Quantum Chemistry

Sequential and concerted C-C and C-O bond dissociation in the Coulomb explosion of 2-propanol
Bittner, D. ; Gope, K. ; Livshits, E. ; Baer, R. ; Strasser, D. Sequential and concerted C-C and C-O bond dissociation in the Coulomb explosion of 2-propanol. Journal of Chemical Physics 2022, 157, 074309. Publisher's Version
Linear Weak Scalability of Density Functional Theory Calculations without Imposing Electron Localization
Fabian, M. D. ; Shpiro, B. ; Baer, R. Linear Weak Scalability of Density Functional Theory Calculations without Imposing Electron Localization. J. Chem. Theory Comput. 2022, acs.jctc.1c00829. Publisher's VersionAbstract

Linear scaling density functional theory (DFT) approaches to the electronic structure of materials are often based on the tendency of electrons to localize in large atomic and molecular systems. However, in many cases of actual interest, such as semiconductor nanocrystals, system sizes can reach a substantial extension before significant electron localization sets in, causing a considerable deviation from linear scaling. Herein, we address this class of systems by developing a massively parallel DFT approach which does not rely on electron localization and is formally quadratic scaling yet enables highly efficient linear wall-time complexity in the weak scalability regime. The method extends from the stochastic DFT approach described in Fabian et al. (WIRES: Comp. Mol. Sci. 2019, e1412) but is entirely deterministic. It uses standard quantum chemical atomcentered Gaussian basis sets to represent the electronic wave functions combined with Cartesian real-space grids for some operators and enables a fast solver for the Poisson equation. Our main conclusion is that when a processor-abundant high-performance computing (HPC) infrastructure is available, this type of approach has the potential to allow the study of large systems in regimes where quantum confinement or electron delocalization prevents linear scaling.

Stochastic Vector Techniques in Ground-State Electronic Structure
Baer, R. ; Neuhauser, D. ; Rabani, E. Stochastic Vector Techniques in Ground-State Electronic Structure. Annu. Rev. Phys. Chem. 2022, 73, annurev–physchem–090519–045916. Publisher's VersionAbstract

We review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss highly effective techniques to reduce statistical errors. Finally, we review the use of stochastic vector techniques for calculating correlation energies within the secondorder Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods.

High frequency limit of spectroscopy
Nazarov, V. U. ; Baer, R. High frequency limit of spectroscopy. Journal of Chemical Physics 2022, 157, 084112.Abstract

We consider an arbitrary quantum mechanical system, initially in its ground-state, exposed to a time-dependent electromagnetic pulse with a carrier frequency ω0 and a slowly varying envelope of finite duration. By working out a solution to the time-dependent Schrödinger equation in the high-ω0 limit, we find that, to the leading order in ω−10, a perfect self-cancellation of the system’s linear response occurs as the pulse switches off. Surprisingly, the system’s observables are, nonetheless, describable in terms of a combination of its linear density response function and nonlinear functions of the electric field. An analysis of a jellium slab and jellium sphere models reveals a very high surface sensitivity of the considered setup, producing a richer excitation spectrum than accessible within the conventional linear response regime. On this basis, we propose a new spectroscopic technique, which we provisionally name the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the traditional dipole selection rules, and the clarity of theoretical interpretation utilizing the linear response time-dependent density functional theory, NLHFPS has a potential to evolve into a powerful characterization method for nanoscience and nanotechnology

Time-resolving the ultrafast H2 roaming chemistry and H3+ formation using extreme-ultraviolet pulses
Livshits, E. ; Luzon, I. ; Gope, K. ; Baer, R. ; Strasser, D. Time-resolving the ultrafast H2 roaming chemistry and H3+ formation using extreme-ultraviolet pulses. Communications Chemistry 2020, 3 49. Publisher's Version livshits2020time.pdf
Dopant levels in large nanocrystals using stochastic optimally tuned range-separated hybrid density functional theory
Lee, A. J. ; Chen, M. ; Li, W. ; Neuhauser, D. ; Baer, R. ; Rabani, E. Dopant levels in large nanocrystals using stochastic optimally tuned range-separated hybrid density functional theory. Physical Review B 2020, 102, 035112. Publisher's Version lee2020dopant.pdf
Range-separated stochastic resolution of identity: Formulation and application to second-order Green’s function theory
Dou, W. ; Chen, M. ; Takeshita, T. Y. ; Baer, R. ; Neuhauser, D. ; Rabani, E. Range-separated stochastic resolution of identity: Formulation and application to second-order Green’s function theory. The Journal of Chemical Physics 2020, 153, 074113. Publisher's VersionAbstract

