Paul E. Maslen

Q-Chem 2.0: A High-Performance Ab Initio Electronic Structure Program Package

Q‐Chem 2.0 is a new release of an electronic structure program package, capable of performing first principles calculations on the ground and excited states of molecules using both density functional theory and wave function‐based methods. A review of the technical features contained within Q‐Chem 2.0 is presented. This article contains brief descriptive discussions of the key physical features of all new algorithms and theoretical models, together with sample calculations that illustrate their performance.

The harmonic frequencies of benzene

Abstract We report calculations for the harmonic frequencies of C6H6 and C6D6. Our most sophisticated quantum chemistry values are obtained with the MP2 method and a TZ2P+f basis set (288 basis functions), which are the largest such calculations reported on benzene to date. Using the SCF density, we also calculate the frequencies using the exchange and correlation expressions of density functional theory. We compare our calculated harmonic frequencies with those deduced from experiment by Goodman, Ozkabak and Thakur. The density functional frequencies appear to be more reliable predictions than the MP2 frequencies and they are obtained at significantly less cost.

Closely approximating second-order Mo/ller–Plesset perturbation theory with a local triatomics in molecules model

A new ansatz for local electron correlation is introduced, which truncates double substitutions subject to a triatomics in molecules (TRIM) criterion. TRIM includes all double substitutions in which one occupied-virtual substitution is atomic while the other substitution can be nonlocal (a cubic number, before cutoffs). With an additional approximation, the TRIM second-order Mo/ller–Plesset perturbation theory (MP2) model can be noniteratively solved; this is the model that is implemented. Results are shown for absolute energies of alkane and polyene chains, rotational barriers of substituted ethylenes and benzenes, and association energies of the water and neon dimers. Over 99.7% of the untruncated MP2 energy is recovered for the test cases, and the relative energies of small systems are in error by less than 0.1 kcal/mol. By contrast, a diatomics in molecules (DIM) truncation recovers about 95% of the full MP2 energy, and yields errors several times larger for relative energies.

Non-iterative local second order Møller–Plesset theory

Abstract Second order Moller–Plesset perturbation theory (MP2) is formulated in terms of atom-centred occupied and virtual orbitals. Both the occupied and the virtual orbitals are non-orthogonal. A new parameter-free atoms-in-molecules local approximation is employed to reduce the cost of the calculation to cubic scaling, and a quasi-canonical two-particle basis is introduced to enable the solution of the local MP2 equations via explicit matrix diagonalisation rather than iteration.

A tensor formulation of many-electron theory in a nonorthogonal single-particle basis

We apply tensor methods to formulate theories of electron correlation in nonorthogonal basis sets. The resulting equations are manifestly invariant to nonorthogonal basis transformations, between functions spanning either the occupied or virtual subspaces of the one-particle Hilbert space. The tensor approach is readily employed in either first or second quantization. As examples, second-order Mo/ller–Plesset perturbation theory, and coupled cluster theory with single and double substitutions, including noniterative triples, are recast using the tensor formalism. This gives equations which are invariant to larger classes of transformations than existing expressions. Procedures for truncating these equations are discussed.

Noniterative local second order Mo/ller–Plesset theory: Convergence with local correlation space

We extend our noniterative local correlation method [P. E. Maslen and M. Head-Gordon, Chem. Phys. Lett., 283, 102 (1998)] by defining a hierarchy of local spaces, ranging from small to large. The accuracy of the local method is then examined as a function of the size of the local space. A medium size local space recovers 98% of the MP2 correlation energy, and reproduces fine details of the potential energy surface such as rotational barriers with an RMS error of 0.2 kcal/mol and a maximum error of 0.4 kcal/mol. A large local space recovers 99.5% of the correlation energy and yields rotational barriers with a RMS error of 0.05 kcal/mol and a maximum error of 0.1 kcal/mol, at significantly increased computational cost.

An accurate local model for triple substitutions in fourth order Møller–Plesset theory and in perturbative corrections to singles and doubles coupled cluster methods

Abstract Two noniterative local models for evaluating the contribution of triple substitutions to the electron correlation energy (as needed in MP4 and CCSD(T)), are developed. The occupied space is spanned by a minimal basis, and the virtual space by an extended basis of atom-centered functions. The triple substitutions are truncated by an atomic criterion such that either zero or one electrons can be transferred between atoms. The covalent model asymptotically recovers 70% of the triples correlation energy for poly-ynes with a 6-31G* basis, while the singly-ionic model recovers 99%.

Accurate local approximations to the triples correlation energy: formulation, implementation and tests of 5th-order scaling models

Local models for the triples part of the MP4 or CCSD(T) energy are formulated in terms of atom-labelled functions to describe the occupied and virtual orbital spaces. These models retain triple substitutions in which at most one of the three orbital replacements involves a change of atom. This reduces the number of triple substitutions from scaling with the 6th power of molecule size to scaling with the 4th power, and reduces the computational cost from 7th order to 5th order. Non-locality in the triple substitutions is dominated by terms in which an electron is scattered twice, while the other two singly scattered electrons exhibit non-locality that is similar to that seen in double substitutions. Two non-iterative computational models are designed around this observation. The first, ionic2, allows for non-locality only in the doubly-scattered electron, and recovers around 95% of the triples correlation energy (in the large-molecule limit). The second, ionic*, also approximately accounts for the effect of simultaneous non-locality of the doubly-scattered electron and the singly scattered electrons, and recovers over 99% of the triples energy. The latter yields a maximum error of 0.23 kcal mol−1 and an RMS error of 0.05 kcal mol−1 in the MP4/6-31G* triples energies of 179 closed shell molecules from the G3 database. A one-parameter empirical local model is introduced which recovers typically 99.7% of the MP4 triples correlation energy, and reduces the maximum error to 0.03 kcal mol−1 and the RMS error to 0.01 kcal mol−1. An implementation of these models is described which manifests the 5th-order scaling of cost with molecule size, without requiring storage of the local triples or the vvvo integrals.

The tensor properties of energy gradients within a non-orthogonal basis

Abstract The application of standard minimization techniques to electronic structure theory calculations often requires the formation of an electronic energy gradient. The tensor nature of the electronic gradient, while implicitly treated within an orthogonal basis set, manifests itself explicitly in a non-orthogonal basis set. We apply simple tensor theory to define the electronic gradient in an arbitrary reference frame using the energy minimization method of Li, Nunes and Vanderbilt in a non-orthogonal basis as a concrete example. The minimal basis HeH + energy surface is used to portray the strong effect of consistently accounting for these tensor properties versus neglecting them.

Higher analytic derivatives

This is the third in a series of papers on the ab initio calculation of the third and fourth derivatives of the energy of a molecule. In this paper derivatives with respect to electric field components, as well as with respect to nuclear coordinates are considered. A knowledge of these derivatives yields, in particular, the dipole surface up to third order, the polarizability surface up to second order, the hyperpolarizability surface up to first order, and the second hyperpolarizability. These quantities may be obtained with minimal modification of the fourth derivative of the SCF energy program described earlier. The dipole third derivatives, the polarizability second derivatives, and the hyperpolarizability first derivatives are calculated analytically for the first time. Together with the anharmonic energy derivatives, the dipole surface enables the calculation of infrared intensities for fundamental, overtones and combination bands. The scattering intensities in the Raman effect for fundamentals, ove...