[Show abstract][Hide abstract] ABSTRACT: We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of four small molecules: N2, CO2, H2CO, and C2H4. The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.
[Show abstract][Hide abstract] ABSTRACT: We provide a pedagogical introduction to the two main variants of real-space
quantum Monte Carlo methods for electronic-structure calculations: variational
Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge
on the subject, we review in depth the Metropolis-Hastings algorithm used in
VMC for sampling the square of an approximate wave function, discussing details
important for applications to electronic systems. We also review in detail the
more sophisticated DMC algorithm within the fixed-node approximation,
introduced to avoid the infamous Fermionic sign problem, which allows one to
sample a more accurate approximation to the ground-state wave function.
Throughout this review, we discuss the statistical methods used for evaluating
expectation values and statistical uncertainties. In particular, we show how to
estimate nonlinear functions of expectation values and their statistical
uncertainties.
[Show abstract][Hide abstract] ABSTRACT: Quantum chemistry methods exploiting density-functional approximations for
short-range electron-electron interactions and second-order M{{\o}}ller-Plesset
(MP2) perturbation theory for long-range electron-electron interactions have
been implemented for periodic systems using Gaussian-type basis functions and
the local correlation framework. The performance of these range-separated
double hybrids has been benchmarked on a significant set of systems including
rare-gas, molecular, ionic, and covalent crystals. The use of
spin-component-scaled MP2 for the long-range part has been tested as well. The
results show that the value of $\mu$ = 0.5 bohr^{--1} for the range-separation
parameter usually used for molecular systems is also a reasonable choice for
solids. Overall, these range-separated double hybrids provide a good accuracy
for binding energies using basis sets of moderate sizes such as cc-pVDZ and
aug-cc-pVDZ.
The Journal of Chemical Physics 06/2015; 143(10). DOI:10.1063/1.4922996 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider several spin-unrestricted random-phase approximation (RPA) variants for calculating correlation
energies, with and without range separation, and test them on datasets of atomization energies and reaction barrier heights. We show that range separation greatly improves the accuracy of all RPA variants for these properties. Moreover, we show that a RPA variant with exchange, hereafter referred to as RPAx-SO2, first proposed by Szabo and Ostlund [J. Chem. Phys. 67, 4351 (1977)] in a spin-restricted closed-shell formalism, and extended here to a spin-unrestricted formalism, provides on average the most accurate range-separated RPA variant for atomization energies and reaction barrier heights. Since this range-separated RPAx-SO2 method had already been shown to be among the most accurate range-separated RPA variants for weak intermolecular interactions [J. Toulouse et al., J. Chem. Phys. 135, 084119 (2011)], this works confirms range-separated RPAx-SO2 as a promising method for general chemical applications.
The Journal of Chemical Physics 04/2015; 142(15):154123. DOI:10.1063/1.4918710 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this paper, an alternative method to range-separated linear-response
time-dependent density-functional theory and perturbation theory is proposed to
improve the estimation of the energies of a physical system from the energies
of a partially interacting system. Starting from the analysis of the Taylor
expansion of the energies of the partially interacting system around the
physical system, we use an extrapolation scheme to improve the estimation of
the energies of the physical system at an intermediate point of the
range-separated or linear adiabatic connection where either the
electron--electron interaction is scaled or only the long-range part of the
Coulomb interaction is included. The extrapolation scheme is first applied to
the range-separated energies of the helium and beryllium atoms and of the
hydrogen molecule at its equilibrium and stretched geometries. It improves
significantly the convergence rate of the energies toward their exact limit
with respect to the range-separation parameter. The range-separated
extrapolation scheme is compared with a similar approach for the linear
adiabatic connection, highlighting the relative strengths and weaknesses of
each approach.
