Computational Benchmarking for Ultrafast Electron Dynamics: Wave Function Methods vs Density Functional Theory.

Attosecond electron dynamics in small- and medium-sized molecules, induced by an ultrashort strong optical pulse, is studied computationally for a frozen nuclear geometry. The importance of exchange and correlation effects on the nonequilibrium electron dynamics induced by the interaction of the molecule with the strong optical pulse is analyzed by comparing the solution of the time-dependent Schrödinger equation based on the correlated field-free stationary electronic states computed with the equationof-motion coupled cluster singles and doubles and the complete active space multi-configurational self-consistent field methodologies on one hand, and various functionals in real-time time-dependent density functional theory (TDDFT) on the other. We aim to evaluate the performance of the latter approach, which is very widely used for nonlinear absorption processes and whose computational cost has a more favorable scaling with the system size. We focus on LiH as a toy model for a nontrivial molecule and show that our conclusions carry over to larger molecules, exemplified by ABCU (C10H19N). The molecules are probed with IR and UV pulses whose intensities are not strong enough to significantly ionize the system. By comparing the evolution of the time-dependent field-free electronic dipole moment, as well as its Fourier power spectrum, we show that TD-DFT performs qualitatively well in most cases. Contrary to previous studies, we find almost no changes in the TD-DFT excitation energies when excited states are populated. Transitions between states of different symmetries are induced using pulses polarized in different directions. We observe that the performance of TD-DFT does not depend on the symmetry of the states involved in the transition.

New implementation of high-level correlated methods using a general block tensor library for high-performance electronic structure calculations.

This article presents an open-source object-oriented C++ library of classes and routines to perform tensor algebra.The primary purpose of the library is to enable post-Hartree­Fock electronic structure methods; however, the code is general enough to be applicable in other areas of physical and computational sciences. The library supports tensors of arbitrary order (dimensionality), size, and symmetry. Implemented data structures and algorithms operate on large tensors by splitting them into smaller blocks, storing them both in core memory and in files on disk, and applying divide-and-conquer-type parallel algorithms to perform tensor algebra. The library offers a set of general tensor symmetry algorithms and a full implementation of tensor symmetries typically found in electronic structure theory: permutational, spin, and molecular point group symmetry. The Q-Chem electronic structure software uses this library to drive coupled-cluster, equation-of-motion, and algebraic-diagrammatic construction methods.

De-perturbative corrections for charge-stabilized double ionization potential equation-of-motion coupled-cluster method.

Charge stabilization improves the numeric performance of double ionization potential equation-of-motion (EOM-DIP) method when using unstable (autoionizing) dianion references. However, the stabilization potential introduces an undesirable perturbation to the target states' energies. Here we introduce and benchmark two approaches for removing the perturbation caused by the stabilization. The benchmark calculations of excitation energies in selected diradicals illustrate that the so-called core correction based on evaluating the perturbation in a small basis set is robust and yields reliable EOM-DIP values, i.e., the errors of 0.0-0.3 eV against a similar-level coupled-cluster approach.

Using the charge-stabilization technique in the double ionization potential equation-of-motion calculations with dianion references.

The charge-stabilization method is applied to double ionization potential equation-of-motion (EOM-DIP) calculations to stabilize unstable dianion reference functions. The auto-ionizing character of the dianionic reference states spoils the numeric performance of EOM-DIP limiting applications of this method. We demonstrate that reliable excitation energies can be computed by EOM-DIP using a stabilized resonance wave function instead of the lowest energy solution corresponding to the neutral + free electron(s) state of the system. The details of charge-stabilization procedure are discussed and illustrated by examples. The choice of optimal stabilizing Coulomb potential, which is strong enough to stabilize the dianion reference, yet, minimally perturbs the target states of the neutral, is the crux of the approach. Two algorithms of choosing optimal parameters of the stabilization potential are presented. One is based on the orbital energies, and another--on the basis set dependence of the total Hartree-Fock energy of the reference. Our benchmark calculations of the singlet-triplet energy gaps in several diradicals show a remarkable improvement of the EOM-DIP accuracy in problematic cases. Overall, the excitation energies in diradicals computed using the stabilized EOM-DIP are within 0.2 eV from the reference EOM spin-flip values.

Excited and ionized states of the ozone molecule with full triples coupled cluster methods.

The role of connected triple excitations in coupled cluster (CC) calculations of vertical excitation energies, ionization potentials, and the electron affinity of the ozone molecule is evaluated. The equation of motion (EOM) and Fock space (FS) multireference CC approaches with full triples have been used in the calculations. The effect of the T(3) and R(3) operators significantly improve the EOM CCSD results for all considered quantities. A similar behavior is observed in the case of the FS-CC calculations. The FS-CC calculations with full triples have been obtained only for the intermediate Hamiltonian realization of the FS approach as the standard formulation diverges. The latter results are rigorously linked, and less expensive since smaller matrices are diagonalized.

Improving upon the accuracy for doubly excited states within the coupled cluster singles and doubles theory.

