Written by two leading experts in the field, this book explores the 'many-body' methods that have become the dominant approach in determining molecular structure, properties and interactions. With a tight focus on the highly popular Many-Body Perturbation Theory (MBPT) and Coupled-Cluster theories (CC), the authors present a simple, clear, unified approach to describe the mathematical tools and diagrammatic techniques employed. Using this book the reader will be able to understand, derive and confidently implement relevant algebraic equations for current and even new multi-reference CC methods. Hundreds of diagrams throughout the book enhance reader understanding through visualization of computational procedures and extensive referencing allows further exploration of this evolving area. With an extensive bibliography and detailed index, this book will be suitable for graduates and researchers within quantum chemistry, chemical physics and atomic, molecular and solid-state physics.

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The equations of the coupled-pair many-electron theory (CPMET) are extended to incorporate the effect of both unlinked and linked triexcited clusters. The minimal basis correlation energy of the BHS molecule in the ground state is calculated using the ordinary as well as extended CPMET in various degrees of approximation, and the relative importance of linked and unlinked triexcited clusters is studied. The results afford an unambiguous conclusion for closed-shell systems that, in contrast to the situation with tetraexcited states, unlinked triexcited clusters are negligible relative to the linked ones. It is shown that the extended CPMET reproduces the full configuration-interaction results to a very high degree of accuracy.

The COLUMBUS program system is a collection of Fortran programs for performing general multireference single-and double-excitation configuration interaction (MRSLICI) wave function optimization based on the graphical unitary group approach. The program system also includes integral generation, SCF and MCSCF orbital optimization, integral transformation, and wave function analysis programs. The original program system was written in 1980 to 1981. Since that time, it has evolved into one of the most popular MRSDCI program systems used in the computational chemistry community. The discussion of this evolution will include the exploitation of efficient matrix-matrix and matrix-vector product computational kernels, the use of generally contracted symmetry-adapted orbital basis sets, general Hamiltonian diagonalization procedures, energy-based internal walk selection, flexible DRT specification, improved coupling-coefficient evaluation methods, coupled-pair functional and multireference CPF capabilities, and density matrix construction. The numerous versions of the program system that are maintained at different sites and on different computers are now in the process of being merged. The source code for this combined version will be made available to the computational chemistry community. The source code for a specific computer may be generated from the source code for another computer by a single pass through a simple filter utility that is included with the program system. The directly supported computers will initially include various models of VAX, Cray, FPS, IBM, CDC, and ETA machines with the addition of other machines shortly thereafter. The ongoing developments of the COLUMBUS system that are discussed include a new method for computing analytic energy gradients for MRSDCI wave functions. This effective-density-matrix based method avoids the "coupled perturbed MCSCF" solutions for each coordinate direction, avoids the transformation of any derivative-integral quantities from the AO to the MO basis, avoids the transformation of the coupling coefficients from the MO to the AO basis, allows a subset of the MCSCF doubly occupied orbitals to be frozen in the CI wave function, and allows the MRSLXI wave function to be generated from general reference CSFs that are not necessarily related to the MCSCF expansion CSFS.

Analytical potential models are designed for simulations of water with excess protons. The potentials describe both intramolecular and intermolecular interactions, and allow dissociation and formation of the species (H2O)nH+. The potentials are parametrized in the form of interactions between H+ and O2− ions, with additional three-body (H–O–H) interaction terms and self-consistent treatment of the polarizability of the oxygen ions. The screening of electrostatic interactions caused by the overlap of the electron clouds in the real molecules is modeled by functions modifying the electric field at short distances. The model was derived by fitting to the potential surface of the H5O2+ ion and other species, as obtained from ab initio MP2 calculations employing an extensive basis set. Emphasis was put on modeling the potential-energy surface for the proton-transfer reaction. Potential-surface profiles, geometry-optimized structures and formation energies of H5O2+, protonated water clusters [H+(H2O)n, n=2–4] and water clusters [(H2O)n, n=1–6] using these potentials are presented and compared to results using quantum-chemical calculations. The potential models can well reproduce ab initio results for the H5O2+ ion, and can provide formation energies and structures of both protonated-water and water-only clusters that agree favorably with ab initio MP2 calculations.

Three forms of quasidegenerate perturbation theory are discussed and compared in terms of a common general formulation based on a similarity transformation which decouples the model space and complementary space components of the Hamiltonian. The discussion is limited to formal, rather than many-body (diagrammatic), aspects. Particular attention is focused on a ’’canonical’’ form of van Vleck perturbation theory, for which new and highly compact formulas are obtained. Detailed comparisons are made with the Kirtman–Certain–Hirschfelder form of the van Vleck approach and with the approach based on intermediate normalization which has been used as the basis for most of the diagrammatic formulations of quasidegenerate perturbation theory.

The COLUMBUS Program System allows high-level quantum chemical calculations based on the multiconfiguration self-consistent field, multireference configuration interaction with singles and doubles, and the multireference averaged quadratic coupled cluster methods. The latter method includes size-consistency corrections at the multireference level. Nonrelativistic (NR) and spin-orbit calculations are available within multireference configuration interaction (MRCI). A prominent feature of COLUMBUS is the availability of analytic energy gradients and nonadiabatic coupling vectors for NR MRCI. This feature allows efficient optimization of stationary points and surface crossings (minima on the crossing seam). Typical applications are systematic surveys of energy surfaces in ground and excited states including bond breaking. Wave functions of practically any sophistication can be constructed limited primarily by the size of the CI expansion rather than by its complexity. A massively parallel CI step allows state-of-the art calculations with up to several billion configurations. Electrostatic embedding of point charges into the molecular Hamiltonian gives access to quantum mechanical/molecular mechanics calculations for all wave functions available in COLUMBUS. The analytic gradient modules allow on-the-fly nonadiabatic photodynamical simulations of interesting chemical and biological problems. Thus, COLUMBUS provides a wide range of highly sophisticated tools with which a large variety of interesting quantum chemical problems can be studied. C 2011 John

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