Victor F. Lotrich

Parallel implementation of electronic structure energy, gradient, and Hessian calculations

ACES III is a newly written program in which the computationally demanding components of the computational chemistry code ACES II [J. F. Stanton et al., Int. J. Quantum Chem. 526, 879 (1992); [ACES II program system, University of Florida, 1994] have been redesigned and implemented in parallel. The high-level algorithms include Hartree-Fock (HF) self-consistent field (SCF), second-order many-body perturbation theory [MBPT(2)] energy, gradient, and Hessian, and coupled cluster singles, doubles, and perturbative triples [CCSD(T)] energy and gradient. For SCF, MBPT(2), and CCSD(T), both restricted HF and unrestricted HF reference wave functions are available. For MBPT(2) gradients and Hessians, a restricted open-shell HF reference is also supported. The methods are programed in a special language designed for the parallelization project. The language is called super instruction assembly language (SIAL). The design uses an extreme form of object-oriented programing. All compute intensive operations, such as tensor contractions and diagonalizations, all communication operations, and all input-output operations are handled by a parallel program written in C and FORTRAN 77. This parallel program, called the super instruction processor (SIP), interprets and executes the SIAL program. By separating the algorithmic complexity (in SIAL) from the complexities of execution on computer hardware (in SIP), a software system is created that allows for very effective optimization and tuning on different hardware architectures with quite manageable effort.

Ab initio density functional theory: the best of both worlds?

Density functional theory (DFT), in its current local, gradient corrected, and hybrid implementations and their extensions, is approaching an impasse. To continue to progress toward the quality of results demanded by todays ab initio quantum chemistry encourages a new direction. We believe ab initio DFT is a promising route to pursue. Whereas conventional DFT cannot describe weak interactions, photoelectron spectra, or many potential energy surfaces, ab initio DFT, even in its initial, optimized effective potential, second-order many-body perturbation theory form [OEP (2)-semi canonical], is shown to do all well. In fact, we obtain accuracy that frequently exceeds MP2, being competitive with coupled-cluster theory in some cases. Furthermore, this is accomplished within a relatively fast computational procedure that scales like iterative second order. We illustrate our results with several molecular examples including Ne2,Be2,F2, and benzene.

Benchmark studies on the building blocks of DNA. 1. Superiority of coupled cluster methods in describing the excited states of nucleobases in the Franck-Condon region.

Equation of motion excitation energy coupled-cluster (EOMEE-CC) methods including perturbative triple excitations have been used to set benchmark results for the excitation energy and oscillator strength of the building units of DNA, i.e., cytosine, guanine, adenine and thymine. In all cases the lowest twelve transitions have been considered including valence and Rydberg ones. Triple-ζ basis sets with diffuse functions have been used and the results are compared to CC2, CASPT2, TDDFT, and DFT/MRCI results from the literature. The results clearly show that it is only the EOMEE-CCSD(T) that is capable of providing accuracy of about 0.1 eV. EOMEE-CCSD systematically overshoots the energy of all types of transitions by 0.1-0.3 eV, whereas CC2 is surprisingly accurate for ππ* transitions but fails (often badly) for nπ* and Rydberg transitions. DFT and CASPT2 seem to give reliable results for the lowest transition, but the error increases fast with the excitation level. The differences in the excitation energies often change the energy ordering of the states, which should even influence the conclusions of excited state dynamics obtained with these approximate methods. The results call for further benchmark calculations on larger building blocks of DNA (nucleosides, basis pairs) at the CCSD(T) level.

Ab initio correlation functionals from second-order perturbation theory

Orbital-dependent exchange-correlation functionals are not limited by the explicit dependence on the density and present an attractive alternative to conventional functionals. With the successful implementation of the exact orbital-dependent exchange functional, the challenge lies in developing orbital-dependent approximations for the correlation functional. Ab initio many-body methods can provide such approximations. In particular, perturbation theory with the Kohn-Sham model as the reference [Görling and Levy, Phys. Rev. A 50, 196 (1994)] defines the exact correlation functional via an infinite perturbation series. The second-order term of these series gives the lowest-order approximation to the correlation functional. However, it has been suggested [Bartlett et al., J. Chem. Phys. 122, 034104 (2005)] that the Kohn-Sham Hamiltonian is not the optimal choice for the perturbation expansion and a different reference Hamiltonian may lead to an improved perturbation series and more accurate second-order approximation. Here, we demonstrate explicitly that the modified series can be used to define superior functional and potential. We present results of atomic and molecular calculations with both second-order functionals. Our results demonstrate that the modified functional offers a significantly improved description of the correlation effects as it does not suffer from convergence problems and results in energies and densities that are more accurate than those obtained with second-order Møller-Plesset perturbation theory or generalized-gradient approximation functionals.

Efficient Electronic Integrals and their Generalized Derivatives for Object Oriented Implementations of Electronic Structure Calculations

For the new parallel implementation of electronic structure methods in ACES III (Lotrich et al., in preparation) the present state‐of‐the‐art algorithms for the evaluation of electronic integrals and their generalized derivatives were implemented in new object oriented codes with attention paid to efficient execution on modern processors with a deep hierarchy of data storage including multiple caches and memory banks. Particular attention has been paid to define proper integral blocks as basic building objects. These objects are stand‐alone units and are no longer tied to any specific software. They can hence be used by any quantum chemistry code without modification. The integral blocks can be called at any time and in any sequence during the execution of an electronic structure program. Evaluation efficiency of these integral objects has been carefully tested and it compares well with other fast integral programs in the community. Correctness of the objects has been demonstrated by several application runs on real systems using the ACES III program.

