Matthew L. Leininger

Psi4: an open-source ab initio electronic structure program

The Psi4 program is a new approach to modern quantum chemistry, encompassing Hartree–Fock and density‐functional theory to configuration interaction and coupled cluster. The program is written entirely in C++ and relies on a new infrastructure that has been designed to permit high‐efficiency computations of both standard and emerging electronic structure methods on conventional and high‐performance parallel computer architectures. Psi4 offers flexible user input built on the Python scripting language that enables both new and experienced users to make full use of the programs capabilities, and even to implement new functionality with moderate effort. To maximize its impact and usefulness, Psi4 is available through an open‐source license to the entire scientific community.

PSI3: An open‐source Ab Initio electronic structure package

PSI3 is a program system and development platform for ab initio molecular electronic structure computations. The package includes mature programming interfaces for parsing user input, accessing commonly used data such as basis‐set information or molecular orbital coefficients, and retrieving and storing binary data (with no software limitations on file sizes or file‐system‐sizes), especially multi‐index quantities such as electron repulsion integrals. This platform is useful for the rapid implementation of both standard quantum chemical methods, as well as the development of new models. Features that have already been implemented include Hartree‐Fock, multiconfigurational self‐consistent‐field, second‐order Møller‐Plesset perturbation theory, coupled cluster, and configuration interaction wave functions. Distinctive capabilities include the ability to employ Gaussian basis functions with arbitrary angular momentum levels; linear R12 second‐order perturbation theory; coupled cluster frequency‐dependent response properties, including dipole polarizabilities and optical rotation; and diagonal Born‐Oppenheimer corrections with correlated wave functions. This article describes the programming infrastructure and main features of the package. PSI3 is available free of charge through the open‐source, GNU General Public License.

Anchoring the water dimer potential energy surface with explicitly correlated computations and focal point analyses

Ten stationary points on the water dimer potential energy surface have been characterized with the coupled-cluster technique which includes all single and double excitations as well as a perturbative approximation of triple excitations [CCSD(T)]. Using a triple-ζ basis set with two sets of polarization functions augmented with higher angular momentum and diffuse functions [TZ2P(f,d)+dif], the fully optimized geometries and harmonic vibrational frequencies of these ten stationary points were determined at the CCSD(T) theoretical level. In agreement with other ab initio investigations, only one of these ten stationary points is a true minimum. Of the other nine structures, three are transition structures, and the remaining are higher order saddle points. These high-level ab initio results indicate that the lowest lying transition state involved in hydrogen interchange is chiral, of C1 symmetry rather than Cs as suggested by recently developed 6D potential energy surfaces. The one- and n-particle limits of t...

Is Mo/ller–Plesset perturbation theory a convergent ab initio method?

Recent studies have seriously questioned the use of higher-order Mo/ller–Plesset perturbation theory (MPn) in describing electron correlation in atomic and molecular systems. Here we first reinvestigate with improved numerical techniques previously controversial and disturbing MPn energetic series for Ne, F−, HF, BH, C2 and N2. Conspicuously absent in previous work is research on the convergence of MPn spectroscopic constants, and thus complete MPn (energy, re, ωe) series were then computed for (BH, HF, CN+, C2 and N2) through the high orders (MP25, MP21, MP13, MP39 and MP19) within the correlation consistent family of basis sets. A persistent, slowly decaying ringing pattern in the C2 energy series was tracked out to MP155. Finally, new energy series were generated and analyzed through MP167 for Cl− and MP39 for Ar and HCl. The MPn energy and property series variously display rapid or slow convergence, monotonic or oscillatory decay, highly erratic or regular behavior, or early or late divergence, all de...

Structures and vibrational frequencies in the full configuration interaction limit: Predictions for four electronic states of methylene using a triple-zeta plus double polarization (TZ2P) basis

Benchmark energies, geometries, dipole moments, and harmonic vibrational frequencies are determined for four states of methylene (CH2) by solving the electronic Schrodinger equation exactly for a triple-ζ plus double polarization (TZ2P) basis with the restrictions that the core orbital remains doubly occupied and the highest-lying virtual orbital is deleted. Approximate models of electron correlation are evaluated based on their ability to match the exact, full configuration interaction results. Predictions from configuration interaction with all single, double, triple, and quadruple substitutions (CISDTQ) and coupled-cluster including singles, doubles, and triples (CCSDT) are virtually identical to the full CI results for all but the c 1A1 state, which is poorly described by a single-configuration reference. In agreement with previous work, the c state remains slightly bent at the TZ2P full CI level of theory, with a bond angle of 170.1° and a barrier to linearity of only 25 cm−1.

