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The revised, regularized Tao–Mo (rregTM) exchange-correlation density functional approximation (DFA) [A. Patra, S. Jana, and P. Samal, J. Chem. Phys. 153, 184112 (2020) and Jana et al., J. Chem. Phys. 155, 024103 (2021)] resolves the order-of-limits problem in the original TM formulation while preserving its valuable essential behaviors. Those include performance on standard thermochemistry and solid data sets that is competitive with that of the most widely explored meta-generalized-gradient-approximation DFAs (SCAN and r2SCAN) while also providing superior performance on elemental solid magnetization. Puzzlingly however, rregTM proved to be intractable for de-orbitalization via the approach of Mejía-Rodríguez and Trickey [Phys. Rev. A 96, 052512 (2017)]. We report investigation that leads to diagnosis of how the regularization in rregTM of the z indicator functions (z = the ratio of the von-Weizsäcker and Kohn–Sham kinetic energy densities) leads to non-physical behavior. We propose a simpler regularization that eliminates those oddities and that can be calibrated to reproduce the good error patterns of rregTM. We denote this version as simplified, regularized Tao–Mo, sregTM. We also show that it is unnecessary to use rregTM correlation with sregTM exchange: Perdew–Burke–Ernzerhof correlation is sufficient. The subsequent paper shows how sregTM enables some progress on de-orbitalization. [ABSTRACT FROM AUTHOR]

The Pauli kinetic energy functional and its functional derivative, termed Pauli potential, play a crucial role in the successful implementation of orbital-free density functional theory for electronic structure calculations. However, the exact forms of these two quantities are not known. Therefore, perforce, one employs the approximate forms for the Pauli functional or Pauli potential for performing orbital-free density functional calculations. In the present study, we developed a feed-forward neural network-based representation for the Pauli potential using a 1-dimensional (1-D) model system. We expanded density in terms of basis functions, and the coefficients of the expansion were used as input to a feed-forward neural network. Using the neural network-based representation of the Pauli potential, we calculated the ground-state densities of the 1-D model system by solving the Euler equation. We calculated the Pauli kinetic energy using the neural network-based Pauli potential employing the exact relation between the Pauli kinetic energy functional and the potential. The sum of the neural network-based Pauli kinetic energy and the von Weizsäcker kinetic energy resulted in an accurate estimation of the total kinetic energy. The approach presented in this paper can be employed for the calculation of Pauli potential and Pauli kinetic energy, obviating the need for a functional derivative. The present study is an important step in the advancement of application of machine learning-based techniques toward the orbital-free density functional theory-based methods. [ABSTRACT FROM AUTHOR]

Accurate theoretical prediction of the band offsets at interfaces of semiconductor heterostructures can often be quite challenging. Although density functional theory has been reasonably successful to carry out such calculations, efficient, accurate semilocal functionals are desirable to reduce the computational cost. In general, the semilocal functionals based on the generalized gradient approximation (GGA) significantly underestimate the bulk bandgaps. This, in turn, results in inaccurate estimates of the band offsets at the heterointerfaces. In this paper, we investigate the performance of several advanced meta-GGA functionals in the computational prediction of band offsets at semiconductor heterojunctions. In particular, we investigate the performance of r2SCAN (two times revised strongly constrained and appropriately normed functional), rMGGAC (revised semilocal functional based on cuspless hydrogen model and Pauli kinetic energy density functional), mTASK (modified Aschebrock and Kümmel meta-GGA functional), and local modified Becke–Johnson exchange-correlation functionals. Our results strongly suggest that these meta-GGA functionals for supercell calculations perform quite well, especially, when compared to computationally more demanding GW calculations. We also present band offsets calculated using ionization potentials and electron affinities, as well as band alignment via the branch point energies. Overall, our study shows that the aforementioned meta-GGA functionals can be used within the density functional theory framework to estimate the band offsets in semiconductor heterostructures with predictive accuracy. [ABSTRACT FROM AUTHOR]

Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integration may lead to deviations from equipartition. Fortunately, backward error analysis allows us to obtain a higher-order estimate of the quantity that is actually subject to equipartition. This is related to a shadow Hamiltonian, which converges to the specified Hamiltonian only when the time-step size approaches zero. This paper deals with discretization effects in a straightforward way. With a small computational overhead, we obtain refined versions of the kinetic and potential energies, whose sum is a suitable estimator of the shadow Hamiltonian. Then, we tune the thermostatting procedure by employing the refined kinetic energy instead of the conventional one. This procedure is shown to reproduce a canonical ensemble compatible with the refined system, as opposed to the original one, but canonical averages regarding the latter can easily be recovered by reweighting. Water, modeled as a rigid body, is an excellent test case for our proposal because its numerical stability extends up to time steps large enough to yield pronounced discretization errors in Verlet-type integrators. By applying our new approach, we were able to mitigate discretization effects in equilibrium properties of liquid water for time-step sizes up to 5 fs. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate that it is possible to apply collocation to compute vibrational energy levels of a five-atom molecule using an exact kinetic energy operator (with cross terms and coordinatedependent coefficients). This is made possible by using (1) a pruned basis of products of univariate functions; (2) a Smolyak grid made from nested sequences of grids for each coordinate; (3) a collocation method that obviates the need to solve a generalized eigenvalue problem; (4) an efficient sequential transformation between the (nondirect product) grid and the (nondirect product) basis representations; and (5) hierarchical univariate functions that make it possible to avoid storing large intermediate vectors. The accuracy of the method is confirmed by computing 500 vibrational energy levels of methane. [ABSTRACT FROM AUTHOR]

A systematic way of improving exchange-correlation energy functionals of density functional theory has been to make them satisfy more and more exact relations. Starting from the initial generalized gradient approximation (GGA) functionals, this has culminated into the recently proposed SCAN (strongly constrained and appropriately normed) functional that satisfies several known constraints and is appropriately normed. The ultimate test for the functionals developed is the accuracy of energy calculated by employing them. In this paper, we test these exchange-correlation functionals--the GGA hybrid functionals B3LYP and PBE0 and the meta-GGA functional SCAN--from a different perspective. We study how accurately these functionals reproduce the exchange-correlation energy when electron-electron interaction is scaled as αVee with α varying between 0 and 1. Our study reveals interesting comparison between these functionals and the associated difference Tc between the interacting and the non-interacting kinetic energy for the same density. [ABSTRACT FROM AUTHOR]

In order to simulate the exact universal density functional, approximations are nowadays constructed by permitting more flexibility in its ansatz. In view of the difficulty of defining a systematically improvable form for it, this paper argues that an alternative way could be considered. It falls within the class of hybrid functionals with multi-determinant wave functions. The parameter controlling the hybridization is considered as variable. The invariance of the exact result with respect to changes in this variable is used to introduce information about the system under consideration, and to correct the density functional result. The construction considered in this paper accelerates convergence from the model system to the physical one, in the vicinity of the latter. The method, at the present level of implementation, should be seen as a starting point for further development, and not necessarily as a computationally advantageous tool. [ABSTRACT FROM AUTHOR]

Accurate and computationally efficient exchange-correlation functionals are critical to the successful application of linear-scaling density functional theory (DFT). Local and semi-local functionals of the density are naturally compatible with linear-scaling approaches, having a general form which assumes the locality of electronic interactions and which can be efficiently evaluated by numerical quadrature. Presently, the most sophisticated and flexible semi-local functionals are members of the meta-generalized-gradient approximation (meta-GGA) family, and depend upon the kinetic energy density, τ, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of τ-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for τ-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement τ-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the τ-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the τ-dependent exchange-correlation potential and kinetic energy density in terms of the strictly localized, self-consistently optimized orbitals used by ONETEP. To validate the numerical accuracy of our self-consistent meta-GGA implementation, we performed calculations using the B97M-V and PKZB meta-GGAs on a variety of small molecules. Using only a minimal basis set of self-consistently optimized local orbitals, we obtain energies in excellent agreement with large basis set calculations performed using other codes. Finally, to establish the linear-scaling computational cost and applicability of our approach to large-scale calculations, we present the outcome of self-consistent meta-GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms. [ABSTRACT FROM AUTHOR]

