Tensor hypercontracted ppRPA: reducing the cost of the particle-particle random phase approximation from O(r(6)) to O(r(4)).

In recent years, interest in the random-phase approximation (RPA) has grown rapidly. At the same time, tensor hypercontraction has emerged as an intriguing method to reduce the computational cost of electronic structure algorithms. In this paper, we combine the particle-particle random phase approximation with tensor hypercontraction to produce the tensor-hypercontracted particle-particle RPA (THC-ppRPA) algorithm.

The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r(4)) scaling.

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions.

Comparison of low-rank tensor expansions for the acceleration of quantum chemistry computations.

Low-rank spectral expansion and tensor hypercontraction are two promising techniques for reducing the size of the two-electron excitation tensor by factorizing it into products of smaller tensors. Both methods can potentially realize an O(r(4)) quantum chemistry method where r is the number of one-electron orbitals. We compare the two factorizations in this paper by applying them to the parametric 2-electron reduced density matrix method with the M functional [D.

Achieving partial decoherence in surface hopping through phase correction.

Fewest-switches surface hopping is one of the simplest and most popular methods for the computational study of nonadiabatic processes. Recently, a very simple phase correction was introduced to the traditional surface hopping algorithm, substantially improving its accuracy with essentially no associated computational cost [N. Shenvi, J.

Nonadiabatic dynamics at metal surfaces: independent electron surface hopping with phonon and electron thermostats.

Independent Electron Surface Hopping (IESH) is a computational method for accounting for nonadiabatic electronic transitions in simulations of molecular motion at metal surfaces. IESH is applicable in cases of strong coupling where the electronic friction model is suspect, and has been demonstrated to accurately reproduce the results of detailed molecular beam experiments on vibrationally inelastic scattering of nitric oxide from the (111) surface of gold. However, in its original form, IESH represents a closed system without energy flow outside the local region of explicitly included substrate atoms.

Multiquantum vibrational excitation of NO scattered from Au(111): quantitative comparison of benchmark data to ab initio theories of nonadiabatic molecule-surface interactions.

Surface phenomena: measurements of absolute probabilities are reported for the vibrational excitation of NO(v=0→1,2) molecules scattered from a Au(111) surface. These measurements were quantitatively compared to calculations based on ab initio theoretical approaches to electronically nonadiabatic molecule-surface interactions. Good agreement was found between theory and experiment (see picture; T(s) =surface temperature, P=excitation probability, and E=incidence energy of translation).

An algebraic operator approach to electronic structure.

In this paper, we introduce an algebraic approach to electronic structure calculations. Our approach constructs a Jordan algebra based on the second-quantized electronic Hamiltonian. From the structure factor of this algebra, we show that we can calculate the energy of the ground electronic state of the Hamiltonian operator.

Phase-corrected surface hopping: correcting the phase evolution of the electronic wavefunction.

In this paper, we show that a remarkably simple correction can be made to the equation of motion which governs the evolution of the electronic wavefunction over some prescribed nuclear trajectory in the fewest-switches surface hopping algorithm. This corrected electronic equation of motion can then be used in conjunction with traditional or modified surface hopping methods to calculate nonadiabatic effects in large systems. Although the correction adds no computational cost to the algorithm, it leads to a dramatic improvement in scattering probabilities for all model problems studied thus far.

Decoherence and surface hopping: when can averaging over initial conditions help capture the effects of wave packet separation?

Fewest-switches surface hopping (FSSH) is a popular nonadiabatic dynamics method which treats nuclei with classical mechanics and electrons with quantum mechanics. In order to simulate the motion of a wave packet as accurately as possible, standard FSSH requires a stochastic sampling of the trajectories over a distribution of initial conditions corresponding, e.g.

Simultaneous-trajectory surface hopping: a parameter-free algorithm for implementing decoherence in nonadiabatic dynamics.

In this paper, we introduce a trajectory-based nonadiabatic dynamics algorithm which aims to correct the well-known overcoherence problem in Tully's popular fewest-switches surface hopping algorithm. Our simultaneous-trajectory surface hopping algorithm propagates a separate classical trajectory on each energetically accessible adiabatic surface. The divergence of these trajectories generates decoherence, which collapses the particle wavefunction onto a single adiabatic state.

A new approach to decoherence and momentum rescaling in the surface hopping algorithm.

As originally proposed, the fewest switches surface hopping (FSSH) algorithm does not allow for decoherence between wavefunction amplitudes on different adiabatic surfaces. In this paper, we propose an inexpensive correction to standard FSSH dynamics wherein we explicitly model the decoherence of nuclear wave packets on distinct electronic surfaces. Our augmented fewest switches surface hopping approach is conceptually simple and, thus far, it has allowed us to capture several key features of the exact quantum results.