An alternative strategy of computations for double character excited states has been examined. The basic idea is to employ the reference function specific to the excited state of interest, as opposed to the traditionally used reference function, usually corresponding to the ground state, specific to the entire spectrum of a molecule. The procedure is used within the framework of the coupled cluster singles and doubles (CCSD) method. The conventional spin-conserving CC approach as well as its spin-flip (SF) extension has been analyzed. For the latter, two variants are considered, changing the S(z) value of the reference function by one [equation-of-motion (EOM)-SF] and two (EOM-2SF). The accuracy of the methods is benchmarked for the C(2) and C(4) molecules and referred to the full configuration interaction (FCI) or CC singles, doubles, and triples results. The vertical and adiabatic excitation energies, equilibrium geometries, and harmonic frequencies are studied. A significant improvement is demonstrated for the excitation energies of doubly excited states. Comparing these values with the FCI method, the errors of the conventional EOM CCSD method of about 1.7-2.2 eV are reduced to about 0.0-0.4 eV for the SF method. An improvement is also shown for the equilibrium geometries and harmonic frequencies.

Parallel implementation of the equation-of-motion coupled-cluster singles and doubles method and application for radical adducts of cytosine.

The equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method has been implemented into the massively parallel ACES III program using two alternative strategies: (1) storing the entire EOM Hamiltonian matrix prior to diagonalization and (2) recomputing the four-virtual part of the matrix from integrals in a direct mode. The second is found to be far more efficient. EOM-CC shows virtually ideal scaling from 32 to 256 processors. With basis sets as large as 552 functions, the program was applied to determine vertical excitation energies for five cytosine radical adducts of -OH and -H at three sites C5, C6, and N3. These radicals are considered to play an important role in radiation induced DNA damage. The excitation energy spectrum shows two distinct patterns for the lowest transitions distinguishing the C6-OH, C6-H, and N3-H adducts from the C5-OH and C5-H. The results indicate that the two lowest transitions of the C6-OH isomer should contribute to the experimentally observed absorption maximum at 2.88 eV, while the third and fourth transitions of C6-OH and the two lowest transitions of C5-OH contribute to the 3.65 eV absorption maximum. We also report the CCSD with noniterative triples correction [CCSD(T)] relative energies of the C5-OH and C6-OH adducts using 1000 processors.

Ground state potential energy surfaces and bound states of M-He dimers (M=Cu,Ag,Au): a theoretical investigation.

We present an ab initio investigation on the ground state interaction potentials [potential energy surface (PES)] between helium and the group 11 metal atoms: copper, silver, and gold. To the best of our knowledge, there are no previous theoretical PESs proposed for Cu-He and Au-He, and a single one for Ag-He [Z. J. Jakubek and M. Takami, Chem. Phys. Lett. 265, 653 (1997)], computed about 10 years ago at MP2 level and significantly improved by our study. To reach a high degree of accuracy in the determination of the three M-He potentials (M=Cu,Ag,Au), we performed extensive series of test computations to establish the appropriate basis set, the theoretical method, and the computational scheme for these systems. For each M-He dimer we computed the PES at the CCSD(T) level of theory, starting from the reference unrestricted Hartree-Fock wave function. We described the inner shells with relativistic small core pseudopotentials, and we adopted high quality basis sets for the valence electrons. We also performed CCSDT computations in a limited set of M-He internuclear distances, adopting a medium-sized basis set, such as to define for each dimer a CCSD(T) to CCSDT correction term and to improve further the quality of the CCSD(T) interaction potentials. The Cu-He complex has minimum interaction energy (E(min)) of -28.4 microhartree at the internuclear distance of 4.59 A (R(min)), and the short-range repulsive wall starts at 4.04 A (R(E=0)). Quite interestingly, the PES of Ag-He is more attractive (E(min)=-33.8 microhartree) but presents nearly the same R(min) and R(E=0) values, 4.60 and 4.04 A, respectively. The interaction potential for Au-He is markedly deeper and shifted at shorter distances as compared to the lighter complexes, with E(min)=-69.6 microhartree, R(min)=4.09 A and R(E=0)=3.60 A. As a first insight in the structure of M-He(n) aggregates, we determined the rovibrational structure of the three M-He dimers. The Cu-He and Ag-He potentials support just few rotational excitations, while the Au-He PES admits also a bound vibrational excitation.

Different equation-of-motion coupled cluster methods with different reference functions: the formyl radical.

The doublet and quartet excited states of the formyl radical have been studied by the equation-of-motion (EOM) coupled cluster (CC) method. The S(z) spin-conserving singles and doubles (EOM-EE-CCSD) and singles, doubles, and triples (EOM-EE-CCSDT) approaches, as well as the spin-flipped singles and doubles (EOM-SF-CCSD) method have been applied, subject to unrestricted Hartree-Fock (HF), restricted open-shell HF, and quasirestricted HF references. The structural parameters, vertical and adiabatic excitation energies, and harmonic vibrational frequencies have been calculated. The issue of the reference function choice for the spin-flipped (SF) method and its impact on the results has been discussed using the experimental data and theoretical results available. The results show that if the appropriate reference function is chosen so that target states differ from the reference by only single excitations, then EOM-EE-CCSD and EOM-SF-CCSD methods give a very good description of the excited states. For the states that have a non-negligible contribution of the doubly excited configurations one is able to use the SF method with such a reference function, that in most cases the performance of the EOM-SF-CCSD method is better than that of the EOM-EE-CCSD approach.