We develop a range-separated stochastic resolution of identity (RS-SRI) approach for the four-index electron repulsion integrals, where the larger terms (above a predefined threshold) are treated using a deterministic RI and the remaining terms are treated using a SRI. The approach is implemented within a second-order Green’s function formalism with an improved O(N3) scaling with the size of the basis set, N. Moreover, the RS approach greatly reduces the statistical error compared to the full stochastic version [T. Y. Takeshita et al., J. Chem. Phys. 151, 044114 (2019)], resulting in computational speedups of ground and excited state energies of nearly two orders of magnitude, as demonstrated for hydrogen dimer chains and water clusters.

Energy window stochastic density functional theory
Chen, M. ; Baer, R. ; Neuhauser, D. ; Rabani, E. Energy window stochastic density functional theory. The Journal of Chemical Physics 2019, 151, 114116. Publisher's Version chen2019energy.pdf
Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum
Dou, W. ; Takeshita, T. Y. ; Chen, M. ; Baer, R. ; Neuhauser, D. ; Rabani, E. Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum. Journal of Chemical Theory and Computation 2019. Publisher's VersionAbstract

We develop a stochastic resolution of identity approach to the real-time second-order Green’s function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green’s function [Takeshita et al. J. Chem. Phys. 2019, 151, 044114]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(Ne5) down to O(Ne3) where Ne is the number of electrons. This is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to Ne ≈ 1000 electrons.

Transition to metallization in warm dense helium-hydrogen mixtures using stochastic density functional theory within the Kubo-Greenwood formalism
Cytter, Y. ; Rabani, E. ; Neuhauser, D. ; Preising, M. ; Redmer, R. ; Baer, R. Transition to metallization in warm dense helium-hydrogen mixtures using stochastic density functional theory within the Kubo-Greenwood formalism. Physical Review B 2019, 100. Publisher's VersionAbstract

Abstract The Kubo-Greenwood (KG) formula is often used in conjunction with Kohn-Sham (KS) density functional theory (DFT) to compute the optical conductivity, particularly for warm dense mater. For applying the KG formula, all KS eigenstates and eigenvalues up to an energy cutoff are required and thus the approach becomes expensive, especially for high temperatures and large systems, scaling cubically with both system size and temperature. Here, we develop an approach to calculate the KS conductivity within the stochastic DFT (sDFT) framework, which requires knowledge only of the KS Hamiltonian but not its eigenstates and values. We show that the computational effort associated with the method scales linearly with system size and reduces in proportion to the temperature unlike the cubic increase with traditional deterministic approaches. In addition, we find that the method allows an accurate description of the entire spectrum, including the high-frequency range, unlike the deterministic method which is compelled to introduce a high-frequency cut-off due to memory and computational time constraints. We apply the method to helium-hydrogen mixtures in the warm dense matter regime at temperatures of \textbackslashsim60\textbackslashtext\kK\ and find that the system displays two conductivity phases, where a transition from non-metal to metal occurs when hydrogen atoms constitute \textbackslashsim0.3 of the total atoms in the system.

Quantum Monte Carlo assessment of density functionals for π-electron molecules: ethylene and bifuran
Ospadov, E. ; Rothstein, S. M. ; Baer, R. Quantum Monte Carlo assessment of density functionals for π-electron molecules: ethylene and bifuran. Molecular Physics 2019, 117, 2241–2250. Publisher's VersionAbstract

We perform all-electron, pure-sampling quantum Monte Carlo (QMC) calculations on ethylene and bifuran molecules. The orbitals used for importance sampling with a single Slater determinant are generated from Hartree-Fock and density functional theory (DFT). Their fixed-node energy provides an upper bound to the exact energy. The best performing density functionals for ethylene are BP86 and M06, which account for 99% of the electron correlation energy. Sampling from the π-electron distribution with these orbitals yields a quadrupole moment comparable to coupled cluster CCSD(T) calculations. However, these, and all other density functionals, fail to agree with CCSD(T) while sampling from electron density in the plane of the molecule. For bifuran, as well as ethylene, a correlation is seen between the fixed-node energy and deviance of the QMC quadrupole moment estimates from those calculated by DFT. This suggests that proximity of DFT and QMC densities correlates with the quality of the exchange nodes of the DFT wave function for both systems.

