Ab initioquantum chemistry: Methodology and applications

Abstract

This Perspective provides an overview of state-of-the-art ab initio quantum chemical methodology and applications. The methods that are discussed include coupled cluster theory, localized second-order Moller-Plesset perturbation theory, multireference perturbation approaches, and density functional theory. The accuracy of each approach for key chemical properties is summarized, and the computational performance is analyzed, emphasizing significant advances in algorithms and implementation over the past decade. Incorporation of a condensed-phase environment by means of mixed quantum mechanical͞molecular mechanics or self-consistent reaction field techniques, is presented. A wide range of illustrative applications, focusing on materials science and biology, are discussed briefly.coupled cluster ͉ density functional theory ͉ second-order Modler-Plesser perturbation theory ͉ mixed quantum͞molecular mechanics O ver the past three decades, ab initio quantum chemistry has become an essential tool in the study of atoms and molecules and, increasingly, in modeling complex systems such as those arising in biology and materials science. The underlying core technology is computational solution of the electronic Schrodinger equation; given the positions of a collection of atomic nuclei, and the total number of electrons in the system, calculate the electronic energy, electron density, and other properties by means of a well defined, automated approximation (a ''model chemistry''). The ability to obtain ''goodenough'' solutions to the electronic Schrodinger equation for systems containing tens, or even hundreds, of atoms has revolutionized the ability of theoretical chemistry to address important problems in a wide range of disciplines; the Nobel Prize awarded to John Pople and Walter Kohn in 1998 is a reflection of this observation.In its exact form, the electronic Schrodinger equation is a many-body problem, whose computational complexity grows exponentially with the number of electrons, and hence, a brute force solution is intractable. Hartree-Fock theory, a mean field approach, produces reasonable results for many properties but is incapable of providing a robust description of reactive chemical events in which electron correlation has a major role. Thus, a key problem has been the development of treatments of electron correlation that exhibit a tractable scaling in computational effort with the size of the system. The considerable progress that has been made along these lines is outlined below.Given a well defined theoretical framework of approximation, the next requirement is efficient computational implementation. Considerable sophistication is required to achieve acceptable accuracy and efficiency; the leading quantum chemistry programs are millions of lines of computer code, and mathematical algorithms to reduce formal scaling of computational effort with system size have an increasingly crucial role in meeting the challenge of handling complex system relevant to practical applications. Below, the most important comp...

Theoretical studies on bimolecular reaction dynamics

“…Thus a potential energy surface is first calculated by solving the Schrödinger equation for the electrons with fixed positions of the nuclei. For reliable predictions, these electronic structure computations normally have to be done by using the most accurate ab initio methods that allow for electron correlation so that the crucial transition-state region of the reaction is described accurately (4). Once the potential energy surface is calculated and fitted to a suitable functional form then, in the most accurate quantum dynamics theory, the timeindependent or time-dependent Schröd-inger equation is solved for the nuclei by using quantum scattering theory.…”

Finite-temperature second-order many-body perturbation theory revisited

“…In practice, perturbation theory is most powerful when a low-order expansion suffices. The most widely used post-Hartree-Fock method for the ground-state energy of an interacting many-electron system is second-order Møller-Plesset perturbation theory (MP2) [6,7,8,9], which is second-order time-independent perturbation theory for nondegenerate states, employing anĤ 0 that equals the ground-state Fock operator [10] assuming a closed-shell system. MP2 works best when the ground-state Hartree-Fock HOMO-LUMO gap is, in some sense, not too small; MP2 diverges when the HOMO-LUMO gap vanishes [11,12,13].…”

Generalization of Dielectric-Dependent Hybrid Functionals to Finite Systems

“…We used the latter code to solve the TDDFT equations in the adiabatic approximation, where the exchange-correlation potential was described by the functional of Eq. (10). We note that the evaluation of empty electronic states is not necessary in TDDFT calculations, when following the procedure of Ref.…”

“…In the case of molecules, methods adopted for their optoelectronic properties include ab initio quantum chemistry (QC) techniques [7][8][9][10] and hybrid density functionals [11][12][13][14]. While QC and MBPT methods have proven accurate for several classes of molecules and solids [15,16], they remain computationally more demanding than DFT-based techniques; they are limited to smaller-sized systems, and they have rarely been applied in conjunction with ab initio molecular dynamics or Monte Carlo simulations.…”