pinecone/core-2020-05-10-deduplication huggingface dataset:
Orbital entanglement in quantum chemistry

The basic concepts of orbital entanglement and its application to chemistry
are briefly reviewed. The calculation of orbital entanglement measures from
correlated wavefunctions is discussed in terms of reduced $n$-particle density
matrices. Possible simplifications in their evaluation are highlighted in case
of seniority-zero wavefunctions. Specifically, orbital entanglement allows us
to dissect electron correlation effects in its strong and weak contributions,
to determine bond orders, to assess the quality and stability of active space
calculations, to monitor chemical reactions, and to identify points along the
reaction coordinate where electronic wavefunctions change drastically. Thus,
orbital entanglement represents a useful and intuitive tool to interpret
complex electronic wavefunctions and to facilitate a qualitative understanding
of electronic structure and how it changes in chemical processes.Comment: 7 pages, 2 figure
Magic State Distillation and Gate Compilation in Quantum Algorithms for
  Quantum Chemistry

Quantum algorithms for quantum chemistry map the dynamics of electrons in a
molecule to the dynamics of a coupled spin system. To reach chemical accuracy
for interesting molecules, a large number of quantum gates must be applied
which implies the need for quantum error correction and fault-tolerant quantum
computation. Arbitrary fault-tolerant operations can be constructed from a
small, universal set of fault-tolerant operations by gate compilation. Quantum
chemistry algorithms are compiled by decomposing the dynamics of the coupled
spin-system using a Trotter formula, synthesizing the decomposed dynamics using
Clifford operations and single-qubit rotations, and finally approximating the
single-qubit rotations by a sequence of fault-tolerant single-qubit gates.
Certain fault-tolerant gates rely on the preparation of specific single-qubit
states referred to as magic states. As a result, gate compilation and magic
state distillation are critical for solving quantum chemistry problems on a
quantum computer. We review recent progress that has improved the efficiency of
gate compilation and magic state distillation by orders of magnitude.Comment: 17 pages, 3 figures, 1 table in Int. J. Quantum Chem. 201
Quantum chemical studies of asymmetric reactions: Historical aspects and recent examples

This is the peer reviewed version of the following article: K. H., Hopmann Int. J. Quantum Chem. 2015, 115, 1232–1249. DOI: 10.1002/qua.24882, which has been published in final form at <a href=http://dx.doi.org/10.1002/qua.24882>http://dx.doi.org/10.1002/qua.24882</a>. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Asymmetric catalysis is essential for the synthesis of chiral compounds such as pharmaceuticals,
agrochemicals, fragrances, and flavors. For rational improvement of asymmetric reactions, detailed
mechanistic insights are required. The usefulness of quantum mechanical (QM) studies for understanding
the stereocontrol of asymmetric reactions was first demonstrated around 40 years ago,
with impressive developments since then: from single-point Hartree-Fock/STO-3G calculations on
small organic molecules (1970s), to the first full reaction pathway involving a metal-complex (1980s),
to the beginning of the density functional theory (DFT)-area, albeit typically involving truncated
models (1990s), to current state-of-the-art calculations reporting free energies of complete organometallic
systems, including solvent and dispersion corrections. The combined studies show that the
stereocontrol in asymmetric reactions largely is exerted by non-bonding interactions, including CH/π
attraction and repulsive forces. The ability to rationalize experimental results opens up for the
possibility to predict enantioselectivities or to design novel catalysts on basis of in silico results
A general method to describe intersystem crossing dynamics in trajectory
  surface hopping

Intersystem crossing is a radiationless process that can take place in a
molecule irradiated by UV-Vis light, thereby playing an important role in many
environmental, biological and technological processes. This paper reviews
different methods to describe intersystem crossing dynamics, paying attention
to semiclassical trajectory theories, which are especially interesting because
they can be applied to large systems with many degrees of freedom. In
particular, a general trajectory surface hopping methodology recently developed
by the authors, which is able to include non-adiabatic and spin-orbit couplings
in excited-state dynamics simulations, is explained in detail. This method,
termed SHARC, can in principle include any arbitrary coupling, what makes it
generally applicable to photophysical and photochemical problems, also those
including explicit laser fields. A step-by-step derivation of the main
equations of motion employed in surface hopping based on the fewest-switches
method of Tully, adapted for the inclusion of spin-orbit interactions, is
provided. Special emphasis is put on describing the different possible choices
of the electronic bases in which spin-orbit can be included in surface hopping,
highlighting the advantages and inconsistencies of the different approaches.Comment: 47 pages, 4 figure
Gaussian Approximation Potentials: a brief tutorial introduction

