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.

In search of discrete symmetry violations beyond the standard model: Thorium monoxide reloaded.

We present an updated electron electric dipole moment (EDM) effective electric field of Eeff= 75.2 GV/cm and 229Th magnetic hyperfine interaction constant A|| = -1266 MHz, the nucleon-electron scalar-pseudoscalar interaction constant WS = 106.0 kHz, and the molecule-frame static electric dipole moment D = -4.41 D for the Δ13 science state of ThO. The criticisms of the results from Fleig and Nayak [J. Mol. Spectrosc. 300, 16 (2014)] made in Skripnikov and Titov [J. Chem. Phys. 142, 024301 (2015)] are addressed and largely found to be unsubstantiated within the framework of the present approach. The present findings confirm the slightly relaxed constraints on relevant beyond-standard-model parameters, in particular the electron EDM, de, and the nucleon-electron scalar-pseudoscalar coupling constant, CS.

General active space commutator-based coupled cluster theory of general excitation rank for electronically excited states: implementation and application to ScH.

We present a new implementation of general excitation rank coupled cluster theory for electronically excited states based on the single-reference multi-reference formalism. The method may include active-space selected and/or general higher excitations by means of the general active space concept. It may employ molecular integrals over the four-component Lévy-Leblond Hamiltonian or the relativistic spin-orbit-free four-component Hamiltonian of Dyall. In an initial application to ground- and excited states of the scandium monohydride molecule we report spectroscopic constants using basis sets of up to quadruple-zeta quality and up to full iterative triple excitations in the cluster operators. Effects due to spin-orbit interaction are evaluated using two-component multi-reference configuration interaction for assessing the accuracy of the coupled cluster results.

Two- and four-component relativistic generalized-active-space coupled cluster method: implementation and application to BiH.

A string-based coupled-cluster method of general excitation rank and with optimal scaling which accounts for special relativity within the four-component framework is presented. The method opens the way for the treatment of multi-reference problems through an active-space inspired single-reference based state-selective expansion of the model space. The evaluation of the coupled-cluster vector function is implemented by considering contractions of elementary second-quantized operators without setting up the amplitude equations explicitly. The capabilities of the new method are demonstrated in application to the electronic ground state of the bismuth monohydride molecule. In these calculations simulated multi-reference expansions with both doubles and triples excitations into the external space as well as the regular coupled-cluster hierarchy up to full quadruples excitations are compared. The importance of atomic outer core-correlation for obtaining accurate results is shown. Comparison to the non-relativistic framework is performed throughout to illustrate the additional work of the transition to the four-component relativistic framework both in implementation and application. Furthermore, an evaluation of the highest order scaling for general-order expansions is presented.

The electronic structure of the triiodide ion from relativistic correlated calculations: a comparison of different methodologies.

The triiodide ion I(3)(-) 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.

Large-scale parallel configuration interaction. II. Two- and four-component double-group general active space implementation with application to BiH.

We present a parallel implementation of a large-scale relativistic double-group configuration interaction (CI) program. It is applicable with a large variety of two- and four-component Hamiltonians. The parallel algorithm is based on a distributed data model in combination with a static load balancing scheme. The excellent scalability of our parallelization scheme is demonstrated in large-scale four-component multireference CI (MRCI) benchmark tests on two of the most common computer architectures, and we also discuss hardware-dependent aspects with respect to possible speedup limitations. With the new code we have been able to calculate accurate spectroscopic properties for the ground state and the first excited state of the BiH molecule using extensive basis sets. We focused, in particular, on an accurate description of the splitting of these two states which is caused by spin-orbit coupling. Our largest parallel MRCI calculation thereby comprised an expansion length of 2.7x10(9) Slater determinants.

Four-component relativistic coupled cluster and configuration interaction calculations on the ground and excited states of the RbYb molecule.

We present high-level four-component coupled cluster and multireference configuration interaction calculations of potential energy curves, dipole moment, Franck-Condon factors and spectroscopic constants of the newly formed RbYb molecule. From finite-field calculations we obtain an electric dipole moment for RbYb of almost 1 D. In combination with its magnetic dipole moment this makes RbYb an excellent candidate for trapping and for studying dipolar interaction in the ultracold regime. Significant Franck-Condon factors are found between the rovibronic ground state and the lowest rovibrational levels of the first excited 2Sigma1/2+ state but also between a broad range of rovibrational levels of the 2Pi1/2 and 2Pi3/2 states. This allows for several two-step approaches to reach the rovibronic ground state after initial photoassociation.

