The DIRAC code for relativistic molecular calculations

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree?Fock, Kohn?Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.Fil: Saue, Trond. Université Paul Sabatier; Francia. Centre National de la Recherche Scientifique; FranciaFil: Bast, Radovan. Uit The Arctic University Of Norway; NoruegaFil: Gomes, André Severo Pereira. University Of Lille.; Francia. Centre National de la Recherche Scientifique; FranciaFil: Jensen, Hans Jorgen Aa.. University of Southern Denmark; DinamarcaFil: Visscher, Lucas. Vrije Universiteit Amsterdam; Países BajosFil: Aucar, Ignacio Agustín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; Argentina. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Física; ArgentinaFil: Di Remigio, Roberto. Uit The Arctic University of Norway; NoruegaFil: Dyall, Kenneth G.. Dirac Solutions; Estados UnidosFil: Eliav, Ephraim. Universitat Tel Aviv.; IsraelFil: Fasshauer, Elke. Aarhus University. Department of Bioscience; DinamarcaFil: Fleig, Timo. Université Paul Sabatier; Francia. Centre National de la Recherche Scientifique; FranciaFil: Halbert, Loïc. Centre National de la Recherche Scientifique; Francia. University Of Lille.; FranciaFil: Hedegård, Erik Donovan. Lund University; SueciaFil: Helmich-Paris, Benjamin. Max-planck-institut Für Kohlenforschung; AlemaniaFil: Ilias, Miroslav. Matej Bel University; EslovaquiaFil: Jacob, Christoph R.. Technische Universität Braunschweig; AlemaniaFil: Knecht, Stefan. Eth Zürich, Laboratorium Für Physikalische Chemie; SuizaFil: Laerdahl, Jon K.. Oslo University Hospital; NoruegaFil: Vidal, Marta L.. Department Of Chemistry; DinamarcaFil: Nayak, Malaya K.. Bhabha Atomic Research Centre; IndiaFil: Olejniczak, Malgorzata. University Of Warsaw; PoloniaFil: Olsen, Jógvan Magnus Haugaard. Uit The Arctic University Of Norway; NoruegaFil: Pernpointner, Markus. Kybeidos Gmbh; AlemaniaFil: Senjean, Bruno. Universiteit Leiden; Países BajosFil: Shee, Avijit. Department Of Chemistry; Estados UnidosFil: Sunaga, Ayaki. Tokyo Metropolitan University; JapónFil: van Stralen, Joost N. P.. Vrije Universiteit Amsterdam; Países Bajo

Upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs for the BrCN⁺^2Pi _{frac{1}{2}} and ^2Pi _{frac{3}{2}} states determined by applying the FSCC method in combination with the Dirac–Coulomb Hamiltonian (DC-FSCC)

<p><strong>Figure 3.</strong> Upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs for the BrCN⁺^2\Pi _{\frac{1}{2}} and ^2\Pi _{\frac{3}{2}} states determined by applying the FSCC method in combination with the Dirac–Coulomb Hamiltonian (DC-FSCC).</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Geometry parameters, vibrational frequencies and RT parameters for the BrCN⁺ cation

<p><b>Table 1.</b> Geometry parameters, vibrational frequencies and RT parameters for the BrCN⁺ cation. Hereby, bond lengths are given in Å, vibrational frequencies (ω) and RT parameters <em>c</em> and <em>d</em> are given in wavenumbers for the NR, scalar relativistic (SF) and four-component (DC) treatment. For the DC case the distances for the lower and (upper) surface are both listed, where ε is dimensionless. <em>c</em>_calc and <em>c</em>_fit denote the values obtained by equations (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn28" target="_blank">28</a>), (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn29" target="_blank">29</a>) and via the fit. The parameter <em>d</em> does not apply in the absence of the SO coupling.</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Geometry parameters for the XCN (X=Cl, Br) molecules as used in equations (25) and (27)

<p><strong>Figure 1.</strong> Geometry parameters for the XCN (X=Cl, Br) molecules as used in equations (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn25" target="_blank">25</a>) and (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn27" target="_blank">27</a>).</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Split upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs of the BrCN⁺²Π state determined by applying FSCC in combination with an NR Hamiltonian

<p><strong>Figure 2.</strong> Split upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs of the BrCN⁺²Π state determined by applying FSCC in combination with an NR Hamiltonian. The SF curves look almost identical and are not plotted separately.</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Four-Component Polarization Propagator Calculations of Electron Excitations: Spectroscopic Implications of Spin-Orbit Coupling Effects

A complete implementation of the polarization propagator based on the Dirac-Coulomb Hamiltonian is presented and applied to excitation spectra of various systems. Hereby the effect of spin-orbit coupling on excitation energies and transition moments is investigated in detail. The individual perturbational contributions to the transition moments could now be separately analyzed for the first time and show the relevance of one- and two-particle terms. In some systems different contributions to the transition moments partially cancel each other and do not allow for simple predictions. For the outer valence spectrum of the H2Os(CO)4 complex a detailed final state analysis is performed explaining the sensitivity of the excitation spectrum to spin-orbit effects. Finally, technical issues of handling double group symmetry in the relativistic framework and methodological aspects of our parallel implementation are discussed