We present a swift walk-through of our recent work that uses machine learning to  t
interatomic potentials based on quantum mechanical data. We describe our Gaussian
Approximation Potentials (GAP) framework, discuss a variety of descriptors, how to
train the model on total energies and derivatives and the simultaneous use of multiple
models of di erent complexity. We also show a small example using QUIP, the software
sandbox implementation of GAP that is available for non-commercial use.
1A.P.B. is supported by a Leverhulme Early Career Fellowship and the Isaac Newton Trust.
We would like to thank our referees for their comments during the revision process.This is the author accepted manuscript. The final version is available via Wiley at http://onlinelibrary.wiley.com/doi/10.1002/qua.24927/abstract
Geometric phases in quantum information

The rise of quantum information science has opened up a new venue for
applications of the geometric phase (GP), as well as triggered new insights
into its physical, mathematical, and conceptual nature. Here, we review this
development by focusing on three main themes: the use of GPs to perform robust
quantum computation, the development of GP concepts for mixed quantum states,
and the discovery of a new type of topological phases for entangled quantum
systems. We delineate the theoretical development as well as describe recent
experiments related to GPs in the context of quantum information.Comment: Minor changes, journal reference adde
Spherical-harmonics expansion method for density-matrix simulations of quantum electron dynamics in continuum states

Article first published online: 10 AUG 2015Spherical-harmonics expansion method is proposed to solve the quantum time-evolution equations for density matrices numerically in momentum space. This method facilitates efficient real-time simulations of quantum electron dynamics in continuum states through extension of our previous formalism developed for discrete states. Numerical accuracy and efficiency are demonstrated through two examples: (i) multiphoton ionization of a one-electron atom in intense laser field, and (ii) real-time dynamics of plasma oscillations in electron liquids. In case (i), coupled dynamics of density matrices for bound and continuum states reveals an enhancement of multiphoton ionization over the Keldysh approximation through resonant intermediate states
Resonating Valence Bond Quantum Monte Carlo: Application to the ozone
  molecule

We study the potential energy surface of the ozone molecule by means of
Quantum Monte Carlo simulations based on the resonating valence bond concept.
The trial wave function consists of an antisymmetrized geminal power arranged
in a single-determinant that is multiplied by a Jastrow correlation factor.
Whereas the determinantal part incorporates static correlation effects, the
augmented real-space correlation factor accounts for the dynamics electron
correlation. The accuracy of this approach is demonstrated by computing the
potential energy surface for the ozone molecule in three vibrational states:
symmetric, asymmetric and scissoring. We find that the employed wave function
provides a detailed description of rather strongly-correlated multi-reference
systems, which is in quantitative agreement with experiment.Comment: 5 page, 3 figure
Theoretical study of atoms by the electronic kinetic energy density and
  stress tensor density

We analyze the electronic structure of atoms in the first, second and third
periods using the electronic kinetic energy density and stress tensor density,
which are local quantities motivated by quantum field theoretic consideration,
specifically the rigged quantum electrodynamics. We compute the zero surfaces
of the electronic kinetic energy density, which we call the electronic
interfaces, of the atoms. We find that their sizes exhibit clear periodicity
and are comparable to the conventional atomic and ionic radii. We also compute
the electronic stress tensor density and its divergence, tension density, of
the atoms, and discuss how their electronic structures are characterized by
them.Comment: 29 pages, 6 figure
Density-Matrix Propagation Driven by Semiclassical Correlation

