Computational Chemistry: Reviews of Current Trends

The following sections are included:

• Preface

• CONTENTS

This article discusses an important problem of multiple solutions of the nonlinear coupled-cluster (CC) equations. The main topics of this work are the interpretation of multiple solutions of the single-reference (SR) CC equations and the relationship between solutions of equations representing different SRCC approximations. The focus is on the SRCC theories involving higher–than–biexcited clusters. Basic mathematical concepts are illustrated by several examples of multiple solutions of SRCC equations resulting from the homotopy calculations. The homotopy method is used to obtain complete sets of solutions of nonlinear SRCC equations involving singles and doubles (CCSD), singles, doubles, and triples (CCSDT), and singles, doubles, triples, and quadruples (CCSDTQ) for a four-electron ab initio molecular system consisting of two hydrogen molecules. Along with the complete CCSD, CCSDT, and CCSDTQ schemes, the quadratic CCSD, CCSDT, and CCSDTQ approximations, and the quadratic configuration-interaction (QCI) method with singles and doubles (QCISD), are considered. The effect of the truncation scheme used to define the cluster operator and the effect of neglecting higher–than–bilinear terms on the structure of solutions of the SRCC equations are investigated in detail. The correspondence between multiple solutions of the CCSD, CCSDT, and full CI equations is established by employing the continuation procedure based on the formalism of β-nested equations. The fundamental theorem is proved that provides a rationale for the observed relationships between multiple solutions characterizing the approximate and the exact CC theories. Various implications of the Fundamental Theorem of the Formalism of β-Nested Equations and several interesting aspects of the formalism of β-nested equations, including the importance of the Fundamental Theorem of the Formalism of β-Nested Equations for new developments in CC theory, are discussed. A new approach to electron correlation in atoms and molecules, termed the method of moments of CC equations (MMCC), which is a direct consequence of the Fundamental Theorem of the Formalism of β-Nested Equations, is described. A hierarchy of MMCC approximations, including the renormalized and completely renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) methods, which can be viewed as generalizations of the well-known CCSD[T], CCSD(T), CCSD(TQ_f), and CCSDT(Q_f) schemes, is introduced. The performance of selected MMCC approaches is illustrated by the results of pilot calculations for the HF molecule.

The computational theory for the time-dependent calculation of the solution of the Schrödinger equation for two electrons is reviewed. A discussion of the time-dependent Hartree-Fock theory and the Dirac-Frenkel variational principle is critiqued, and a new time-dependent exchange, correlation theory is presented. The present work is concerned with the solution of the resultant time-dependent orbital equations in terms of long-time propagators. The development of propagators for the solution of the Schrödinger equation is presently a very active area of research. The need for accurate short-time propagators results from the attempt to model atomic and molecular dynamics in rapidly varying time-dependent fields. Long-time propagators are needed for two basic problems: (1) extraction of eigenvalues and eigenvectors for large systems by time-dependent spectral methods; and (2) reaction dynamics, both for time-independent and time-dependent potentials. Various long-time propagators are reviewed including several polynomial methods. Specifically, the Chebyshev and Hermite polynomial methods, and a new synthetic-cartesian-exponential polynomial propagator, are compared and contrasted. This last method is new and is apparently unique among polynomial propagators since it is unitary and conserves the norm. The discrete variable representation, pseudo-spectral method is discussed as the mechanism of choice for performing the operator mapping.

Roothaan equations have been modified with the aim of avoiding basis set superposition error (BSSE) at the Hartree-Fock level of theory. The resulting scheme, called SCF-MI (Self Consistent Field for Molecular Interactions), underlines its special suitability for the computation of intermolecular interactions. In the present work we report with some details the generalisation of the theory to the case of K interacting fragments. The method provides a complete a priori elimination of the BSSE while taking into account the natural non orthogonality of the MO's of the interacting fragments. Several application examples of the SCF-MI approach are presented and discussed. We mainly concentrate on large van der Waals systems (nucleic acid base pair complexes) and water molecular cluster studies.

Aromatic stacking of nucleic acid bases is one of the key players in determining the structure and dynamics of nucleic acids. The arrangement of nucleic acid bases with extensive overlap of their aromatic rings gave rise to numerous often contradictory suggestions about the physical origins of stacking and the possible role of delocalized electrons in stacked aromatic B systems, leading to some confusion about the issue. The recent advance of computer hardware and software finally allowed the application of state of the art quantum-mechanical approaches with inclusion of electron correlation effects to study aromatic base stacking, now providing an ultimitate qualitative description of the phenomenon. Base stacking is determined by an interplay of the three most commonly encountered molecular interactions: dispersion attraction, electrostatic interaction, and short-range repulsion. Unusual (aromatic-stacking specific) energy contributions were in fact not evidenced and are not necessary to describe stacking. The currently used simple empirical potential form, relying on atom-centered constant point charges and Lennard-Jones van der Waals terms, is entirely able to reproduce the essential features of base stacking. Thus, we can conclude that base stacking is in principle one of the best described interactions in current molecular modeling and it allows to study base stacking in DNA using large-scale classical molecular dynamics simulations. Neglect of cooperativity of stacking and amino group pyramidalization appears to be the most serious approximation of the currently used force field form.

The following sections are included:

• Introduction

• Theory
  • Variational Transition State Theory
  • Multidimensional Semiclassical Tunneling Methods
  • Electronic Structure calculations

• Applications: Kinetics of Proton Transfer in freebase porphyrin
  • Energetics
  • Mechanism
  • Kinetics

• Prospects for protein kinetics

• Conclusions

• Acknowledgments

• Bibliography

Properties of fluoro (F), chloro (Cl) and bromo (Br) substituted methane (CH₄), silane (SiH₄) and germane (GeH₄) are revealed based on results of rigorous ab initio quantum-mechanical calculations at the conventional post-Hartree-Fock second-order perturbation level (MP2 method) and density functional theory with the combined Becke3-LYP exchange-correlation energy functional (DFT(B3LYP method) using the 6-311G(2d,2p)-type basis set. Among discussed properties are molecular parameters (geometries, rotational constants, dipole moments) and vibrational IR spectra (harmonic wavenumbers, absolute intensities). For parent molecules (methane, silane, germane) the results of calculations based on MP2, coupled-cluster CCSD(T) and DFT(B3LYP) methods with the use of 6-311G(2d,2p) and 6-311G(2df,2pd)-type basis sets are presented. The theoretical values are compared with the available experimental data. The effect of substitution H ⇒ F ⇒ Cl ⇒ Br, and C ⇒ Si ⇒ Ge on the change of molecular properties and IR spectra of the species in question are discussed.

The following sections are included:

• INDEX