Intersystem crossing and characterization of dark states in the pyrimidine nucleobases uracil, thymine, and 1-methylthymine.

The ground and low-lying excited states of the pyrimidine nucleo bases uracil, thymine, and 1-methylthymine have been characterized using ab initio coupled-cluster with approximate doubles (CC2) and a combination of density functional theory (DFT) and semiempirical multireference configuration interaction (MRCI) methods. Intersystem crossing rate constants have been determined perturbationally by employing a nonempirical one-center mean-field approximation to the Breit-Pauli spin-orbit operator for the computation of electronic coupling matrix elements. Our results clearly indicate that the S(2)((1)pi-->pi*)-->T(2)((3)n-->pi*) process cannot compete with the subpicosecond decay of the S(2) population due to spin-allowed nonradiative transitions, whereas the T(1)((3)pi-->pi*) state is populated from the intermediate S(1)((1)n-->pi*) state on a subnanosecond time scale. Hence, it is very unlikely that the S(1)((1)n-->pi*) state corresponds to the long-lived dark state observed in the gas phase.

Theoretical investigation of the excited states of 2-nitrobenzyl and 4,5-methylendioxy-2-nitrobenzyl caging groups.

The photochemistry of caged compounds of the o-nitrobenzyl type has been investigated thoroughly in the past. However, even recently new side reactions have been discovered. Earlier, we reported [Bley, F., K. Schaper, and H. Görner (2008), Photochem. Photobiol.84 162-171] that we found long-lived triplet states which do not lead to product formation for the bathochromic absorbing compounds with 4,5-methylendioxy-2-nitrobenzyl caging group. Here, we report on theoretical studies which explain the special behavior of these compounds. These studies reveal that the bathochromic shift of absorption for these compounds compared with o-nitrobenzyl compounds themselves is not due to a shift in energy of the involved states, but due to a substantial change of oscillator strength of the respective transitions. The lack of reactivity of the triplet state of 4,5-methylendioxy-2-nitrobenzyl compounds can be attributed to state switching. In the triplet manifold the lowest state is a nonreactive charge transfer state, while the lowest state in the singlet manifold is a reactive local excitation in the nitro-group. From these results we conclude that it will be most likely not possible to create derivatives of caged compounds based on the o-nitrobenzyl caging group which have absorption which is shifted even more strongly to longer wavelengths.

A direct relativistic four-component multiconfiguration self-consistent-field method for molecules.

A new direct relativistic four-component Kramers-restricted multiconfiguration self-consistent-field (KR-MCSCF) code for molecules has been implemented. The program is based upon Kramers-paired spinors and a full implementation of the binary double groups (D(2h)(*) and subgroups). The underlying quaternion algebra for one-electron operators was extended to treat two-electron integrals and density matrices in an efficient and nonredundant way. The iterative procedure is direct with respect to both configurational and spinor variational parameters; this permits the use of large configuration expansions and many basis functions. The relativistic minimum-maximum principle is implemented in a second-order restricted-step optimization algorithm, which provides sharp and well-controlled convergence. This paper focuses on the necessary modifications of nonrelativistic MCSCF methodology to obtain a fully variational KR-MCSCF implementation. The general implementation also allows for the use of molecular integrals from a two-component relativistic Hamiltonian as, for example, the Douglas-Kroll-Hess variants. Several sample applications concern the determination of spectroscopic properties of heavy-element atoms and molecules, demonstrating the influence of spin-orbit coupling in MCSCF approaches to such systems and showing the potential of the new method.

Electronic and vibrational spectroscopy of 1-methylthymine and its water clusters: the dark state survives hydration.

Electronic and vibrational gas phase spectra of 1-methylthymine (1MT) and 1-methyluracil (1MU) and their clusters with water are presented. Mass selective IR/UV double resonance spectra confirm the formation of pyrimidine-water clusters and are compared to calculated vibrational spectra obtained from ab initio calculations. In contrast to Y. He, C. Wu, W. Kong; J. Phys. Chem. A, 2004, 108, 94 we are able to detect 1MT/1MU and their water clusters via resonant two-photon delayed ionization under careful control of the applied water-vapor pressure. The long-living dark electronic state of 1MT and 1MU detected by delayed ionization, survives hydration and the photostability of 1MT/1MU cannot be attributed solely to hydration. Oxygen coexpansions and crossed-beam experiments indicate that the triplet state population is probably small compared to the (1)n pi* and/or hot electronic ground state population. Ab initio theory shows that solvation of 1MT by water does not lead to a substantial modification of the electronic relaxation and quenching of the (1)n pi* state. Relaxation pathways via (1)pi pi*(1)-n pi*(1) and (1)pi pi*-S(0) conical intersections and barriers have been identified, but are not significantly altered by hydration.

