M0ller-Plesset perturbation theory wavefunction

In the BAC-MP4 method, an additional error in determining heats of formation occurs for open-shell molecules. This error arises from the use of the unrestricted Hartree-Fock (UHF) wavefunction in calculating the M0ller-Plesset perturbation theory energy. We include a BAC spin correction energy term, Ebac (Spin), given by... 

The M0ller-Plesset perturbation theory [26] corresponds to the application of the stationary perturbation theory to the calculation of the correlation energy using the Hartree-Fock Slater determinant as the zeroth order wavefunction. These methods are denoted MPn where n is the order of the perturbative corrections included. In the M0ller-Plesset method, the unperturbed Hamiltonian operator is chosen as a sum of Fock operators... 

Field (CASSCF) Second-order Perturbation Theory (CAS-PT2) Configuration Interaction Core-Valence Correlation Effects Coupled-cluster Theory Experimental Data Evaluation and Quality Control G2 Theory Heats of Formation Isoelectronic Isogyric Reactions M0ller-Plesset Perturbation Theory Numerical Hartree-Fock Methods for Molecules r 12-Dependent Wavefunctions Relativistic Theory and Applications Spectroscopy Computational Methods Spin Contamination Transition Metals Applications,... 

AMI Basis Sets Correlation Consistent Sets Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Coupled-cluster Theory Density Functional Theory (DFT), Hartree-Fock (HF) and the Self-consistent Field Diradicals Electronic Wavefunctions Analysis G2 Theory M0ller-Plesset Perturbation Theory Natural Bond Orbital Methods Spin Contamination. 

For second-order many body or M0ller-Plesset perturbation theory (MBPT2 or MP2 see M0ller-Plesset Perturbation Theory), the first-order wavefunction, I l, can be written as... 

The spin projection methods discussed so far apply the projection after the wavefunction has been determined. A second approach is to construct the wavefunction so that there is no spin contamination from the beginning. This leads to methods such as ROHF and restricted open-shell M0ller-Plesset perturbation theory (ROMPn)," and to valence bond, MCSCF, and Cl and MRDCI methods that use spin-adapted configurations. 

In M0ller-Plesset theory, first-order perturbation theory does not improve on the HF energy because the zeroth-order Hamiltonian is not itself the HF Hamiltonian. However, first-order perturbation theory can be useful for estimating energetic effects associated with operators that extend the HF Hamiltonian. Typical examples of such terms include the mass-velocity and one-electron Darwin corrections that arise in relativistic quantum mechanics. It is fairly difficult to self-consistently optimize wavefunctions for systems where these tenns are explicitly included in the Hamiltonian, but an estimate of their energetic contributions may be had from simple first-order perturbation theory, since that energy is computed simply by taking the expectation values of the operators over the much more easily obtained HF wave functions. 

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