Physical Review A 03/2015; 91(3). DOI:10.1103/PhysRevA.91.032519 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We explore the possibility of calculating electronic excited states by using
perturbation theory along a range-separated adiabatic connection. Starting from
the energies of a partially interacting Hamiltonian, a first-order correction
is defined with two variants of perturbation theory: a straight-forward
perturbation theory, and an extension of the G{\"o}rling--Levy one that has the
advantage of keeping the ground-state density constant at each order in the
perturbation. Only the first, simpler, variant is tested here on the helium and
beryllium atoms and on the dihydrogene molecule. The first-order correction
within this perturbation theory improves significantly the total ground-and
excited-state energies of the different systems. However, the excitation
energies are mostly deterio-rated with respect to the zeroth-order ones, which
may be explained by the fact that the ionization energy is no longer correct
for all interaction strengths. The second variant of the perturbation theory
should improve these results but has not been tested yet along the
range-separated adiabatic connection.
[Show abstract][Hide abstract] ABSTRACT: Range-separated density-functional theory
(DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum
L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number
X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.
The Journal of Chemical Physics 12/2014; 142(7). DOI:10.1063/1.4907920 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present a study of the variation of total energies and excitation energies along a range-separated adiabatic connection. This connection links the non-interacting Kohn-Sham electronic system to the physical interacting system by progressively switching on the electron-electron interactions whilst simultaneously adjusting a one-electron effective potential so as to keep the ground-state density constant. The interactions are introduced in a range-dependent manner, first introducing predominantly long-range, and then all-range, interactions as the physical system is approached, as opposed to the conventional adiabatic connection where the interactions are introduced by globally scaling the standard Coulomb interaction. Reference data are reported for the He and Be atoms and the H2 molecule, obtained by calculating the short-range effective potential at the full configuration-interaction level using Lieb's Legendre-transform approach. As the strength of the electron-electron interactions increases, the excitation energies, calculated for the partially interacting systems along the adiabatic connection, offer increasingly accurate approximations to the exact excitation energies. Importantly, the excitation energies calculated at an intermediate point of the adiabatic connection are much better approximations to the exact excitation energies than are the corresponding Kohn-Sham excitation energies. This is particularly evident in situations involving strong static correlation effects and states with multiple excitation character, such as the dissociating H2 molecule. These results highlight the utility of long-range interacting reference systems as a starting point for the calculation of excitation energies and are of interest for developing and analyzing practical approximate range-separated density-functional methodologies.
The Journal of Chemical Physics 07/2014; 141(4):044123. DOI:10.1063/1.4890652 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We test the performance of a number of two- and one-parameter double-hybrid
approximations, combining semilocal exchange-correlation density functionals
with periodic local second-order M{\o}ller-Plesset (LMP2) perturbation theory,
for calculating lattice energies of a set of molecular crystals: urea,
formamide, ammonia, and carbon dioxide. All double-hybrid methods perform
better on average than the corresponding Kohn-Sham calculations with the same
functionals, but generally not better than standard LMP2. The one-parameter
double-hybrid approximations based on the PBEsol density functional gives
lattice energies per molecule with an accuracy of about 6 kJ/mol, which is
similar to the accuracy of LMP2. This conclusion is further verified on
molecular dimers and on the hydrogen cyanide crystal.
The Journal of Chemical Physics 07/2014; 141(4):044105. DOI:10.1063/1.4890439 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Within exact electron density-functional theory, we investigate Kohn-Sham
(KS) potentials, orbital energies, and non-interacting kinetic energies of the
fractional ions of Li, C and F. We use quantum Monte Carlo densities as input,
which are then fitted, interpolated at non-integer electron numbers $N$, and
inverted to produce accurate KS potentials $v_s^N(r)$. We study the dependence
of the KS potential on $N$, and in particular we numerically confirm the
existence of the theoretically predicted spatially constant discontinuity of
$v_s^N(r)$ as $N$ passes through an integer. We further show that, for all the
cases considered, the inner orbital energies and the non-interacting kinetic
energy are nearly piecewise linear functions of $N$. This leads us to propose a
simple approximation of the KS potential $v_s^N(r)$ at any fractional electron
number $N$ which uses only quantities of the systems with the adjacent integer
electron numbers.