Methods based on propagation of the one-body reduced density-matrix hold much
promise for the simulation of correlated many-electron dynamics far from
equilibrium, but difficulties with finding good approximations for the
interaction term in its equation of motion have so far impeded their
application. These difficulties include the violation of fundamental physical
principles such as energy conservation, positivity conditions on the density,
or unchanging natural orbital occupation numbers. We review some of the recent
efforts to confront these problems, and explore a semiclassical approximation
for electron correlation coupled to time-dependent Hartree-Fock propagation. We
find that this approach captures changing occupation numbers, and excitations
to doubly-excited states, improving over TDHF and adiabatic approximations in
density-matrix propagation. However, it does not guarantee $N$-representability
of the density-matrix, consequently resulting sometimes in violation of
positivity conditions, even though a purely semiclassical treatment preserves
these conditions.Comment: Submitted to Int. J. Quant. Che
Recent advances in solid-state NMR computational spectroscopy: The case of alumino-silicate glasses

Solid-state NMR spectroscopy and computational approaches such as Molecular Dynamics (MD) simulations and Density Functional Theory have proven to be very useful and versatile techniques for studying the structure and the dynamics of noncrystalline materials if a direct comparison between experiment and theory is established. In this review, the basic concepts in first-principle modeling of solid-state NMR spectra of oxide glasses are presented. There are three theoretical ingredients in the computational recipe. First, classical or ab initio molecular dynamics simulations are employed to generate the structural models of the glasses of interest. Second, periodic Density Functional Theory calculations coupled with the gauge including projector augmented-wave (GIPAW) algorithm form the basis for the ab initio calculations of NMR parameters (chemical shielding and quadrupolar parameters). Finally, Spin-effective Hamiltonian are employed to simulate the solid-state NMR spectra directly comparable with the experimental counterparts. As an example of this methodology, the investigation of the local and medium range structure of Na-Ca silicate and aluminosilicate glasses that are usually employed as simplified models for basaltic, andesitic and rhyolitic magmas will be reported. We will show how the direct comparison of the theoretical NMR spectra of MD derived structural models with the experimental counterparts allows gaining new insights into the atomistic structure of very complex oxide glasses
Comment on "Benchmarking Compressed Sensing, Super-Resolution, and
  Filter Diagonalization"

In a recent paper [Int. J. Quant. Chem. (2016) DOI: 10.1002/qua.25144,
arXiv:1502.06579] Markovich, Blau, Sanders, and Aspuru-Guzik presented a
numerical evaluation and comparison of three methods, Compressed Sensing (CS),
Super-Resolution (SR), and Filter Diagonalization (FDM), on their ability of
"recovering information" from time signals, concluding that CS and RS
outperform FDM. We argue that this comparison is invalid for the following
reasons. FDM is a well established method designed for solving the harmonic
inversion problem or, similarly, for the problem of spectral estimation, and as
such should be applied only to problems of this kind. The authors incorrectly
assume that the problem of data fitting is equivalent to the spectral
estimation problem, regardless of what parametric form is used, and,
consequently, in all five numerical examples FDM is applied to the wrong
problem. Moreover, the authors' implementation of FDM turned out to be
incorrect, leading to extremely bad results, caused by numerical instabilities.
As we demonstrate here, if implemented correctly, FDM could still be used for
fitting the data, at least for the time signals composed of damped sinusoids,
resulting in superior performance. In addition, we show that the published
article is full of inaccuracies, mistakes and incorrect statements.Comment: 4 pages, 2 figure
Gaussian continuum basis functions for calculating high-harmonic
  generation spectra

We explore the computation of high-harmonic generation spectra by means of
Gaussian basis sets in approaches propagating the time-dependent
Schr{\"o}dinger equation. We investigate the efficiency of Gaussian functions
specifically designed for the description of the continuum proposed by Kaufmann
et al. [J. Phys. B 22, 2223 (1989)]. We assess the range of applicability of
this approach by studying the hydrogen atom, i.e. the simplest atom for which
"exact" calculations on a grid can be performed. We notably study the effect of
increasing the basis set cardinal number, the number of diffuse basis
functions, and the number of Gaussian pseudo-continuum basis functions for
various laser parameters. Our results show that the latter significantly
improve the description of the low-lying continuum states, and provide a
satisfactory agreement with grid calculationsfor laser wavelengths $\lambda$0 =
800 and 1064 nm. The Kaufmann continuum functions therefore appear as a
promising way of constructing Gaussian basis sets for studying molecular
electron dynamics in strong laser fields using time-dependent quantum-chemistry
approaches
The ExoMol project: Software for computing large molecular line lists