Active-space N-representability constraints for variational two-particle reduced density matrix calculations.

The ground-state energy of a system of fermions can be calculated by minimizing a linear functional of the two-particle reduced density matrix (2-RDM) if an accurate set of N-representability conditions is applied. In this Letter we introduce a class of linear N-representability conditions based on exact calculations on a reduced active space. Unlike wave-function-based approaches, the 2-RDM methodology allows us to combine information from calculations on different active spaces.

Dynamical steering and electronic excitation in NO scattering from a gold surface.

Nonadiabatic coupling of nuclear motion to electronic excitations at metal surfaces is believed to influence a host of important chemical processes and has generated a great deal of experimental and theoretical interest. We applied a recently developed theoretical framework to examine the nature and importance of nonadiabatic behavior in a system that has been extensively studied experimentally: the scattering of vibrationally excited nitric oxide molecules from a Au(111) surface. We conclude that the nonadiabatic transition rate depends strongly on both the N-O internuclear separation and the molecular orientation and, furthermore, that molecule-surface forces can steer the molecule into strong-coupling configurations.

The initial and final states of electron and energy transfer processes: diabatization as motivated by system-solvent interactions.

For a system which undergoes electron or energy transfer in a polar solvent, we define the diabatic states to be the initial and final states of the system, before and after the nonequilibrium transfer process. We consider two models for the system-solvent interactions: A solvent which is linearly polarized in space and a solvent which responds linearly to the system. From these models, we derive two new schemes for obtaining diabatic states from ab initio calculations of the isolated system in the absence of solvent.

Nonadiabatic dynamics at metal surfaces: independent-electron surface hopping.

Recent experiments have shown convincing evidence for nonadiabatic energy transfer from adsorbate degrees of freedom to surface electrons during the interaction of molecules with metal surfaces. In this paper, we propose an independent-electron surface hopping algorithm for the simulation of nonadiabatic gas-surface dynamics. The transfer of energy to electron-hole pair excitations of the metal is successfully captured by hops between electronic adiabats.

Phase-space surface hopping: nonadiabatic dynamics in a superadiabatic basis.

In this paper, we construct a phase-space surface hopping algorithm for use in systems that exhibit strong nonadiabatic coupling. The algorithm is derived from a representation of the electronic basis which is a function of the nuclear phase-space coordinates rather than the nuclear position coordinates. This phase-space adiabatic basis can be understood in the context of Berry's superadiabatic basis formalism as the first-order superadiabatic correction to the conventional position-space adiabatic basis.

Controlling spin contamination using constrained density functional theory.

We have extended the constrained density functional theory (DFT) approach to explicitly control the magnitude of spin contamination. Unlike a restricted or restricted open-shell approach, the present method allows finer granularity, not only constraining the magnitude of the spin contamination but also allowing for the possibility of applying the constraint to a subsystem of a much larger system. This allows for the description of spin polarization where physically meaningful, while simultaneously enabling the reduction of spurious overpolarization that is present in many DFT functionals.

Transition state barriers in multidimensional Marcus theory.

Multidimensional Marcus theory is the extension of traditional Marcus theory to systems in which multiple particles are transferred. Rather than the intersecting parabolas of Marcus theory, multidimensional Marcus theory involves the intersection of paraboloids. In this paper, we examine the conditions under which a full multidimensional treatment of these paraboloids is necessary and when it is possible to use a simpler one-dimensional formalism.

Semiclassical dynamics of electron transfer at metal surfaces.

In this Letter, we demonstrate that nonadiabatic dynamics of molecular scattering from metal surfaces can be efficiently simulated by semiclassical Gaussian wave packet propagation on a local complex potential. The method relies on the wideband limit decoupling of the nuclear equations of motion on different electronic states. If the continuum diabatic potential surfaces are assumed to be parallel, the number of Gaussian wave packets spawned scales at most linearly with propagation time, allowing efficient propagation of nuclear dynamics.

Vibrational relaxation of NO on Au(111) via electron-hole pair generation.

Recent experiments have demonstrated the breakdown of the Born-Oppenheimer approximation when NO undergoes inelastic scattering from a Au(111) surface. In this paper, we provide a simple theoretical model for understanding this phenomenon. Our model predicts multiquanta vibrational relaxation through the creation of high-energy electron-hole pair excitations in the metal.

Efficient chemical kinetic modeling through neural network maps.

An approach to modeling nonlinear chemical kinetics using neural networks is introduced. It is found that neural networks based on a simple multivariate polynomial architecture are useful in approximating a wide variety of chemical kinetic systems. The accuracy and efficiency of these ridge polynomial networks (RPNs) are demonstrated by modeling the kinetics of H(2) bromination, formaldehyde oxidation, and H(2)+O(2) combustion.