In this paper, we improve the collocation method for computing vibrational spectra that was presented in Avila and Carrington, Jr. [J. Chem. Phys. 139, 134114 (2013)]. Using an iterative eigensolver, energy levels and wavefunctions are determined from values of the potential on a Smolyak grid. The kinetic energy matrix-vector product is evaluated by transforming a vector labelled with (nondirect product) grid indices to a vector labelled by (nondirect product) basis indices. Both the transformation and application of the kinetic energy operator (KEO) scale favorably. Collocation facilitates dealing with complicated KEOs because it obviates the need to calculate integrals of coordinate dependent coefficients of differential operators. The ideas are tested by computing energy levels of HONO using a KEO in bond coordinates. [ABSTRACT FROM AUTHOR]

The conventional Nosé-Hoover type deterministic thermostat scheme for controlling temperature by configurational variables (Braga-Travis (BT) thermostat) is non-ergodic for systems with a few degrees of freedom. While for the original Nosé-Hoover kinetic thermostat ergodicity has been achieved by controlling the higher order moments of kinetic energy, the issues of nonergodicity of BT thermostat persists. In this paper, we introduce two new measures of configurational temperature (second and third order) based on the generalized temperature-curvature relationship and obtain a family of deterministic thermostatting schemes by selectively (and simultaneously) controlling the different orders of temperatures through pseudo-friction terms. The ergodic characteristics of the proposed thermostats are tested using a single harmonic oscillator through statistical (normality of joint distributions at different Poincare sections) as well as dynamical tests (difference of the minimum and maximum largest Lyapunov exponent). Our results indicate that simultaneously controlling the first and the second order configurational temperatures (C1,2 thermostat) is sufficient to make the dynamics ergodic. A 2000 particle Lennard-Jones system is subjected to (i) equilibrium and (ii) sudden temperature change under BT and C1,2 thermostatting schemes. The C1,2 thermostat is found to be more robust than the BT thermostat without increasing computational costs. [ABSTRACT FROM AUTHOR]

In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree-Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA. [ABSTRACT FROM AUTHOR]

Properties of exact density functionals provide useful constraints for the development of new approximate functionals. This paper focuses on convex sums of ground-level densities. It is observed that the electronic kinetic energy of a convex sum of degenerate ground-level densities is equal to the convex sum of the kinetic energies of the individual degenerate densities. (The same type of relationship holds also for the electron-electron repulsion energy.) This extends a known property of the Levy-Valone Ensemble Constrained-Search and the Lieb Legendre-Transform refomulations of the Hohenberg-Kohn functional to the individual components of the functional. Moreover, we observe that the kinetic and electron-repulsion results also apply to densities with fractional electron number (even if there are no degeneracies), and we close with an analogous point-wise property involving the external potential. Examples where different degenerate states have different kinetic energy and electron-nuclear attraction energy are given; consequently, individual components of the ground state electronic energy can change abruptly when the molecular geometry changes. These discontinuities are predicted to be ubiquitous at conical intersections, complicating the development of universally applicable density-functional approximations. [ABSTRACT FROM AUTHOR]

In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-"coupled"- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code. [ABSTRACT FROM AUTHOR]

The high-resolution (2 + 1) resonance-enhanced multiphoton-ionization photoelectron spectroscopy (REMPI-PS) can be obtained by measuring the photoelectron intensity at a given kinetic energy and scanning the single p phase step position. In this paper, we further demonstrate that the highresolution (2 + 1) REMPI-PS cannot be achieved at any measured position of the kinetic energy by this measurement method, which is affected by the laser spectral bandwidth. We propose a double p phase step modulation to eliminate the effect of the laser spectral bandwidth, and show the advantage of the double p phase step modulation on achieving the high-resolution (2 + 1) REMPI-PS by considering the contributions involving on- and near-resonant three-photon excitation pathways. [ABSTRACT FROM AUTHOR]

