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The high computational scaling with the basis set size and the number of correlated electrons is a bottleneck limiting applications of coupled cluster algorithms, in particular for calculations based on two- or four-component relativistic Hamiltonians, which often employ uncontracted basis sets. This problem may be alleviated by replacing canonical Hartree–Fock virtual orbitals by natural orbitals (NOs). In this paper, we describe the implementation of a module for generating NOs for correlated wavefunctions and, in particular, second order Møller–Plesset perturbation frozen natural orbitals (MP2FNOs) as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [Pototschnig et al. J. Chem. Theory Comput. 17, 5509, (2021)]. Our implementation can manipulate complex or quaternion density matrices, thus allowing for the generation of both Kramers-restricted and Kramers-unrestricted MP2FNOs. Furthermore, NOs are re-expressed in the parent atomic orbital (AO) basis, allowing for generating coupled cluster singles and doubles NOs in the AO basis for further analysis. By investigating the truncation errors of MP2FNOs for both the correlation energy and molecular properties—electric field gradients at the nuclei, electric dipole and quadrupole moments for hydrogen halides HX (X = F–Ts), and parity-violating energy differences for H2Z2 (Z = O–Se)—we find MP2FNOs accelerate the convergence of the correlation energy in a roughly uniform manner across the Periodic Table. It is possible to obtain reliable estimates for both energies and the molecular properties considered with virtual molecular orbital spaces truncated to about half the size of the full spaces. [ABSTRACT FROM AUTHOR]

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, 1593–1604 (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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present a study of the electronic structure of the [UO2]+, [UO2]2 +, [UO2]3+, NUO, [NUO]+, [NUO]2+, [NUN]-, NUN, and [NUN]+ molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin-orbit coupling and Gaunt interactions are compared to results obtained with the Dirac-Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity). [ABSTRACT FROM AUTHOR]

Quantum-mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the frozen density embedding formulation of subsystem density-functional theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlap matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against coupled-cluster calculations and achieves chemical accuracy for the systems considered for intermolecular separations ranging from hydrogen-bond distances to tens of Ångstroms. Numerical examples are provided for molecular clusters comprised of up to 56 non-covalently bound molecules. [ABSTRACT FROM AUTHOR]

The triiodide ion I3- exhibits a complex photodissociation behavior, the dynamics of which are not yet fully understood. As a first step toward determining the full potential energy surfaces of this species for subsequent simulations of its dissociation processes, we investigate the performance of different electronic structure methods [time-dependent density functional theory, complete active space perturbation theory to second order (CASPT2), Fock-space coupled cluster and multireference configuration interaction] in describing the ground and excited states of the triiodide ion along the symmetrical dissociation path. All methods apart from CASPT2 include scalar relativity and spin-orbit coupling in the orbital optimization, providing useful benchmark data for the more common two-step approaches in which spin-orbit coupling is introduced in the configuration interaction. Time-dependent density functional theory with the statistical averaging of model orbital potential functional is off the mark for this system. Another choice of functional may improve performance with respect to vertical excitation energies and spectroscopic constants, but all functionals are likely to face instability problems away from the equilibrium region. The Fock-space coupled cluster method was shown to perform clearly best in regions not too far from equilibrium but is plagued by convergence problems toward the dissociation limit due to intruder states. CASPT2 shows good performance at significantly lower computational cost, but is quite sensitive to symmetry breaking. We furthermore observe spikes in the CASPT2 potential curves away from equilibrium, signaling intruder state problems that we were unable to curb through the use of level shifts. Multireference configuration interaction is, in principle, a viable option, but its computational cost in the present case prohibits use other than for benchmarking purposes. [ABSTRACT FROM AUTHOR]

Relativistic coupled cluster theory is used to determine accurate electric field gradients in order to provide a theoretical value for the nuclear quadrupole moment of 139La. Here we used the diatomic lanthanum monohalides LaF, LaCl, LaBr, and LaI as accurate nuclear quadrupole coupling constants are available from rotational spectroscopy by Rubinoff et al. [J. Mol. Spectrosc. 218, 169 (2003)]. The resulting nuclear quadrupole moment for 139La (0.200±0.006 barn) is in excellent agreement with earlier work using atomic hyperfine spectroscopy [0.20(1) barn]. [ABSTRACT FROM AUTHOR]

The ground and excited states of the UO2 molecule have been studied using a Dirac-Coulomb intermediate Hamiltonian Fock-space coupled cluster approach (DC-IHFSCC). This method is unique in describing dynamic and nondynamic correlation energies at relatively low computational cost. Spin-orbit coupling effects have been fully included by utilizing the four-component Dirac-Coulomb Hamiltonian from the outset. Complementary calculations on the ionized systems UO2+ and UO22+ as well as on the ions U4+ and U5+ were performed to assess the accuracy of this method. The latter calculations improve upon previously published theoretical work. Our calculations confirm the assignment of the ground state of the UO2 molecule as a 3[uppercase_phi_synonym]2u state that arises from the 5f17s1 configuration. The first state from the 5f2 configuration is found above 10 000 cm-1, whereas the first state from the 5f16d1 configuration is found at 5 047 cm-1. [ABSTRACT FROM AUTHOR]

An implementation of the relativistic multireference Fock-space coupled cluster method is presented which allows simultaneous calculation of potential surfaces for different oxidation states and electronic levels of a molecule, yielding values for spectroscopic constants and transition energies. The method is tested in pilot calculations on the I[sub 2] and HgH molecules, and is shown to give a good and balanced description of various electronic states and energies. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present an EOMCCSD (equation of motion coupled cluster with singles and doubles) study of excited states of the small [UO2]2+ and [UO2]+ model systems as well as the larger UVIO2(saldien) complex. In addition, the triples contribution within the EOMCCSDT and CR-EOMCCSD(T) (completely renormalized EOMCCSD with non-iterative triples) approaches for the [UO2]2+ and [UO2]+ systems as well as the active-space variant of the CR-EOMCCSD(T) method-CR-EOMCCSd(t)-for the UVIO2(saldien) molecule are investigated. The coupled cluster data were employed as benchmark to choose the 'best' appropriate exchange-correlation functional for subsequent time-dependent density functional (TD-DFT) studies on the transition energies for closed-shell species. Furthermore, the influence of the saldien ligands on the electronic structure and excitation energies of the [UO2]+ molecule is discussed. The electronic excitations as well as their oscillator dipole strengths modeled with TD-DFT approach using the CAM-B3LYP exchange-correlation functional for the [UVO2(saldien)]- with explicit inclusion of two dimethyl sulfoxide molecules are in good agreement with the experimental data of Takao et al. [Inorg. Chem. 49, 2349 (2010)]. [ABSTRACT FROM AUTHOR]

New implementations of the Lévy-Leblond, zeroth-order regular approach (ZORA) and spin-free Dirac equation are presented within the framework of the four-component relativistic program system DIRAC. This implementation allows systematic incorporation of relativistic effects at different levels of theory and corresponding computational cost. One of the possibilities of the new code is to neglect the effect of spin-orbit coupling in the orbital optimization process and introduce it in a later stage of the calculation. This method is shown to be unstable despite the boundedness of the spin-orbit operator itself. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]