Instability of the Al4(2-) "all-metal aromatic" ion and its implications.

Al42 - is a prototype structural unit of a new class of "all-metal aromatic" molecules. Without stabilizing counterions this species is unstable with respect to electron autodetachment in the gas phase. We estimated the height of the repulsive Coulomb barrier to approximately 2.7 eV and calculated a lifetime of 9 fs. This is a short lifetime: The only way to study the isolated dianion experimentally is to use electron scattering techniques. Investigations of the validity of bound-state quantum chemical calculations on the isolated species show that the results suffer from significant admixture of continuum states to the bound-state wave function depending on the basis set. Calculations of molecular properties can therefore give essentially arbitrary results for this ill-defined system, as is demonstrated for the energy and nuclear magnetic shieldings. This substantiates that results from calculations on the isolated dianion should be approached with caution.

Large-scale parallel configuration interaction. I. Nonrelativistic and scalar-relativistic general active space implementation with application to (Rb-Ba)+.

We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.

Quantum-chemical investigation of the structures and electronic spectra of the nucleic acid bases at the coupled cluster CC2 level.

We study the ground-state structures and singlet- and triplet-excited states of the nucleic acid bases by applying the coupled cluster model CC2 in combination with a resolution-of-the-identity approximation for electron interaction integrals. Both basis set effects and the influence of dynamic electron correlation on the molecular structures are elucidated; the latter by comparing CC2 with Hartree-Fock and Møller-Plesset perturbation theory to second order. Furthermore, we investigate basis set and electron correlation effects on the vertical excitation energies and compare our highest-level results with experiment and other theoretical approaches. It is shown that small basis sets are insufficient for obtaining accurate results for excited states of these molecules and that the CC2 approach to dynamic electron correlation is a reliable and efficient tool for electronic structure calculations on medium-sized molecules.

The generalized active space concept for the relativistic treatment of electron correlation. III. Large-scale configuration interaction and multiconfiguration self-consistent-field four-component methods with application to UO2.

We present an implementation for large-scale relativistic electronic structure calculations including spin-dependent contributions and electron correlation in a fully variational procedure. The modular implementation of the double group configuration interaction (CI) program into a multiconfiguration self-consistent-field (MCSCF) code allows for the treatment of large CI expansions in both the spinor optimization step and the post-MCSCF dynamic electron correlation step. As an illustration of the potential of the new code, we calculate the spectroscopic properties of the UO2 molecule where we study the ground state and a few excited states in vertical and adiabatic calculations.

Calculation of electric-field gradients based on higher-order generalized Douglas-Kroll transformations.

In this paper, the calculation of electric-field-like properties based on higher-order Douglas-Kroll-Hess (DKH) transformations is discussed. The electric-field gradient calculated within the Hartree-Fock self-consistent field framework is used as a representative property. The properties are expressed as an analytic first derivative of the four-component Dirac energy and the nth-order DKH energy, respectively. The differences between a "forward" transformation of the relativistic energy or the "back transformation" of the wave function is discussed in some detail. Detailed test calculations were carried out on the electric-field gradient at the halogen nucleus in the series HX (X=F,Cl,Br,I,At) for which extensive reference data are available. The DKH method is shown to reproduce (spin-free) four-component Dirac-Fock results to an accuracy of better than 99% which is significantly closer than previous DKH studies. The calculations of both the Hamiltonian and the property operator are shown to be essentially converged after the second-order transformation, even for elements as heavy as At. In addition, we have obtained results within the density-functional framework using the DKHZ and zeroth-order regular approximation (ZORA) methods. The latter results included picture-change effects at the scalar relativistic variant of the ZORA-4 level and were shown to be in quantitative agreement with earlier results obtained by van Lenthe and Baerends. The picture-change effects are somewhat smaller for the ZORA method compared to DKH. For heavier elements significant differences in the field gradients predicted by the two methods were found. Based on comparison with four-component Dirac-Kohn-Sham calculations, the DKH results are more accurate. Compared to the spin-free Dirac-Kohn-Sham reference values, the ZORA-4 formalism did not improve the results of the ZORA calculations.