The bending and torsional degrees of freedom in S1 acetylene, C2H2, are subject to strong vibrational resonances and rovibrational interactions, which create complex vibrational polyad structures even at low energy. As the internal energy approaches that of the barrier to cis-trans isomerization, these energy level patterns undergo further large-scale reorganization that cannot be satisfactorily treated by traditional models tied to local minima of the potential energy surface for nuclear motion. Experimental spectra in the region near the cis-trans transition state have revealed these complicated new patterns. In order to understand near-barrier spectroscopic observations and to predict the detailed effects of cis-trans isomerization on the rovibrational energy level structure, we have performed reduced dimension rovibrational variational calculations of the S1 state. In this paper, we present the methodological details, several of which require special care. Our calculation uses a high accuracy ab initio potential surface and a fully symmetrized extended complete nuclear permutation inversion group theoretical treatment of a multivalued internal coordinate system that is appropriate for large amplitude bending and torsional motions. We also discuss the details of the rovibrational basis functions and their symmetrization, as well as the use of a constrained reduced dimension rovibrational kinetic energy operator. [ABSTRACT FROM AUTHOR]

Expressions for reaction rate constants in multidimensional chemical systems are derived by applying semiclassical approximation to the quantum path integrals of the ImF formulation of reaction rate theory. First, the transverse degrees of freedom orthogonal to the reaction coordinate are treated within the steepest descent approximation, after which the semiclassical approximation is applied to the remaining reaction coordinate. Thus derived, the semiclassical expressions account for the multidimensional nature of quantum effects and accurately incorporate nuclear quantum effects such as multidimensional tunneling and zero point energies. The obtained expressions are applicable in the broad temperature range from the deep tunneling to high-temperature regimes. The present paper provides derivation of the semiclassical instanton expressions proposed by Kryvohuz [J. Chem. Phys. 134, 114103 (2011)]. [ABSTRACT FROM AUTHOR]

We present a new procedure for computing a rovibrational spectrum of a polyatomic molecule and apply it to methane. The Schrödinger equation is solved, numerically exactly, by using a nested contracted basis. Rovibrational wavefunctions are computed in a |v>|JKM> basis, where |v> is a vibrational wavefunction and |JKM> is a symmetric top wavefunction. In turn, the |v> are obtained by solving a vibrational Schrödinger equation with basis functions that are products of contracted bend and stretch functions. At all stages of the calculation we exploit parity symmetry. The calculations are done in internal coordinates that facilitate the treatment of large amplitude motion. An Eckart molecule-fixed frame is used by numerically computing coefficients of the kinetic energy operator. The efficacy of the method is demonstrated by calculating a large number of converged J = 10 methane rovibrational levels in the Tetradecad polyad. No previous calculation of rovibrational levels of methane includes as many levels as we report in this paper. [ABSTRACT FROM AUTHOR]

We show that by using a rectangular collocation method with a small basis of parameterized functions, it is possible to compute a vibrational spectrum by solving the Schrödinger equation in 7D from a small number of ab initio calculations without a potential surface. The method is ideal for spectra of molecules adsorbed on a surface. In this paper, it is applied to calculate experimentally relevant energy levels of acetic acid adsorbed on the (101) surface of anatase TiO2. In this case, to obtain levels of experimental accuracy, increasing the number of dimensions from 4 to 7 increases the number of required potential points from about 1000 to about 10 000 and the number of basis functions from 126 to 792: the scaling is very attractive. [ABSTRACT FROM AUTHOR]

This paper presents the multi-channel generalization of the center-of-mass kinetic energy elimination approach [B. Simmen et al., Mol. Phys. 111, 2086 (2013)] when the Schrödinger equation is solved variationally with explicitly correlated Gaussian functions. The approach has immediate relevance in many-particle systems which are handled without the Born–Oppenheimer approximation and can be employed also for Dirac-type Hamiltonians. The practical realization and numerical properties of solving the Schrödinger equation in laboratory-frame Cartesian coordinates are demonstrated for the ground rovibronic state of the H 2 + = { p + , p + , e − } ion and the H2 = {p+, p+, e−, e−} molecule. [ABSTRACT FROM AUTHOR]

We present in this paper an (e, 2e + ion) investigation of the dissociative ionization of methane by 54 eV electron impact employing the advanced reaction microscope. By measuring two electrons and the ion in the final state in triple coincidence, the species of the ions are identified and the energies deposited into the target are determined. The species and the kinetic energies of the fragmented ion show strong dependence on the intermediate states of the parent ion. Possible decay pathways for the production of different species of ions are analyzed. [ABSTRACT FROM AUTHOR]