Martin Head-Gordon

A fifth-order perturbation comparison of electron correlation theories

Abstract Electron correlation theories such as configuration interaction (CI), coupled-cluster theory (CC), and quadratic configuration interaction (QCI) are assessed by means of a Moller-Plesset perturbation expansion of the correlation energy up to fifth order. The computational efficiencies and relative merits of the different techniques are outlined. A new augmented version of coupled-cluster theory, denoted as CCSD(T), is proposed to remedy some of the deficiencies of previous augmented coupled-cluster models.

Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections

We report re-optimization of a recently proposed long-range corrected (LC) hybrid density functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, omegaB97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent systems, omegaB97X-D shows slight improvement over other empirical dispersion-corrected density functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as omegaB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.

Quadratic configuration interaction. A general technique for determining electron correlation energies

A general procedure is introduced for calculation of the electron correlation energy, starting from a single Hartree–Fock determinant. The normal equations of (linear) configuration interaction theory are modified by introducing new terms which are quadratic in the configuration coefficients and which ensure size consistency in the resulting total energy. When used in the truncated configuration space of single and double substitutions, the method, termed QCISD, leads to a tractable set of quadratic equations. The relation of this method to coupled‐cluster (CCSD) theory is discussed. A simplified method of adding corrections for triple substitutions is outlined, leading to a method termed QCISD(T). Both of these new procedures are tested (and compared with other procedures) by application to some small systems for which full configuration interaction results are available.

MP2 energy evaluation by direct methods

Abstract An efficient algorithm is presented for evaluating the second-order Moller-Plesset (MP2) energy directly from two-electron integrals in the atomic orbital basis, i.e. the integrals are not stored. The floating point operation count and memory requirements are analyzed, and illustrative calculations are presented. This direct MP2 method should be useful for large molecule calculations, where, due to storage limitations, conventional disk-based MP2 procedures are often not feasible.

Gaussian‐1 theory: A general procedure for prediction of molecular energies

A general procedure is developed for the computation of the total energies of molecules at their equilibrium geometries. Ab initio molecular orbital theory is used to calculate electronic energies by a composite method, utilizing large basis sets (including diffuse‐sp, double‐d and f‐polarization functions) and treating electron correlation by Mo/ller–Plesset perturbation theory and by quadratic configuration interaction. The theory is also used to compute zero‐point vibrational energy corrections. Total atomization energies for a set of 31 molecules are found to agree with experimental thermochemical data to an accuracy greater than 2 kcal mol−1 in most cases. Similar agreement is achieved for ionization energies, electron and proton affinities. Residual errors are assessed for the total energies of neutral atoms.

A direct MP2 gradient method

Abstract We present a direct method for evaluating the gradient of the second-order Moller-Plesset (MP2) energy without storing any quartic quantities, such as two-electron repulsion integrals (ERIs), double substitution amplitudes or the two-particle density matrix. For an N -basis-function calculation, N 3 memory is required, and the ERIs and their first derivatives are computed up to O (number of occupied orbitals) times, plus additional ERI evaluations to obtain the Hartree-Fock (HF) orbitals and solve the coupled perturbed HF equation. Larger amounts of memory are used to reduce the O evaluations in the MP2 step. The floating point operation count is still proportional to ON 4 , as in conventional MP2 gradient codes since ERI evaluation is just an N 4 step. Illustrative calculations are reported to assess the performance of the algorithm.

Semi-direct algorithms for the MP2 energy and gradient

Abstract The cost (via the number of two-electron integral evaluations) and the maximum size of a direct second-order Mooller-Plesset (MP2) energy or gradient calculation are both determined by the available computer memory. Therefore we formulate semi-direct MP2 methods that utilize disk space (which is usually much larger than memory size) for the steps that require most storage. In terms of the molecular basis set size, they require as little as quadratic memory and cubic disk. The amount of input/output transfer between memory and disk is quartic plus the cost of transpositions, which is between quartic and quintic. A variety of calculations are presented comparing the fully direct, semi-direct and conventional algorithms. The semi-direct methods are shown to be superior to conventional algorithms despite requiring less disk space, and are also often preferred over the direct methods.

Time-dependent density functional theory within the Tamm–Dancoff approximation

Abstract A computationally simple method for molecular excited states, namely, the Tamm–Dancoff approximation to time-dependent density functional theory, is proposed and implemented. This method yields excitation energies for several closed- and open-shell molecules that are essentially of the same quality as those obtained from time-dependent density functional theory itself, when the same exchange-correlation functional is used.

Current Status of the AMOEBA Polarizable Force Field

Molecular force fields have been approaching a generational transition over the past several years, moving away from well-established and well-tuned, but intrinsically limited, fixed point charge models toward more intricate and expensive polarizable models that should allow more accurate description of molecular properties. The recently introduced AMOEBA force field is a leading publicly available example of this next generation of theoretical model, but to date, it has only received relatively limited validation, which we address here. We show that the AMOEBA force field is in fact a significant improvement over fixed charge models for small molecule structural and thermodynamic observables in particular, although further fine-tuning is necessary to describe solvation free energies of drug-like small molecules, dynamical properties away from ambient conditions, and possible improvements in aromatic interactions. State of the art electronic structure calculations reveal generally very good agreement with AMOEBA for demanding problems such as relative conformational energies of the alanine tetrapeptide and isomers of water sulfate complexes. AMOEBA is shown to be especially successful on protein-ligand binding and computational X-ray crystallography where polarization and accurate electrostatics are critical.

Analytic MP2 frequencies without fifth-order storage. Theory and application to bifurcated hydrogen bonds in the water hexamer

Abstract An obstacle to obtaining vibrational frequencies of large molecules via second-order Moller—Plesset (MP2) theory has been the need to store transformed electron repulsion integral derivatives in the molecular orbital (MO) basis. A semi-direct algorithm for eliminating this fifth-order storage is described in which small batches of MO integral derivatives are made at a time, their contributions to the MP2 second derivatives are evaluated, and then they are discarded. No extra computation is required. We locate and characterize a transition structure of the water hexamer cluster which exhibits a bifurcated hydrogen bond structure, at the MP2/6–31 + G* level of theory.