Making Sense of Coulomb Explosion Imaging
Luzon, I. ; Livshits, E. ; Gope, K. ; Baer, R. ; Strasser, D. Making Sense of Coulomb Explosion Imaging. J. Phys. Chem. Lett. 2019, 10, 1361–1367. Publisher's VersionAbstract

A multifaceted agreement between ab initio theoretical predictions and experimental measurements, including branching ratios, channel-specific kinetic energy release, and three-body momentum correlation spectra, leads to the identification of new mechanisms in Coulomb-explosion (CE) induced two- and three-body breakup processes in methanol. These identified mechanisms include direct nonadiabatic Coulomb explosion responsible for CO bond-breaking, a long-range “ inverse harpooning” dominating the production of H2+ + HCOH+, a transient proton migration leading to surprising energy partitioning in three-body fragmentation and other complex dynamics forming products such as H2O+ and H3+. These mechanisms provide general concepts that should be useful for analyzing future time-resolved Coulomb explosion imaging of methanol as well as other molecular systems. These advances are enabled by a combination of recently developed experimental and computational techniques, using weak ultrafast EUV pulses to initiate the CE and a high-level quantum chemistry approach to follow the resulting field-free nonadiabatic molecular dynamics.

Vlček, V. ; Rabani, E. ; Neuhauser, D. ; Baer, R. Stochastic GW calculations for molecules. J. Chem. Theory Comput. 2017, 13, 4997–5003.Abstract

Quasiparticle (QP) excitations are extremely important for understanding and predicting charge transfer and transport in molecules, nanostructures and extended systems. Since density functional theory (DFT) within Kohn-Sham (KS) formulation does not provide reliable QP energies, a many-body perturbation technique within the GW approximation are essential. The steep computational scaling of GW prohibits its use in extended, open boundary, systems with thousands of electrons and more. Recently, a stochastic formulation of GW has been proposed [Phys. Rev. Lett. 113, 076402 (2014)] which scales nearly linearly with the system size, as illustrated for a series of silicon nanocrystals exceeding 3000 electrons. Here, we implement the stochastic GW (sGW) approach to study the ionization potential (IP) of a subset of molecules taken from the "GW 100" benchmark. We show that sGW provides a reliable results in comparison to GW WEST code and to experimental results, numerically establishing its validity. For completeness, we also provide a detailed review of sGW and a summary of the numerical algorithm.

Neuhauser, D. ; Baer, R. ; Zgid, D. Stochastic self-consistent second-order Green’s function method for correlation energies of large electronic systems. J. Chem. Theory Comput. 2017, 13, 5396−5403.Abstract

The second-order Matsubara Green’s function method (GF2) is a robust temperature dependent quantum chemistry approach, extending beyond the random-phase approximation. However, till now the scope of GF2 applications was quite limited as they require computer resources which rise steeply with system size. In each step of the self-consistent GF2 calculation there are two parts: the estimation of the self-energy from the previous step’s Green’s function, and updating the Green’s function from the self-energy. The first part formally scales as the fifth power of the system size while the second has a much gentler cubic scaling. Here, we develop a stochastic approach to GF2 (sGF2) which reduces the fifth power scaling of the first step to merely quadratic, leaving the overall sGF2 scaling as cubic. We apply the method to linear hydrogen chains containing up to 1000 electrons, showing that the approach is numerically stable, efficient and accurate. The stochastic errors are very small, of the order of 0.1% or less of the correlation energy for large systems, with only a moderate computational effort. The first iteration of GF2 is an MP2 calculation that is done in linear scaling, hence we obtain an extremely fast stochastic MP2 (sMP2) method as a by-product. While here we consider finite systems with large band gaps where at low temperatures effects are negligible, the sGF2 formalism is temperature dependent and general and can be applied to finite or periodic systems with small gaps at finite temperatures.

Vlček, V. ; Eisenberg, H. R. ; Steinle-Neumann, G. ; Rabani, E. ; Neuhauser, D. ; Baer, R. Spontaneous charge carrier localization in extended one-dimensional systems. Phys. Rev. Lett. 2016, 116, 186401.Abstract

Charge carrier localization in extended atomic systems has been described previously as being driven by disorder, point defects, or distortions of the ionic lattice. Here we show for the first time by means of first-principles computations that charge carriers can spontaneously localize due to a purely electronic effect in otherwise perfectly ordered structures. Optimally tuned range-separated density functional theory and many-body perturbation calculations within the GW approximation reveal that in trans-polyacetylene and polythiophene the hole density localizes on a length scale of several nanometers. This is due to exchange-induced translational symmetry breaking of the charge density. Ionization potentials, optical absorption peaks, excitonic binding energies, and the optimally tuned range parameter itself all become independent of polymer length as it exceeds the critical localization length. Moreover, we find that lattice disorder and the formation of a polaron result from the charge localization in contrast to the traditional view that lattice distortions precede charge localization. Our results can explain experimental findings that polarons in conjugated polymers form instantaneously after exposure to ultrafast light pulses.