Physical Review A 07/2014; 90(5). DOI:10.1103/PhysRevA.90.050502 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We explore several random phase approximation (RPA) correlation energy
variants within the adiabatic-connection fluctuation-dissipation theorem
approach. These variants differ in the way the exchange interactions are
treated. One of these variants, named dRPA-II, is original to this work and
closely resembles the second-order screened exchange (SOSEX) method. We discuss
and clarify the connections among different RPA formulations. We derive the
spin-adapted forms of all the variants for closed-shell systems, and test them
on a few atomic and molecular systems with and without range separation of the
electron-electron interaction.
Journal of Chemical Theory and Computation 04/2014; 7(10-10). DOI:10.1021/ct200501r · 5.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-approximation (meta-GGA) exchange-correlation density functionals. We construct several variants of one-parameter double-hybrid approximations using the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional and test them on test sets of atomization energies and reaction barrier heights. The most accurate variant uses the uniform coordinate scaling of the density and of the kinetic energy density in the correlation functional, and improves over both standard Kohn-Sham TPSS and second-order Møller-Plesset calculations.
The Journal of Chemical Physics 02/2014; 140(8):084107. DOI:10.1063/1.4865963 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The alternative separation of exchange and correlation energies proposed by Toulouse et al. [Theor. Chem. Acc. 114, 305 (2005)] is explored in the context of multi-configuration range-separated density-functional theory. The new decomposition of the short-range exchange-correlation energy relies on the auxiliary long-range interacting wavefunction rather than the Kohn-Sham (KS) determinant. The advantage, relative to the traditional KS decomposition, is that the wavefunction part of the energy is now computed with the regular (fully interacting) Hamiltonian. One potential drawback is that, because of double counting, the wavefunction used to compute the energy cannot be obtained by minimizing the energy expression with respect to the wavefunction parameters. The problem is overcome by using short-range optimized effective potentials (OEPs). The resulting combination of OEP techniques with wavefunction theory has been investigated in this work, at the Hartree-Fock (HF) and multi-configuration self-consistent-field (MCSCF) levels. In the HF case, an analytical expression for the energy gradient has been derived and implemented. Calculations have been performed within the short-range local density approximation on H2, N2, Li2, and H2O. Significant improvements in binding energies are obtained with the new decomposition of the short-range energy. The importance of optimizing the short-range OEP at the MCSCF level when static correlation becomes significant has also been demonstrated for H2, using a finite-difference gradient. The implementation of the analytical gradient for MCSCF wavefunctions is currently in progress.
The Journal of Chemical Physics 10/2013; 139(13):134113. DOI:10.1063/1.4822135 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study linear-response time-dependent density-functional theory (DFT)
based on the single-determinant range-separated hybrid (RSH) scheme,
i.e. combining a long-range Hartree-Fock exchange kernel with a
short-range DFT exchange-correlation kernel, for calculating electronic
excitation energies of molecular systems. It is an alternative to the
long-range correction (LC) scheme which has a standard full-range DFT
correlation kernel instead of only a short-range one. We discuss the
local-density approximation (LDA) to the short-range
exchange-correlation kernel, and assess the performance of the
linear-response RSH scheme for singlet-singlet and singlet-triplet
valence and Rydberg excitations in the N2, CO, H2CO, C2H4, and C6H6
molecules, and for the first charge-transfer excitation in the C2H4-C2F4
dimer. The introduction of long-range HF exchange corrects the
underestimation of charge-transfer and high-lying Rydberg excitation
energies obtained with standard (semi)local density-functional
approximations, but also leads to underestimated excitation energies to
low-lying spin-triplet valence states which can be cured by the
Tamm-Dancoff approximation. This work thus suggests that the present
linear-response RSH scheme is a reasonable starting approximation for
describing electronic excitation energies, even before adding an
explicit treatment of long-range correlation.
