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In the variational subspace valence bond (VSVB) [G. D. Fletcher, J. Chem. Phys. 142, 134112 (2015)] method, the electronic orbitals comprising the wave function correspond to chemically meaningful objects, such as bonds, lone pairs, atomic cores, and so on. Selected regions of a molecule (for example, a single chemical bond, as opposed to all the bonds) can be modeled with different levels of basis set and possible methods for modeling correlation from the other regions. The interactions between the components of a molecule (say, a bond and a neighboring orbital) can then be studied in detail for their impact on a chemical phenomenon while avoiding the expense of necessarily applying the higher levels and methods to the entire molecule. This work presents the theoretical basis for modeling correlation effects between specific electron pairs by incorporating terms in the inter-electronic coordinates ("r12") into VSVB. The approach is validated with calculations on small systems using single-reference wave functions. [ABSTRACT FROM AUTHOR]

The Kohn variational principle for the log-derivative matrix is used to calculate integral cross sections for H+D2 (v=0, j=0) to D+HD (v’=0,1,2, all j’) at the experimentally accessible collision energies of 0.55 and 1.3 eV. Comparison is made with experimental and theoretical studies in the literature. Product state relative rotational distributions, vibrational branching ratios, and energy partitioning fractions are all in good agreement with the recent experimental results of Rinnen, Kliner, and Zare. Absolute cross sections are compared with the experimental work of Levene et al. and Johnson et al. Our results agree very well with their experiments. It is found that the quasiclassical results of Blais and Truhlar compare well with the present exact quantum mechanical predictions in many respects, however, the product rotational distributions are ‘‘hotter’’ than the quantal ones. [ABSTRACT FROM AUTHOR]

The Newton Variational Principle for the log-derivative matrix (the Y-NVP) is studied in the context of a collinear exchange problem. In contrast to the integral equation methods that calculate the K or the T matrices directly, the matrix elements of the log-derivative Newton functional can be made independent of the scattering energy. This promises considerable savings in computational effort when state to state transition probabilities are calculated at several energies, since the matrix elements of the functional need be calculated only once. Green’s functions defined with respect to a reference energy, called the reference energy Green’s functions (or the REGFs), play a central role in the Y-NVP functional. The REGFs may be defined with or without reference to asymptotic channel energies. If channel dependent REGFs are used, the Y-NVP converges at the same rate as the GNVP for the K or T matrices, when the scattering energy is the same as the reference energy. On the other hand, channel independent REGFs permit even further reductions in computational effort.We use both types of REGFs in the present paper, and compare the rates of convergence. These comparisons show that the convergence rate of the method is not significantly altered by the type of REGF used. Further, we show that the Y-NVP is able to achieve rapid convergence of reactive transition probabilities over a large range of scattering energies, even when scattering resonances are present. An analysis of the computational effort required for each part of the calculation leads to the conclusion that a Y-NVP calculation using a channel independent REGF requires essentially only the same amount of computer time as a log-derivative Kohn (Y-KVP) calculation, while, presumably, offering faster convergence. [ABSTRACT FROM AUTHOR]

A new translational basis set is introduced for quantum reactive scattering calculations that use the log derivative version of the Kohn variational principle. This basis set, which is similar in many respects to that used in electron–atom scattering calculations by Burke and Robb, is obtained by contracting a primitive basis of Lobatto shape functions to the box eigenfunctions of a one-dimensional reference Hamiltonian H0. In addition, a single energy-dependent scattering function is included in the variational expansion to ensure completeness at the boundary of the box. One fairly obvious choice for the reference Hamiltonian in an atom–diatom reaction is suggested, and all of the equations which are actually needed to implement the method in this context are carefully described. Example applications to the three-dimensional F+H2 reaction are then chosen to illustrate the practical potential of the approach. [ABSTRACT FROM AUTHOR]

The log derivative version of the Kohn variational principle is reviewed in the context of a general bimolecular chemical reaction. The basis of this review, namely, the Wigner and Eisenbud general formulation of rearrangement scattering, has been well known for many years. Therefore, so as to avoid any unnecessary confusion, the relationship between their equally famous R matrix theory and Kohn’s variational derivation is carefully described. The log derivative matrix is then eliminated from a basis set representation of Kohn’s principle to leave a unitary and symmetric variational expression for the scattering matrix S. This new expression is expected to find its most fruitful application in the iterative solution of very large quantum scattering problems for which transitions from only a few initial states are required. [ABSTRACT FROM AUTHOR]

