Many-body perturbation theory calculations

G. Maroulis and A. J. Thakkar, J. Chem. Phys., 88, 7623 (1988). Multipole Moments, Polarizabilities and Hyperpolarizabilities for N2 from Fourth-Order Many-Body Perturbation Theory Calculations. [Erratum, ibid., 89, 6558 (1988). 

The Mpller-Plesset (MP) treatment of electron correlation [84] is based on perturbation theory, a very general approach used in physics to treat complex systems [85] this particular approach was described by M0ller and Plesset in 1934 [86] and developed into a practical molecular computational method by Binkley and Pople [87] in 1975. The basic idea behind perturbation theory is that if we know how to treat a simple (often idealized) system then a more complex (and often more realistic) version of this system, if it is not too different, can be treated mathematically as an altered (perturbed) version of the simple one. Mpller-Plesset calculations are denoted as MP, MPPT (M0ller-Plesset perturbation theory) or MBPT (many-body perturbation theory) calculations. The derivation of the Mpller-Plesset method [88] is somewhat involved, and only the flavor of the approach will be given here. There is a hierarchy of MP energy levels MPO, MP1 (these first two designations are not actually used), MP2, etc., which successively account more thoroughly for interelectronic repulsion. 

The text books, encyclopedias and handbooks listed in the previous section are complemented by the computer software and hardware through which practical schemes of computation are realized. In this section, we consider the computer software for carrying out molecular many-body perturbation theory calculations. The computer hardware appropriate for such calculations is considered in section 3.7. 

In this section, we restrict our attention to the available computer software for carrying out many-body perturbation theory calculations for molecular systems. 

The first published quantum chemical code for carrying out molecular many-body perturbation theory calculations was due to D. M. Silverand the present author.The package, which was originally published in Computer Physics Communications in 1978, was written in fortran code for an ibm 360/91 computer. The Computer Physics Communication library numbersU are ... 

M. Kollwitz, M. Haser, and J. Gauss,/. Chem. Phys., 108, 8295 (1998). Non-Abelian Point Group Symmetry in Direct Second-Order Many-Body Perturbation Theory Calculations of NMR Chemical Shifts. 

S. Wilson and D. Moncrieff, On the accuracy of the algebraic approximation in molecular electronic structure calculations. VI. Matrix Hartree-Fock and Many-Body Perturbation Theory Calculations for the Ground State of the Water Molecule, preprint... 

Early non-relativistic many-body perturbation theory studies of correlation energies in molecules established that the error associated with truncation of the finite basis set is most often much more significant than that resulting from truncation of the perturbation expansion.15 The chosen basis set is required to support not only an accurate description of the occupied Hartree-Fock orbitals but also a representation of the virtual spectrum. Over the past twenty years significant progress has been reported on the systematic design of basis sets for electron correlation studies in general and many-body perturbation theory calculations in particular.18... 

In Table 2, the results of Hartree-Fock/Many-Body Perturbation Theory calculations for the argon atom are compared with two relativistic calculations the first using a Dirac-Hartree-Fock-Coulomb reference and the second using a Dirac-Hartree-Fock-Breit independent particle model. 

Table 2 Relativistic and non-relativistic finite basis set many-body perturbation theory calculations for the argon ground state within the no virtual pair approximation...

Universal Basis Sets and Direct ccMBPT. - Early many-body perturbation theory calculations carried out within the algebraic approximation quickly led to the realization that basis set truncation is the dominant source of error in correlation studies seeking high precision when carried out with respect to an apprpriately chosen reference function. In more recent years, the importance of basis set truncation error control has been more widely recognized. We have described the concept of the universal basis set in Section 2.4.4 which provides a general approach to basis set truncation error reduction. 

In this paper, the systematic truncation of a distributed universal even-tempered basis set capable of supporting high precision in both mauix Haitree-Fock and second order many-body perturbation theory calculations is explored using the ground state of the boron fluoride molecule as a prototype. The truncation procedure adopted is based on the magnitude of the orbital expansion coefficients associated with a given basis function in each of the occupied orbitals. 

Diagrammatic many-body perturbation theory calculations of the correlation energy of various diatomic molecules in their ground states using universal basis sets of even-tempered exponential-type functions. Comparison with other approaches. ... 

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.

When developing the large basis sets which are required for the reliable calculation of van der Waals interactions, it is important to ensure that the basis set be constructed and extended in a systematic fashion. In recent work, Wells and Wilson have employed systematic sequences of even-tempered basis sets of Gaussian-type functions in conjunction with many-body perturbation theory calculations to study van der Waals interaction potentials, thereby ensuring basis set superposition errors and size-inconsistency problems are controlled. They used the Boys-Bernardi procedure as a test for the magnitude of the basis set superposition error rather than as a correction. 

Y. Ishikawa, H. M. Quiney. Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave equations. Phys. Rev. A, 47 (1993) 1732-1739. 

G. Maroulis, Electric dipole hyperpolarizability and quadrupole polarizability of methane from finite-field coupled cluster and fourth-order many-body perturbation theory calculations. Chem. Phys. Lett. 226(3 ), 420-426 (1994)... 

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