Eisenberg, H. R. ; Baer, R. Exothermic Mechanism for the Abstraction of Hydrogen from Methane on Li-Doped MgO. 2015, 119, 196–215. Publisher's VersionAbstract

Despite its importance, it is still not known by which mechanism Li-doped MgO catalyzes the oxidative coupling of methane to ethane. Nevertheless, it is commonly assumed that the mechanism goes through catalytic H abstraction from methane via a Li+O– surface defect. In this paper we use first-principles density functional theory calculations to show that the reaction is significantly more exothermic when the Li+O– defect is situated on a step edge instead of on the flat surface. We find that the reaction on the step is exothermic by 0.25 eV, whereas it is endothermic by 0.3 eV on the flat surface. The presence of the Li dopant in the step edge is crucial for the exothermicity of the reaction. These findings suggest that surface steps which include lithium defects could be responsible for the catalytic behavior of Li/MgO. Following the binding of hydrogen to the Li+O– defect on the step edge the methyl radical can either depart to the gas phase or bind to an adjacent step-edge oxygen atom, increasing the exothermicity of the overall process to 0.8 eV. Activation energies of 0.2 eV for the first pathway and 0.5–0.8 eV for the second were calculated.

Neuhauser, D. ; Rabani, E. ; Cytter, Y. ; Baer, R. Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory. J. Phys. Chem. A 2015, 120, 3071–3078.Abstract

We develop a stochastic formulation of the optimally tuned range-separated hybrid density functional theory that enables significant reduction of the computational effort and scaling of the nonlocal exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn–Sham density matrix. The computational cost of the approach is similar to that of usual Kohn–Sham density functional theory, yet it provides a much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a self-consistent Hamiltonian that is central for additional postprocessing, for example, in the stochastic Bethe–Salpeter approach.

Rabani, E. ; Baer, R. ; Neuhauser, D. Time-dependent stochastic Bethe-Salpeter approach. Phys. Rev. B 2015, 91, 235302.Abstract

A time-dependent formulation for electron-hole excitations in extended finite systems, based on the Bethe-Salpeter equation (BSE), is developed using a stochastic wave function approach. The time-dependent formulation builds on the connection between time-dependent Hartree-Fock (TDHF) theory and the configuration-interaction with single substitution (CIS) method. This results in a time-dependent Schrödinger-like equation for the quasiparticle orbital dynamics based on an effective Hamiltonian containing direct Hartree and screened exchange terms, where screening is described within the random-phase approximation (RPA). To solve for the optical-absorption spectrum, we develop a stochastic formulation in which the quasiparticle orbitals are replaced by stochastic orbitals to evaluate the direct and exchange terms in the Hamiltonian as well as the RPA screening. This leads to an overall quadratic scaling, a significant improvement over the equivalent symplectic eigenvalue representation of the BSE. Application of the time-dependent stochastic BSE (TDsBSE) approach to silicon and CdSe nanocrystals up to size of  3000 electrons is presented and discussed.

Gao, Y. ; Neuhauser, D. ; Baer, R. ; Rabani, E. Sublinear scaling for time-dependent stochastic density functional theory. J. Chem. Phys. 2015, 142, 034106.Abstract

A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number ( 16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.

Neuhauser, D. ; Gao, Y. ; Arntsen, C. ; Karshenas, C. ; Rabani, E. ; Baer, R. Breaking the Theoretical Scaling Limit for Predicting Quasiparticle Energies: The Stochastic GW Approach. Phys. Rev. Lett. 2014, 113, 076402.Abstract

We develop a formalism to calculate the quasiparticle energy within the GW many-body perturbation correction to the density functional theory. The occupied and virtual orbitals of the Kohn-Sham Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function G, the polarization potential W, and, thereby, the GW self-energy. The stochastic GW (sGW) formalism relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression, and spatial or temporal stochastic decoupling techniques. Beyond the theoretical interest, the formalism enables linear scaling GW calculations breaking the theoretical scaling limit for GW as well as circumventing the need for energy cutoff approximations. We illustrate the method for silicon nanocrystals of varying sizes with Ne > 3000 electrons.