We present a method for including the geometric phase in quantum reactive scattering computations based on the log derivative version of the Kohn variational principle. A new variational functional is developed which includes the influence of the geometric phase through modifications in the momentum operators. The system investigated is a two-dimensional reactive scattering model which includes the vector potential induced by the magnetic field of an infinitely long solenoid. The coordinates used in this model are analogous to Jacobi coordinates used in atom–diatom systems. Some interesting features of this study include the gauge invariance of the scattering probabilities, symmetry adaptation of the wave function, and the behavior of the probability density in the presence of the geometric phase. [ABSTRACT FROM AUTHOR]

A new approach to calculating quantum functional sensitivity maps of transition probabilities is described in this paper. This approach is based on the log-derivative version of the Kohn variational principle and is applied here to the collinear H+H2 hydrogen exchange reaction. The sensitivity maps provide detailed quantitative information about how variations in the potential energy surface affect the state-to-state transition probabilities. The key issues investigated are (i) the evolution of sensitivity structure in the 0.30–1.50 eV range of total energy; (ii) the comparison of sensitivity structure on the Porter–Karplus, the Liu–Siegbahn–Truhlar–Horowitz, and the double-many-body-expansion potential energy surfaces; and (iii) the range of linearity for first order sensitivity predictions. [ABSTRACT FROM AUTHOR]

Two sensitivity-analysis techniques are used to show how one can predict observables on new or perturbed potential energy surfaces (PES) without doing any additional dynamics calculations on the new PESs. Both techniques require the computation of the observable (O) and its sensitivity to variations in the potential (δO/δV) on just one surface. The first approach uses a simple first order expansion of the observable with respect to δV. The second approach uses a nonlinear least-squares fit of particular features in the observable, and then uses the same functional form to predict the observable on a different PES but with a modified set of fitting parameters. The new fitting parameters are related to the old via a functional Taylor expansion. Both approaches work well when variations in the potential are small. When the potential difference is large, the second approach gives reasonable results even in cases where the first approach is giving spurious predictions. These ideas are tested for the collinear H+H2 reaction within the framework of quantum reactive scattering. The log-derivative version of the Kohn variational principle is used for the scattering calculations. [ABSTRACT FROM AUTHOR]

The effects of features in the potential energy surface on the collinear H+H2 reaction rate coefficient are investigated by the method of quantum functional sensitivity analysis (QFSA). The calculations use QFSA to connect features in the microscopic realm, with their response upon macroscopic quantities of chemical interest, via the intermediary sensitivities of the reactive transition probabilities. While the sensitivities of the individual transition probabilities show considerable structure, there is an attendant loss of structure in the rate coefficient sensitivities because of the thermal averaging. For the range of temperatures used in our study (200–2400 K), the most important region of the potential energy surface is found to be not at the top of the barrier, but rather at the lower energy shoulders of the barrier. There are also regions near the barrier where an increase in the potential surface actually increases the reaction rate! The effects of using different underlying potentials [the Porter–Karplus (PK2), Liu–Siegbahn–Truhlar–Horowitz (LSTH), and double many-body expansion (DMBE) surfaces] on the nature of the results were also compared. The absolute sensitivity magnitudes on the PK2 surface vary considerably from the other two, but the relative change in the rate coefficient is about the same on all three surfaces. Furthermore, the identified regions of importance on the potential surfaces remain essentially the same. The reactive scattering calculations were performed with the log-derivative version of the Kohn variational principle. [ABSTRACT FROM AUTHOR]

The Hartree–Fock method in the General Atomic and Molecular Structure System (GAMESS) quantum chemistry package represents one of the most irregular algorithms in computation today. Major steps in the calculation are the irregular computation of electron repulsion integrals and the building of the Fock matrix. These are the central components of the main self consistent field (SCF) loop, the key hot spot in electronic structure codes. By threading the Message Passing Interface (MPI) ranks in the official release of the GAMESS code, we not only speed up the main SCF loop (4× to 6× for large systems) but also achieve a significant ( > 2 ×) reduction in the overall memory footprint. These improvements are a direct consequence of memory access optimizations within the MPI ranks. We benchmark our implementation against the official release of the GAMESS code on the Intel® Xeon Phi™ supercomputer. Scaling numbers are reported on up to 7680 cores on Intel Xeon Phi coprocessors. [ABSTRACT FROM AUTHOR]