The standard enthalpy of formation of CH2

High-quality ab initio quantum chemical methods, including higher-order coupled cluster and full configuration interaction benchmarks, with basis sets ranging from [C/H] [4s3p1d/2s1p] to [9s8p7d5f4g3h2i/7s6p5d4f3g2h] have been employed to obtain the best technically possible value for the standard enthalpy of formation of X 3B1 CH2 and a 1A1 CH2. Careful extrapolations of finite basis MP2, CCSD, CCSD(T), and CCSDT energies to the complete basis set full configuration interaction limit plus inclusion of small corrections owing to relativistic effects, core correlation, and the diagonal Born–Oppenheimer correction results in the final extrapolated enthalpies of formation of this study, ΔfH0o(X 3B1 CH2)=390.45−0.64+0.68 kJ mol−1 and ΔfH0o(a 1A1 CH2)=428.10−0.64+0.68 kJ mol−1. The computed value for X 3B1 CH2 is in between the best two experimental results of 389.87±0.86 and 390.73±0.66 kJ mol−1. The elaborate calculations leading to these enthalpies of formation also resulted in accurate estimates of the ...

A new diagnostic for open-shell coupled-cluster theory

Abstract We present a new diagnostic for open-shell coupled-cluster theory, readily computed from the single substitution amplitudes in the CCSD wavefunction. The new diagnostic, D1(ROCCSD), is designed to be comparable to the previously proposed D1(CCSD) diagnostic. Unlike other approaches, the D1 diagnostics are independent of system size and have the same invariance properties as the energy with respect to orbital rotations. Calibration of the D1(ROCCSD) diagnostic on 34 molecular systems indicates that for values of D1(ROCCSD) of 0.025 or below the quality of the CCSD results are, in general, excellent, whereas values larger than 0.025 signal inadequacies in the CCSD approach.

Benchmark configuration interaction spectroscopic constants for X 1Σg+ C2 and X 1Σ+ CN+

Explicit full configuration interaction (FCI) computations in a double-ζ plus polarization (DZP) basis, involving as many as 105 million Slater determinants, have been performed to sample the potential energy curves of X 1Σg+ C2 and X 1Σ+ CN+ for benchmark purposes. Quartic force fields have been determined at the optimized structures, and sets of anharmonic spectroscopic constants [re, ωe, Be, De, αe, and ωexe] have been ascertained. Analogous results obtained from high-level but inexact correlation treatments establish a CISDTQ<CCSDT<CISDTQPH≈FCI series of increasing accuracy for the notorious X 1Σg+ C2 and X 1Σ+ CN+ multireference systems. The data also reveal that recent schemes for CI+PT extrapolations to the FCI limit are quite accurate, to within 0.4 mEh, 0.001 A, and 4 cm−1 in the total energy, re, and ωe, respectively. Whether such schemes approximate FCI curves with sufficient smoothness to reproduce the anharmonic data obtained here is elevated as a challenge for future work.

Molecular geometry and vibrational frequencies of ozone from compact variational wave functions explicitly including triple and quadruple substitutions

The performance of a multireference CISD method, CISD[TQ], is compared to that of other approaches which include a large degree of electron correlation, including Brueckner methods. The CISD[TQ] method selects as references all single and double substitutions within an active orbital space. Certain triple and quadruple substitutions from the Hartree–Fock reference are included in the CISD[TQ] wave function as singles and doubles from the selected reference set. This wave function has previously been shown in simpler cases to provide results near to those predicted by the configuration interaction wave function, including all single, double, triple, and quadruple substitutions (CISDTQ). For the challenging multireference case of ozone, the CISD[TQ] wave function yields geometries and harmonic vibrational frequencies with an accuracy similar to the full CCSDT method. These promising results suggest that for difficult multireference problems the CISD[TQ] wave function provides an efficient and accurate appro...

Systematic Study of Selected Diagonalization Methods for Configuration Interaction Matrices

Several modifications to the Davidson algorithm are systematically explored to establish their performance for an assortment of configuration interaction (CI) computations. The combination of a generalized Davidson method, a periodic two‐vector subspace collapse, and a blocked Davidson approach for multiple roots is determined to retain the convergence characteristics of the full subspace method. This approach permits the efficient computation of wave functions for large‐scale CI matrices by eliminating the need to ever store more than three expansion vectors (bi) and associated matrix‐vector products (σi), thereby dramatically reducing the I/O requirements relative to the full subspace scheme. The minimal‐storage, single‐vector method of Olsen is found to be a reasonable alternative for obtaining energies of well‐behaved systems to within μEh accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yield high accuracy (ca. 10−10 Eh) for very large CI problems. Several approximations to the diagonal elements of the CI Hamiltonian matrix are found to allow simple on‐the‐fly computation of the preconditioning matrix, to maintain the spin symmetry of the determinant‐based wave function, and to preserve the convergence characteristics of the diagonalization procedure.