Aaron M. Lee

Q-Chem 2.0: A High-Performance Ab Initio Electronic Structure Program Package

Q‐Chem 2.0 is a new release of an electronic structure program package, capable of performing first principles calculations on the ground and excited states of molecules using both density functional theory and wave function‐based methods. A review of the technical features contained within Q‐Chem 2.0 is presented. This article contains brief descriptive discussions of the key physical features of all new algorithms and theoretical models, together with sample calculations that illustrate their performance.

Non-local propagation of correlations in quantum systems with long-range interactions

The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated and how difficult the system will be to describe numerically. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations to within a linear effective ‘light cone’. However, little is known about the propagation speed in systems with long-range interactions, because analytic solutions rarely exist and because the best long-range bound is too loose to accurately describe the relevant dynamical timescales for any known spin model. Here we apply a variable-range Ising spin chain Hamiltonian and a variable-range XY spin chain Hamiltonian to a far-from-equilibrium quantum many-body system and observe its time evolution. For several different interaction ranges, we determine the spatial and time-dependent correlations, extract the shape of the light cone and measure the velocity with which correlations propagate through the system. This work opens the possibility for studying a wide range of many-body dynamics in quantum systems that are otherwise intractable.The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated [1–4] and how difficult the system will be to describe numerically [5]. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations to within a linear effective light cone [6]. However, little is known about the propagation speed in systems with long-range interactions, since the best long-range bound [7] is too loose to give the correct light-cone shape for any known spin model and since analytic solutions rarely exist. In this work, we experimentally determine the spatial and time-dependent correlations of a far-from-equilibrium quantum many-body system evolving under a long-range Isingor XY-model Hamiltonian. For several different interaction ranges, we extract the shape of the light cone and measure the velocity with which correlations propagate through the system. In many cases we find increasing propagation velocities, which violate the Lieb-Robinson prediction, and in one instance cannot be explained by any existing theory. Our results demonstrate that even modestly-sized quantum simulators are well-poised for studying complicated many-body systems that are intractable to classical computation.

The density functional calculation of nuclear shielding constants using London atomic orbitals

The theory for the calculation of nuclear shielding constants with London atomic orbitals using density functional theory is presented. The theory includes the use of a local exchange–correlation functional which depends on both the electron density ρ(r) and the paramagnetic current density jp(r). The resulting coupled‐perturbed Kohn–Sham equations are presented, together with the working expression for the nuclear shielding tensor. The entire theory has been programmed and exhaustively checked, using standard Gaussian basis sets. A variety of ρ(r) dependent exchange–correlation functionals have been used, together with a current dependence suggested by Vignale, Rasolt, and Geldart. Certain numerical difficulties arose with this form which necessitated a cutoff in its evaluation for low densities. Calculations have been performed on HF, N2, CO, F2, H2O, and CH4. Including the current dependence is seen here to have a slightly deshielding effect. The major deficiency in the reported calculations appears to...

The adiabatic approximation

Abstract Now that ab initio quantum chemistry is capable of calculating vibrational frequencies ‘to an accuracy of a few cm −1 ’, it becomes interesting to examine the magnitude of small contributions. We examine the magnitude of the diagonal Born-Oppenheimer correction on the bondlengths and frequencies of diatomic molecules. We also confirm that it is important to use appropriate atomic masses, rather than nuclear masses.

Many-body localization in a quantum simulator with programmable random disorder

Interacting quantum systems are expected to thermalize, but in some situations in the presence of disorder they can exist in localized states instead. This many-body localization is studied experimentally in a small system with programmable disorder. When a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries1,2 or noninteracting particles in the presence of static disorder3,4,5,6. However, for strong interactions and high excitation energy there are cases, known as many-body localization (MBL), where disordered quantum systems can fail to thermalize7,8,9,10. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmable random disorder to ten spins initialized far from equilibrium. Using experimental and numerical methods we observe the essential signatures of MBL: initial-state memory retention, Poissonian distributed energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where a detailed modelling of MBL becomes impossible.

The determination of hyperpolarizabilities using density functional theory with nonlocal functionals

The theory for the coupled perturbed Kohn–Sham calculation of hyperpolarizabilities using nonlocal density functionals is presented. Results for calculations on formaldehyde, acetonitrile, and methyl fluoride using moderate size basis sets are reported. These results are compared with previous density functional calculations using the local density approximation, Hartree–Fock, and correlated methods, and with the experimental values.

Computation of Coulomb and exchange radial intracule densities

The computation of the Coulomb and exchange components Ju and Ku , respectively, of the Hartree-Fock radial intracule density within the PRISM approach is discussed. Formulae are presented for the even-origin derivatives of these . . quantities and for the even-order moments of Ju . For molecular systems, we demonstrate that Ju has, as expected, . long-range nature comparable with the molecular extent but, in contrast, that Ku is relatively short-range, with delocalisation effects providing additional structure and enhancing the range of the intracule. q 1999 Elsevier Science B.V. All rights reserved.

Insights from Coulomb and exchange intracules

Abstract We contend that the dependence of traditional density functional theory (DFT) on the one-electron density alone is both its strength and its weakness. We argue that progress beyond Kohn–Sham DFT involves the introduction of two-electron information and present intracules as a natural and concise source of this. We define special cases called the J- and K-intracules and discuss these in the context of both model systems and real molecules.

The calculation of magnetisabilities using current density functional theory

Abstract The theory for the calculation of magnetisabilities using current density functional theory, which follows from the original theory of Vignale, Rasolt and Geldart, has been implemented. We present an initial application of this theory to the set of small molecules H 2 , HF, N 2 , CO, H 2 O, and NH 3 .

Computation and analysis of molecular Hartree—Fock momentum intracules

An efficient general algorithm for the computation of molecular momentum intracule densities from Hartree-Fock wavefunctions using Gaussian basis functions is described. The momentum intracules for a number of systems are examined, and comparison with their position space counterparts discussed.