Software design of ACES III with the super instruction architecture

The Advanced Concepts in Electronic Structure (ACES) III software is a completely rewritten implementation for parallel computer architectures of the most used capabilities in ACES II, including the calculation of the electronic structure of molecular ground states and excited states, and determination of molecular geometries and of vibrational frequencies using many‐body and coupled cluster methods. To achieve good performance on modern parallel systems while simultaneously offering a software development environment that allows rapid implementation of new methods and algorithms, ACES III was written using a new software infrastructure, the super instruction architecture comprising a domain‐specific language, super instruction assembly language (SIAL), and a sophisticated runtime environment, super instruction processor (SIP). The architecture of ACES III is described as well as the inner workings of SIAL and SIP. The execution performance of ACES III and the productivity of programming in SIAL are discussed.

Benchmarking for Perturbative Triple-Excitations in EE-EOM-CC Methods

Perturbative triples corrections ((T) and (T̃)) to the equation of motion coupled cluster singles and doubles (EOM-CCSD) are rederived and implemented in a pilot parallel code. The vertical excitation energies of molecules in the test set of Sauer et al. [J. Chem. Theor. Comput. 2009, 5, 555] are reported and compared to the iterative EOM-CCSDT-3 method. The average absolute deviations of EOM-CCSD(T) and EOM-CCSD(T̃) from EOM-CCSDT-3 over this wide test set are 0.06 and 0.18 eV, respectively. The poor performance of the latter suggests misbalanced handling of the (T̃) terms. Scaling curves for EOM-CCSD(T) are also presented to demonstrate the performance across multiple compute nodes, thus enabling the routine and accurate study of excited states for ever larger molecular systems.

RDX Geometries, Excited States, and Revised Energy Ordering of Conformers via MP2 and CCSD(T) Methodologies: Insights into Decomposition Mechanism

The geometries, harmonic frequencies, elec-tronic excitation levels, and energetic orderings of various conformers of RDX have been computed at the ab initio MP2 and CCSD(T) levels, providing more reliable results than have been previously obtained. We observe that the various local minimum-energy conformers are all competitive for being the absolute minimum and that, at reasonable temperatures, several conformers will appreciably contribute to the population of RDX. As a result, we have concluded that any mechanistic study to investigate thermal decomposition can reasonably begin from any one of the cyclohexane conformers of RDX. As such, it is necessary to consider the transition states for each RDX conformer to gauge what the activation energy is. Homolytic bond dissociation has long been speculated to be critical to detonation; we report here the most accurate estimates of homolytic BDEs yet calculated, likely to be accurate within 3 kcal mol(-1). The differences in energy for homolytic BDEs among all the possible RDR conformers are again small, such that most all of the conformers can reasonably be speculated as the next step in the mechanism starting from the RDR radical.

Benchmark studies on the building blocks of DNA. 2. Effect of biological environment on the electronic excitation spectrum of nucleobases.

In the first paper of this series (Szalay; et al. J. Phys. Chem. A, 2012, 116, 6702) we have investigated the excited states of nucleobases. It was shown that it is only the equation of motion excitation energy coupled-cluster (EOMEE-CC) methods, which can give a balanced description for all type of the transitions of these molecules; if the goal is to obtain accurate results with uncertainty of about 0.1 eV only, triples corrections in the form of, e.g., the EOMEE-CCSD(T) method need to be included. In this second paper we extend this study to nucleobases in their biological environment, considering hydration, glycoside bond, and base pairing. EOMEE-CCSD and EOMEE-CCSD(T) methods are used with aug-cc-pVDZ basis. The effect of surrounding water was systematically investigated by considering one to five water molecules at different positions. It was found that hydration can modify the order of the excited states: in particular, nπ* states get shifted above the neighboring ππ* ones. The glycoside bonds effect is smaller, as shown by our calculations on cytidine and guanosine. Here the loss of planarity causes some intensity shift from ππ* to nπ* states. Finally, the guanine-cytosine (GC) Watson-Crick pair was studied; most of the states could be identified as local excitations on one of the bases, but there is also a low-lying charge-transfer state. Significant discrepancy with earlier CASPT2 and TDDFT studies was found for the GC pair and triples effects seem to be essential for all of these systems.

An ab initio study of the (H2O)20H+ and (H2O)21H+ water clusters

The study of the minimum Born–Oppenheimer structures of the protonated water clusters, (H2O)nH+, is performed for n=20 and 21. The structures belonging to four basic morphologies are optimized at the Hartree–Fock, second-order many-body perturbation theory and coupled cluster level, with the 6–31G, 6-31G∗, and 6-311G∗∗ basis sets, using the parallel ACES III program. The lowest energy structure for each n is found to be the cagelike form filled with H2O, with the proton located on the surface. The cage is the distorted dodecahedron for the 21-mer case, and partially rearranged dodecahedral structure for the 20-mer. The results confirm that the lowest energy structure of the magic number n=21 clusters corresponds to a more stable form than that of the 20-mer clusters.