[Show abstract][Hide abstract] ABSTRACT: We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of range-separated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.
The Journal of Chemical Physics 05/2013; 138(19):194106. DOI:10.1063/1.4804981 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We review the Bethe-Salpeter equation (BSE) approach to the calculation
of electronic excitation energies of molecular systems. We recall the
general Green's function many-theory formalism and give the working
equations of the BSE approach within the static GW approximation with
and without spin adaptation in an orbital basis. We apply the method to
the pedagogical example of the H2 molecule in a minimal basis, testing
the effects of the choice of the starting one-particle Green's function.
Using the non-interacting one-particle Green's function leads to
incorrect energy curves for the first singlet and triplet excited states
in the dissociation limit. Starting from the exact one-particle Green's
function leads to a qualitatively correct energy curve for the first
singlet excited state, but still an incorrect energy curve for the
triplet excited state. Using the exact one-particle Green's function in
the BSE approach within the static GW approximation also leads to a
number of additional excitations, all of them being spurious except for
one which can be identified as a double excitation corresponding to the
second singlet excited state.
[Show abstract][Hide abstract] ABSTRACT: We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension of the usual hybrid approximations by essentially adding a fraction λ of exact static correlation in addition to the fraction λ of exact exchange. Test calculations on the cycloaddition reactions of ozone with ethylene or acetylene and the dissociation of diatomic molecules with the Perdew-Burke-Ernzerhof and Becke-Lee-Yang-Parr density functionals show that a good value of λ is 0.25, as in the usual hybrid approximations. The results suggest that the proposed multiconfigurational hybrid approximations can improve over usual density-functional calculations for situations with strong static correlation effects.
The Journal of Chemical Physics 07/2012; 137(4):044104. DOI:10.1063/1.4733672 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.
The Journal of Chemical Physics 03/2012; 136(12):124116. DOI:10.1063/1.3697846 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We provide a rationale for a new class of double-hybrid approximations
introduced by Br\'emond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which
combine an exchange-correlation density functional with Hartree-Fock exchange
weighted by $\l$ and second-order M{\o}ller-Plesset (MP2) correlation weighted
by $\l^3$. We show that this double-hybrid model can be understood in the
context of the density-scaled double-hybrid model proposed by Sharkas et al.
[J. Chem. Phys. 134, 064113 (2011)], as approximating the density-scaled
correlation functional $E_c[n_{1/\l}]$ by a linear function of $\l$,
interpolating between MP2 at $\l=0$ and a density-functional approximation at
$\l=1$. Numerical results obtained with the Perdew-Burke-Ernzerhof density
functional confirms the relevance of this double-hybrid model.
The Journal of Chemical Physics 09/2011; 135(10):101102. DOI:10.1063/1.3640019 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We explore different variants of the random phase approximation to the correlation energy derived from closed-shell ring-diagram approximations to coupled cluster doubles theory. We implement these variants in range-separated density-functional theory, i.e., by combining the long-range random phase approximations with short-range density-functional approximations. We perform tests on the rare-gas dimers He(2), Ne(2), and Ar(2), and on the weakly interacting molecular complexes of the S22 set of Jurečka et al. [P. Jurečka, J. Šponer, J. Černý, and P. Hobza, Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The two best variants correspond to the ones originally proposed by Szabo and Ostlund [A. Szabo and N. S. Ostlund, J. Chem. Phys. 67, 4351 (1977)]. With range separation, they reach mean absolute errors on the equilibrium interaction energies of the S22 set of about 0.4 kcal/mol, corresponding to mean absolute percentage errors of about 4%, with the aug-cc-pVDZ basis set.
The Journal of Chemical Physics 08/2011; 135(8):084119. DOI:10.1063/1.3626551 · 2.95 Impact Factor