The use of variational nuclear motion programs to compute line lists of
transition frequencies and intensities is now a standard procedure. The ExoMol
project has used this technique to generate line lists for studies of hot
bodies such as the atmospheres of exoplanets and cool stars. The resulting line
list can be huge: many contain 10 billion or more transitions. This software
update considers changes made to our programs during the course of the project
to allow for such calculations. This update considers three programs: {\sc Duo}
which computed vibronic spectra for diatomics, {\sc DVR3D} which computes
rotation-vibration spectra for triatomics, and {\sc TROVE} which computes
rotation-vibration spectra for general polyatomic systems. Important updates in
functionality include the calculation of quasibound (resonance) states and
Land\'e $g$-factors by {\sc Duo} and the calculation of resonance states by
{\sc DVR3D}. Significant algorithmic improvements are reported for both {\sc
DVR3D} and {\sc TROVE}. All three programs are publically available from
ccpforge.cse.rl.ac.uk. Future developments are also considered.Comment: 27 pages, 4 figure, 0 tables. Internat. J Quantum Chem (in press)
  Software News & Update articl
Machine Learning for Atomic Forces in a Crystalline Solid:
  Transferability to Various Temperatures

Recently, machine learning has emerged as an alternative, powerful approach
for predicting quantum-mechanical properties of molecules and solids. Here,
using kernel ridge regression and atomic fingerprints representing local
environments of atoms, we trained a machine-learning model on a crystalline
silicon system in order to directly predict the atomic forces at a wide range
of temperatures. Our idea is to construct a machine-learning model using a
quantum-mechanical data set taken from canonical-ensemble simulations at a
higher temperature, or an upper bound of the temperature range. With our model,
the force prediction errors were about 2% or smaller with respect to the
corresponding force ranges, in the temperature region between 300 and 1650 K.
We also verified the applicability to a larger system, ensuring the
transferability with respect to system size.Comment: 20pages, 5 figure
Entropic measures of Rydberg-like harmonic states

The Shannon entropy, the desequilibrium and their generalizations (R\'enyi
and Tsallis entropies) of the three-dimensional single-particle systems in a
spherically-symmetric potential $V(r)$ can be decomposed into angular and
radial parts. The radial part depends on the analytical form of the potential,
but the angular part does not. In this paper we first calculate the angular
entropy of any central potential by means of two analytical procedures. Then,
we explicitly find the dominant term of the radial entropy for the highly
energetic (i.e., Rydberg) stationary states of the oscillator-like systems. The
angular and radial contributions to these entropic measures are analytically
expressed in terms of the quantum numbers which characterize the corresponding
quantum states and, for the radial part, the oscillator strength. In the latter
case we use some recent powerful results of the information theory of the
Laguerre polynomials and spherical harmonics which control the oscillator-like
wavefunctions.Comment: Accepted in International Journal of Quantum Chemistr
On the origin of the relative stability of Zn(II)NTA and Zn(II)NTPA metal complexes. An insight from the IQA, IQF, and pi-FARMS methods

Relative stability of ZnII complexes with nitrilotriacetic acid (ZnNTA) and nitrilotri-3-propionic acid (ZnNTPA) was investigated. Classical analysis of individual interactions using local indices failed to explain the preferential formation of ZnNTA. This work shows that the preferential formation of ZnNTA is not due to the size of coordination 5-membered rings or the absence of the steric CH--HC contacts, as commonly considered. By combining Interacting Quantum Atoms/Fragments, IQA/IQF-defined properties implemented in the π-FARMS (Preorganized-interacting Fragment Attributed Relative Molecular Stability) method, (i) several measures of ZnII „affinity‟ to NTPA were shown to be consistently greater than to NTA and (ii) larger stability of ZnNTA was attributed to coordinated water molecules. Being smaller, NTA occupies less space around the metal centre. This results in less destabilised Zn–OH2 coordination bonds and preorganization energy of H2O fragments being smaller in ZnNTA. Only by summing preorganization energies (of ligand and water fragments) and binding energy between fragments (using π-FARMS method) we recovered the experimental trend. Importantly, the fundamental origin of all major energy components controlling relative stability of metal complexes was pin-pointed using the π-FARMS method.The National Research Foundation of South Africa (Grant Numbers 87777) and the University of Pretoria.http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-461X2018-02-28hb2017Chemistr
Comment on "The Rotation-Vibration Spectrum of Diatomic Molecules with
  the Tietz-Hua Rotating Oscillator"

