculable vibrational matrix elements and energy denominators (Wicke, et al, 1972). 

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