Third-order many-body perturbation theory

A literate program for third-order many-body perturbation theory ring diagram components... 

M. G. Sheppard and K. F. Freed, Effective valence shell Hamiltonian calculations using third-order quasi-degenerate many-body perturbation theory. J. Chem. Phys. 75, 4507 (1981). 

The following section contains a literate program for evaluating the third order ring energy in many-body perturbation theory. The corresponding web... 

This completes a literate program for evaluating third order ring energies in the many-body perturbation theory expansion for closed-shell systems. 

LITERATE MANY-BODY PERTURBATION THEORY PROGRAMMING THIRD-ORDER RING DIAGRAMS... 

S. Wilson, Literate many-body perturbation theory programming Third-order ring diagrams, this volume. 

Many-body methods, based on the linked-cluster expansion (LCE), were first developed by Brueckner [1] and Goldstone [2] in the 1950s for nuclear physics problems. Perturbation-theory applications to atomic and molecular systems (in a numerical, one-center frame) were pioneered by Kelly [3] in the early 1960s. Basis sets were later introduced, first in second-order [4] and then in third-order [5]. The 1970s saw a proliferation of molecular applications with basis sets, under the names of many-body perturbation theory (MBPT) [6] or the Moller-Plesset method [7]. Nowadays, many-body methods offer some of the most powerful tools in the quantum chemistry arsenal, in particular the coupled-cluster (CC) method, and are available in many widely used quantum chemistry program packages. 

Fig. 5. Magnitude of the basis set truncation error in calculations of electron correlation energies for some closed-shell diatomic molecules. S indicates the calculations performed using smaller ba sets, and L designates calculations with larger basis sets, (i), (ii) and (iii) denote many-body perturbation theory calculations of the correlation energy through second, third and fourth order, respectively.

The first approach is Moller-Plesset (MP) many-body perturbation theory. To the Hartree-Fock wavefunction is added a correction corresponding to exciting two electrons to higher energy Hartree-Fock MOs. Second-order, third-order, and fourth-order corrections to the Hartree-Fock total energy are designated MP2, MP3, and MP4, respectively. For double substitutions, i,j (occupied) into m,n (virtual),... 

The vertical excitation energies for the a A B A, C - X transitions at re = 1.9614 ao (the experimental value for the equilibrium internuclear distance in the NH molecule) were calculated by the many-body perturbation theory of second and third order (H" study) [9]. 

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