We present arguments demonstrating that the application of the
Nikiforov-Uvarov polynomial method to solve the Schr\"odinger equation with the
Tietz-Hua potential is valid only when $e^{-b_{h}r_{e}}\leq c_{h}<1$ and
$r_{0}<r<+\infty $. In particular, it is pointed out that the numerical results
with $c_{h}\neq 0$ for the diatomic molecules $\mathrm{HF}$, $\mathrm{N}_{2}$,
$\mathrm{I}_{2}$, $\mathrm{H}_{2}$, $\mathrm{O}_{2}$ and $\mathrm{O}_{2}^{+}$
given in Tables 3-5 by Hamzavi and co-workers are wrong. When $-1\leq c_{h}<0$
or $0<c_{h}<e^{-b_{h}r_{e}}$, this approach is not suitable. In both cases, it
is shown that the solutions of the Schr\"odinger equation are expressed in
terms of the generalized hypergeometric functions $_{2}F_{1}\left(
a,b,c;z\right) $. The determination of the energy levels requires the solution
of transcendantal equations involving the hypergeometric function by means of
the numerical procedure.Comment: 7 pages, no figure
Kinetic Energy Density Functionals by Axiomatic Approach

An axiomatic approach is herein used to determine the physically acceptable
forms for general $D$-dimensional kinetic energy density functionals (KEDF).
The resulted expansion captures most of the known forms of one-point KEDFs. By
statistically training the KEDF forms on a model problem of non-interacting
kinetic energy in 1D (6 terms only), the mean relative accuracy for 1000
randomly generated potentials is found to be better than the standard KEDF by
several orders of magnitudes. The accuracy improves with the number of occupied
states and was found to be better than $10^{-4}$ for a system with four
occupied states. Furthermore, we show that free fitting of the coefficients
associated with known KEDFs approaches the exactly analytic values. The
presented approach can open a new route to search for physically acceptable
kinetic energy density functionals and provide an essential step towards more
accurate large-scale orbital free density functional theory calculations
Numerical Methods for the Inverse Problem of Density Functional Theory

The inverse problem of Kohn-Sham density functional theory (DFT) is often
solved in an effort to benchmark and design approximate exchange-correlation
potentials. The forward and inverse problems of DFT rely on the same equations
but the numerical methods for solving each problem are substantially different.
We examine both problems in this tutorial with a special emphasis on the
algorithms and error analysis needed for solving the inverse problem. Two
inversion methods based on partial differential equation constrained
optimization and constrained variational ideas are introduced. We compare and
contrast several different inversion methods applied to one-dimensional finite
and periodic model systems.Comment: 62 pages, 22 figure
A sobering assessment of small-molecule force field methods for low energy conformer predictions

© 2017 Wiley Periodicals, Inc. We have carried out a large scale computational investigation to assess the utility of common small-molecule force fields for computational screening of low energy conformers of typical organic molecules. Using statistical analyses on the energies and relative rankings of up to 250 diverse conformers of 700 different molecular structures, we find that energies from widely used classical force fields (MMFF94, UFF, and GAFF) show unconditionally poor energy and rank correlation with semiempirical (PM7) and Kohn–Sham density functional theory (DFT) energies calculated at PM7 and DFT optimized geometries. In contrast, semiempirical PM7 calculations show significantly better correlation with DFT calculations and generally better geometries. With these results, we make recommendations to more reliably carry out conformer screening