Troy Van Voorhis

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.

A geometric approach to direct minimization

The approach presented, geometric direct minimization (GDM), is derived from purely geometrical arguments, and is designed to minimize a function of a set of orthonormal orbitals. The optimization steps consist of sequential unitary transformations of the orbitals, and convergence is accelerated using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) approach in the iterative subspace, together with a diagonal approximation to the Hessian for the remaining degrees of freedom. The approach is tested by implementing the solution of the self-consistent field (SCF) equations and comparing results with the standard direct inversion in the iterative subspace (DIIS) method. It is found that GDM is very robust and converges in every system studied, including several cases in which DIIS fails to find a solution. For main group compounds, GDM convergence is nearly as rapid as DIIS, whereas for transition metal-containing systems we find that GDM is significantly slower than DIIS. A hybrid procedure where DIIS is used for the first several iterations and GDM is used thereafter is found to provide a robust solution for transition metal-containing systems.

Benchmark variational coupled cluster doubles results

We present the first application of the Rayleigh–Ritz variational procedure to the coupled cluster doubles trial function. The variational approach is applied to the potential surface of H4, the double dissociation of water and the dissociation of N2, and the results are compared to standard coupled cluster doubles calculations. It is found that the variational approach gives a greatly improved description of strongly correlated systems, where the standard approach is known to fail. Some examination of the basis set dependence of the results is presented.

A perturbative correction to the quadratic coupled-cluster doubles method for higher excitations

A perturbative correction to the quadratic coupled-cluster doubles (QCCD) method is proposed. This correction, QCCD(2), is based on modifying the existing second-order correction to optimized-orbital coupled-cluster doubles to avoid double-counting contributions from quadruple excitations. Comparisons against full configuration interaction calculations are presented for the equilibrium bond distance and harmonic vibrational frequency of the nitrogen molecule and for the dissociation of the nitrogen and water molecules in the cc-pVDZ basis set.

The quadratic coupled cluster doubles model

Abstract Beginning from the bi-variational expression for the standard coupled cluster doubles (CCD) energy, we propose including a term quadratic in the left operator, S † 2 . As this makes the left-hand and right-hand wave functions more similar, the resulting functional should better approximate the variational expression. The energy given by the quadratic functional is extensive and the stationary equations may be solved in O( N 6 ) time. These equations have been implemented and the potential energy surfaces for HF dissociation, H 2 O double dissociation and N 2 dissociation are examined. It is found that the quadratic functional effectively reproduces the fully variational results in all cases.

The imperfect pairing approximation

Abstract We present a wavefunction intended to model the static correlation of molecular systems. This wavefunction is best understood as a generalization of the perfect pairing (PP) approximation, and it is therefore termed the imperfect pairing (IP) approximation. The energy is determined by exploiting the connection between PP and a constrained coupled-cluster approach, and optimizing the orbitals to minimize the energy. We obtain results for some trial systems and find that, while a larger fraction of the correlation energy is recovered in IP than PP, the newer method has certain systematic limitations.

Implementation of generalized valence bond-inspired coupled cluster theories

We present an implementation of the recently proposed imperfect pairing (IP) and generalized valence bond restricted coupled cluster (GVB-RCC) methods. Our algorithm centers on repeated construction of Coulomb and exchange matrices. These operations are the computational bottleneck, scaling with the third power of system size for large systems. Robust optimization of the valence orbitals is attained using a geometrically consistent form of direct minimization. Analytic gradients of the IP and GVB-RCC energies are also obtained by a simple modification of the energy optimization scheme. As an illustration of the potential of these new methods, we use IP to compute the equilibrium geometry and energetics of a Si9H12 cluster that is a crude model for silicon dimerization on the Si(001) surface. We thus demonstrate a valuable role for IP and GVB-RCC as a diagnostic for the accuracy of reduced active space calculations as compared to their full valence analogs.

Connections between coupled cluster and generalized valence bond theories

We explore the fundamental connections between certain approximate coupled cluster (CC) and generalized valence bond (GVB) wave functions. We show that the GVB restricted configuration interaction (GVB-RCI) wave function can be associated with a compact CC expansion in the valence space. However, careful analysis reveals that a standard CC expansion contains terms that are not contained in the GVB-RCI wave function. The offending terms violate an effective pairwise exclusion principle (PEP) that is present in the RCI expansion, but is not enforced in the CC analog. These terms do not affect the size separability of either method. Variational calculations show noticeable improvements to the CC wave function when the PEP is enforced, with the most significant improvements coming near the dissociation limit. We modify the standard CC amplitude equations by removing the PEP violating terms and demonstrate remarkably improved results for the dissociation of N2 and the double dissociation of H2O.

Two-body coupled cluster expansions

We show that the exact ground state wave function for an arbitrary two-body Hamiltonian can be exactly represented by a single reference coupled cluster wave function employing a general two-particle cluster operator. This can be used to construct a set of approximate methods that converge to the exact result and are in some sense complementary to the standard approach of including successively double, triple, quadruple, …, excitations. We present exploratory variational results for the neon atom and the dissociation of N2 to demonstrate the strengths and weaknesses of these generalized coupled cluster approximations.

A nonorthogonal approach to perfect pairing

We present an alternative formulation of perfect pairing (PP) aimed at giving a more faithful representation of the valence correlation energy of an arbitrary molecule. In the new theory, the occupied and virtual orbitals are nonorthogonal amongst themselves but orthogonal to each other. Whereas for the fully orthogonal version of PP one has the number of pairs equal to the number of occupied orbitals, the current formulation allows for an arbitrary number of pairs built from redundant orbitals. We propose setting the number of pairs equal to the number of valence orbitals in the molecule. Preliminary results indicate that the redundant formulation gives qualitatively improved results for delocalized systems such as benzene, while maintaining the attractive features of PP for localized systems.