2,223 research outputs found
Relativistic Cholesky-decomposed density matrix MP2
In the present article, we introduce the relativistic Cholesky-decomposed
density (CDD) matrix second-order M{\o}ller-Plesset perturbation theory (MP2)
energies. The working equations are formulated in terms of the usual
intermediates of MP2 when employing the resolution-of-the-identity
approximation (RI) for two-electron integrals. Those intermediates are obtained
by substituting the occupied and virtual quaternion pseudo-density matrices of
our previously proposed two-component atomic orbital-based MP2 (J. Chem. Phys.
145, 014107 (2016)) by the corresponding pivoted quaternion Cholesky factors.
While working within the Kramers-restricted formalism, we obtain a formal
spin-orbit overhead of 16 and 28 for the Coulomb and exchange contribution to
the 2C MP2 correlation energy, respectively, compared to a non-relativistic
(NR) spin-free CDD-MP2 implementation. This compact quaternion formulation
could also be easily explored in any other algorithm to compute the 2C MP2
energy. The quaternion Cholesky factors become sparse for large molecules and,
with a block-wise screening, block sparse-matrix multiplication algorithm, we
observed an effective quadratic scaling of the total wall time for
heavy-element containing linear molecules with increasing system size. The
total run time for both 1C and 2C calculations was dominated by the contraction
to the exchange energy. We have also investigated a bulky Te-containing
supramolecular complex. For such bulky, three-dimensionally extended molecules
the present screening scheme has a much larger prefactor and is less effective
GW100: A Slater Type Orbital Perspective
We calculate complete basis set (CBS) limit extrapolated ionization
potentials (IP) and electron affinities (EA) with Slater Type Basis sets for
the molecules in the GW100 database. To this end, we present two new Slater
Type orbital (STO) basis sets of triple- (TZ) and quadruple- (QZ)
quality whose polarization is adequate for correlated-electron methods and
which contain extra diffuse functions to be able to correctly calculate
electron affinities of molecules with a positive Lowest Unoccupied Molecular
Orbital (LUMO). We demonstrate, that going from TZ to QZ quality consistently
reduces the basis set error of our computed IPs and EAs and we conclude that a
good estimate of these quantities at the CBS limit can be obtained by
extrapolation. With MADs from 70 to 85 meV, our CBS limit extrapolated
ionization potentials are in good agreement with results from FHI-AIMS,
TURBOMOLE, VASP and WEST while they differ by more than 130 meV on average from
nanoGW. With a MAD of 160 meV, our electron affinities are also in good
agreement with the WEST code. Especially for systems with positive LUMOs, the
agreement is excellent. With respect to other codes, the STO type basis sets
generally underestimate EAs of small molecules with strongly bound LUMOs. With
62 meV for IPs and 93 meV for EAs, we find much better agreement to CBS limit
extrapolated results from FHI-AIMS for a set of 250 medium to large organic
molecules.Comment: Published open access by Journal of chemical theory and computatio
Low-order Scaling by Pair Atomic Density Fitting
We derive a low-scaling algorithm for molecules, using pair atomic
density fitting (PADF) and an imaginary time representation of the Green's
function and describe its implementation in the Slater type orbital (STO) based
Amsterdam density functional (ADF) electronic structure code. We demonstrate
the scalability of our algorithm on a series of water clusters with up to 432
atoms and 7776 basis functions and observe asymptotic quadratic scaling with
realistic threshold qualities controlling distance effects and basis sets of
triple- (TZ) plus double polarization quality. Also owing to a very
small prefactor, with these settings a calculation for the largest of
these clusters takes only 240 CPU hours. With errors of 0.24 eV for HOMO
energies in the GW100 database on the quadruple- level, our
implementation is less accurate than canonical all-electron implementations
using the larger def2-QZVP GTO-tpye basis set. Apart from basis set errors,
this is related to the well-known shortcomings of the GW space-time method
using analytical continuation techniques as well as to numerical issues of the
PADF-approach of accurately representing diffuse AO-products. We speculate,
that these difficulties might be overcome by using optimized auxiliary fit sets
with more diffuse functions of higher angular momenta. Despite these
shortcomings, for subsets of medium and large molecules from the GW5000
database, the error of our approach using basis sets of TZ and augmented DZ
quality is decreasing with system size. On the augmented DZ level we reproduce
canonical, complete basis set limit extrapolated reference values with an
accuracy of 80 meV on average for a set of 20 large organic molecules. We
anticipate our algorithm, in its current form, to be very useful in the study
of single-particle properties of large organic systems such as chromophores and
acceptor molecules.Comment: final version as accepted by JCTC
https://pubs.acs.org/doi/10.1021/acs.jctc.0c0069
Exploring the statically screened G3W2 correction to the GW self-energy: Charged excitations and total energies of finite systems
Electron correlation in finite and extended systems is often described in an
effective single-particle framework within the approximation. Here, we use
the statically screened second-order exchange contribution to the self-energy
() to calculate a perturbative correction to the self-energy. We use
this correction to calculate total correlation energies of atoms, relative
energies, as well as charged excitations of a wide range of molecular systems.
