Curtis L. Janssen

An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations

The closed‐shell CCSD equations are reformulated in order to achieve superior computational efficiency. Using a spin adaptation scheme based on the unitary group approach (UGA), we have obtained a new set of equations that greatly improves our previous formulation. Based on this scheme we have also derived equations for the closed‐shell configuration interaction including all single and double excitations (CISD) case. Both methods have been implemented and tested. For a range of test cases the new CCSD method is more efficient than the earlier CCSD method. The new closed‐shell CISD procedure is faster than the shape‐driven (SD)GUGA algorithm and the new CCSD scheme is less than two times more computation intensive than SDGUGA CISD per iteration.

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.

Concerning zero‐point vibrational energy corrections to electronic energies

For comparison with experimentally obtained thermochemical data, zero‐point vibrational energies (ZPVEs) are required to convert total electronic energies obtained from ab initio quantum mechanical studies into 0 K enthalpies. The currently accepted practice is to employ self‐consistent‐field (SCF) harmonic frequencies that have been scaled to reproduce experimentally observed fundamental frequencies. This procedure introduces systematic errors that result from a recognizable flaw in the method, namely that the correct ZPVE, G(0), is not one half the sum of the fundamental vibrational frequencies. Until better methods for accurately determining ZPVEs are presented, we recommend using different scaling factors for the determination of ZPVEs than those used to compare theoretically determined harmonic frequencies to observed fundamentals.

New diagnostics for coupled-cluster and Møller–Plesset perturbation theory

Abstract We here present new diagnostics for coupled-cluster and Moller–Plesset perturbation theory, readily computed from the single substitution amplitudes in the coupled-cluster singles and doubles wavefunction or in the second-order Moller–Plesset wavefunction. The new diagnostics D1(CCSD) and D1(MP2) have advantages over the previously proposed T 1 and S 2 diagnostics. A clear correlation between the size of the diagnostics and the performance of coupled-cluster and second-order Moller–Plesset perturbation theory is demonstrated for computation of optimum geometries and harmonic vibrational frequencies for a series of 29 small molecules.

The automated solution of second quantization equations with applications to the coupled cluster approach

SummaryTheoretical methods in chemistry frequently involve the tedious solution of complex algebraic equations. Then the solutions, sometimes still quite complex, are usually hand-coded by a programmer into an efficient computer language. During this procedure it is all too easy to make an error which will go undetected. A better approach would be to introduce the computer at an even earlier stage in the development of the theory by programming it to first solve the set of equations and then compile the solution into an efficient computer language. In this research a program has been written in the C programming language which can efficiently compute the quasivacuum expectation value of a product of creation and annihilation operators and scalar arrays. The terms in the resulting expressions are then transformed into a canonical form so that all equivalent terms can be combined. Finally, the equations are compiled into a simple representation which can be rapidly interpreted by a Fortran program. This symbol manipulator has been applied to open-shell coupled cluster theory. Two coupled cluster methods using high-spin open-shell references are presented. In one of these methods, the cluster operator contains the unitary group generators, and products thereof, which generate all single and double excitations with respect to the reference. The other uses a simplified cluster operator which generates equations that must be spin-projected. These methods are compared to other descriptions of electron correlation for the CH2 singlet-triplet splitting and the NH2 potential energy surface.

Accurate structures and binding energies for small water clusters: The water trimer

The global minimum on the water trimer potential energy surface has been investigated by means of second-order Mo/ller-Plesset (MP2) perturbation theory employing the series of correlation-consistent basis sets aug-cc-pVXZ (X = D, T, Q, 5, 6), the largest of which contains 1329 basis functions. Definitive predictions are made for the binding energy and equilibrium structure, and improved values are presented for the harmonic vibrational frequencies. A value of 15.82±0.05 kcal mol−1 is advanced for the infinite basis set frozen core MP2 binding energy, obtained by extrapolation of MP2 correlation energies computed at the aug-cc-pVQZ MP2 geometry. Inclusion of core correlation, using the aug-cc-pCV5Z basis set, has been found to increase the binding energy by 0.08 kcal mol−1, and after consideration of core correlation and higher-order correlation effects, the classical binding energy for the water trimer is estimated to be 15.9±0.2 kcal mol−1. A zero-point vibrational correction of −5.43 kcal mol−1 has bee...

Second-order Møller-Plesset theory with linear R12 terms (MP2-R12) revisited: auxiliary basis set method and massively parallel implementation.

Ab initio electronic structure approaches in which electron correlation explicitly appears have been the subject of much recent interest. Because these methods accelerate the rate of convergence of the energy and properties with respect to the size of the one-particle basis set, they promise to make accuracies of better than 1 kcal/mol computationally feasible for larger chemical systems than can be treated at present with such accuracy. The linear R12 methods of Kutzelnigg and co-workers are currently the most practical means to include explicit electron correlation. However, the application of such methods to systems of chemical interest faces severe challenges, most importantly, the still steep computational cost of such methods. Here we describe an implementation of the second-order Møller-Plesset method with terms linear in the interelectronic distances (MP2-R12) which has a reduced computational cost due to the use of two basis sets. The use of two basis sets in MP2-R12 theory was first investigated recently by Klopper and Samson and is known as the auxiliary basis set (ABS) approach. One of the basis sets is used to describe the orbitals and another, the auxiliary basis set, is used for approximating matrix elements occurring in the exact MP2-R12 theory. We further extend the applicability of the approach by parallelizing all steps of the integral-direct MP2-R12 energy algorithm. We discuss several variants of the MP2-R12 method in the context of parallel execution and demonstrate that our implementation runs efficiently on a variety of distributed memory machines. Results of preliminary applications indicate that the two-basis (ABS) MP2-R12 approach cannot be used safely when small basis sets (such as augmented double- and triple-zeta correlation consistent basis sets) are utilized in the orbital expansion. Our results suggest that basis set reoptimization or further modifications of the explicitly correlated ansatz and/or standard approximations for matrix elements are necessary in order to make the MP2-R12 method sufficiently accurate when small orbital basis sets are used. The computer code is a part of the latest public release of Sandias Massively Parallel Quantum Chemistry program available under GNU General Public License.

A Simulator for Large-Scale Parallel Computer Architectures

Efficient design of hardware and software for large-scale parallel execution requires detailed understanding of the interactions between the application, computer, and network. The authors have developed a macro-scale simulator SST/macro that permits the coarse-grained study of distributed-memory applications. In the presented work, applications using the Message Passing Interface MPI are simulated; however, the simulator is designed to allow inclusion of other programming models. The simulator is driven from either a trace file or a skeleton application. Trace files can be either a standard format Open Trace Format or a more detailed custom format DUMPI. The simulator architecture is modular, allowing it to easily be extended with additional network models, trace file formats, and more detailed processor models. This paper describes the design of the simulator, provides performance results, and presents studies showing how application performance is affected by machine characteristics.

Utilizing High Performance Computing for Chemistry: Parallel Computational Chemistry

Parallel hardware has become readily available to the computational chemistry research community. This perspective will review the current state of parallel computational chemistry software utilizing high-performance parallel computing platforms. Hardware and software trends and their effect on quantum chemistry methodologies, algorithms, and software development will also be discussed.