We show that the second-order correction improves correlation energies with
respect to the RPA and also improves relative energies for many, but not all
considered systems. While the full contribution does not give consistent
improvements over , taking the average of and generally
gives excellent results. Improvements over quasiparticle self-consistent ,
which we show to give very accurate charged excitations in small and medium
molecules by itself, are only minor. quasiparticle energies evaluated
with eigenvalue and orbitals from range-separated hybrids, however, are
tremendously improved upon: The second-order corrected outperforms all
existing methods for the systems considered herein and also does not come
with substantially increased computational cost compared to for
systems with up to 100 atoms.Comment: Revised version as accepted by Physical review B (Phys. Rev. B 2022,
105, 125121, 10.1103/PhysRevB.105.125121) Compared to our first submission, a
programming mistake in our first implementation has been corrected leading to
different (better) result
Characterization of Excited States in Time-Dependent Density Functional Theory Using Localized Molecular Orbitals
Localized molecular orbitals are often used for the analysis of chemical
bonds, but they can also serve to efficiently and comprehensibly compute linear
response properties. While conventional canonical molecular orbitals provide an
adequate basis for the treatment of excited states, a chemically meaningful
identification of the different excited-state processes is difficult within
such a delocalized orbital basis. In this work, starting from an initial set of
supermolecular canonical molecular orbitals, we provide a simple one-step
top-down embedding procedure for generating a set of orbitals which are
localized in terms of the supermolecule, but delocalized over each subsystem
composing the supermolecule. Using an orbital partitioning scheme based on such
sets of localized orbitals, we further present a procedure for the construction
of local excitations and charge-transfer states within the linear response
framework of time-dependent density functional theory (TDDFT). This procedure
provides direct access to approximate diabatic excitation energies and, under
the Tamm--Dancoff approximation, also their corresponding electronic couplings
-- quantities that are of primary importance in modelling energy transfer
processes in complex biological systems. Our approach is compared with a
recently developed diabatization procedure based on subsystem TDDFT using
projection operators, which leads to a similar set of working equations.
Although both of these methods differ in the general localization strategies
adopted and the type of basis functions (Slaters vs. Gaussians) employed, an
overall decent agreement is obtained
Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets
The superposition of atomic potentials (SAP) approach has recently been shown
to be a simple and efficient way to initialize electronic structure
calculations [S. Lehtola, J. Chem. Theory Comput. 15, 1593 (2019)]. Here, we
study the differences between effective potentials from fully numerical density
functional and optimized effective potential calculations for fixed
configurations. We find that the differences are small, overall, and choose
exchange-only potentials at the local density approximation level of theory
computed on top of Hartree-Fock densities as a good compromise. The differences
between potentials arising from different atomic configurations are also found
to be small at this level of theory.
Furthermore, we discuss the efficient Gaussian-basis implementation of SAP
via error function fits to fully numerical atomic radial potentials. The guess
obtained from the fitted potentials can be easily implemented in any
Gaussian-basis quantum chemistry code in terms of two-electron integrals. Fits
covering the whole periodic table from H to Og are reported for
non-relativistic as well as fully relativistic four-component calculations that
have been carried out with fully numerical approaches.Comment: 12 pages, 8 figure
Analytic one-electron properties at the 4-component relativistic coupled cluster level with inclusion of spin-orbit coupling
International audienceArticles you may be interested in Description of spin-orbit coupling in excited states with two-component methods based on approximate coupled-cluster theory An ab initio two-component relativistic method including spin-orbit coupling using the regular approximation We present a formulation and implementation of the calculation of (orbital-unrelaxed) expectation values at the 4-component relativistic coupled cluster level with spin-orbit coupling included from the start. The Lagrangian-based analytical energy derivative technique constitutes the basic theoretical framework of this work. The key algorithms for single reference relativistic coupled cluster have been implemented using routines for general tensor contractions of up to rank-2 tensors in which the direct product decomposition scheme is employed to benefit from double group symmetry. As a sample application, we study the electric field gradient at the bismuth nucleus in the BiX (X = N, P) series of molecules, where the effect of spin-orbit coupling is substantial. Our results clearly indicate that the current reference value for the nuclear quadrupole moment of 209 Bi needs revision. We also have applied our method to the calculation of the parity violating energy shift of chiral molecules. The latter property is strictly zero in the absence of spin-orbit coupling. For the H 2 X 2 (X = O,S,Se,Te) series of molecules the effect of correlation is found to be quite small. Published by AIP Publishing. [http://dx
Relativistic general-order coupled-cluster method for high-precision calculations: Application to Al+ atomic clock
We report the implementation of a general-order relativistic coupled-cluster
method for performing high-precision calculations of atomic and molecular
properties. As a first application, the static dipole polarizabilities of the
ground and first excited states of Al+ have been determined to precisely
estimate the uncertainty associated with the BBR shift of its clock frequency
measurement. The obtained relative BBR shift is -3.66+-0.44 for the 3s^2
^1S_0^0 --> 3s3p ^3P_0^0 transition in Al+ in contrast to the value obtained in
the latest clock frequency measurement, -9+-3 [Phys. Rev. Lett. 104, 070802
(2010)]. The method developed in the present work can be employed to study a
variety of subtle effects such as fundamental symmetry violations in atoms.Comment: 4 pages, 3 tables, submitte
Tight-binding approximations to time-dependent density functional theory: A fast approach for the calculation of electronically excited states
We propose a new method of calculating electronically excited states that combines a density functional theory based ground state calculation with a linear response treatment that employs approximations used in the time-dependent density functional based tight binding (TD-DFTB) approach. The new method termed time-dependent density functional theory TD-DFT+TB does not rely on the DFTB parametrization and is therefore applicable to systems involving all combinations of elements. We show that the new method yields UV/Vis absorption spectra that are in excellent agreement with computationally much more expensive TD-DFT calculations. Errors in vertical excitation energies are reduced by a factor of two compared to TD-DFTB
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