Harmonic Infrared and Raman Spectra in Molecular Environments Using the Polarizable Embedding Model.

We present a fully analytic approach to calculate infrared (IR) and Raman spectra of molecules embedded in complex molecular environments modeled using the fragment-based polarizable embedding (PE) model. We provide the theory for the calculation of analytic second-order geometric derivatives of molecular energies and first-order geometric derivatives of electric dipole moments and dipole-dipole polarizabilities within the PE model. The derivatives are implemented using a general open-ended response theory framework, thus allowing for an extension to higher-order derivatives. The embedding-potential parameters used to describe the environment in the PE model are derived through first-principles calculations, thus allowing a wide variety of systems to be modeled, including solvents, proteins, and other large and complex molecular environments. Here, we present proof-of-principle calculations of IR and Raman spectra of acetone in different solvents. This work is an important step toward calculating accurate vibrational spectra of molecules embedded in realistic environments.

Spatial Contributions to Nuclear Magnetic Shieldings.

We develop a methodology for calculating, analyzing, and visualizing nuclear magnetic shielding densities which are calculated from the current density via the Biot-Savart relation. Atomic contributions to nuclear magnetic shielding constants can be estimated within our framework with a Becke partitioning scheme. The new features have been implemented in the GIMIC program and are applied in this work to the study of the 1H and 13C nuclear magnetic shieldings in benzene (C6H6) and cyclobutadiene (C4H4). The new methodology allows a visual inspection of the spatial origins of the positive (shielding) and negative (deshielding) contributions to the nuclear magnetic shielding constant of a single nucleus, something which has not been hitherto easily accomplished. Analysis of the shielding densities shows that diatropic and paratropic current-density fluxes yield both shielding and deshielding contributions, as the shielding or deshielding is determined by the direction of the current-density flux with respect to the studied nucleus instead of the tropicity. Becke partitioning of the magnetic shieldings shows that the magnetic shielding contributions mainly originate from the studied atom and its nearest neighbors, confirming the localized character of nuclear magnetic shieldings.

Simulating crude oil exposure, uptake and effects in North Atlantic Calanus finmarchicus populations.

A simulation model framework (SYMBIOSES) that includes a 3-dimensional ocean physics and biology model and a model for transport and fate of oil was used to investigate the potential for bioaccumulation and lethal/sublethal effects of oil components in the copepod Calanus finmarchicus in the Lofoten-Vesterålen archipelago of Norway. The oil model is coupled with the biology model by way of a bioaccumulation model, from which mortality and reduction in reproduction are calculated via a total body burden (TBB). The simulation results indicate that copepod body burden levels are affected by the spill type (surface spill, subsea blowout) and the spill timing (spring, autumn). The effects of oil component bioaccumulation on the copepod population for all scenarios are small, though greatest in the subsea blowout scenarios. We attribute this to the limited spatial and temporal overlap between copepods and oil in the environment simulated by the model. The coupling of the processes of oil transport, bioaccumulation/excretion and the associated effects are discussed in the context of the model framework and with a view towards applications for Ecological Risk Assessment (ERA).

Dalton Project: A Python platform for molecular- and electronic-structure simulations of complex systems.

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

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.

Assessing impacts of simulated oil spills on the Northeast Arctic cod fishery.

We simulate oil spills of 1500 and 4500m3/day lasting 14, 45, and 90days in the spawning grounds of the commercial fish species, Northeast Arctic cod. Modeling the life history of individual fish eggs and larvae, we predict deviations from the historical pattern of recruitment to the adult population due to toxic oil exposures. Reductions in survival for pelagic stages of cod were 0-10%, up to a maximum of 43%. These reductions resulted in a decrease in adult cod biomass of <3% for most scenarios, up to a maximum of 12%. In all simulations, the adult population remained at full reproductive potential with a sufficient number of juveniles surviving to replenish the population. The diverse age distribution helps protect the adult cod population from reductions in a single year's recruitment after a major oil spill. These results provide insights to assist in managing oil spill impacts on fisheries.

An oxorhenium complex bearing a chiral cyclohexane-1-olato-2-thiolato ligand: Synthesis, stereochemistry, and theoretical study of parity violation vibrational frequency shifts.

In our effort towards measuring the parity violation energy difference between two enantiomers, a simple chiral oxorhenium complex 5 bearing enantiopure 2-mercaptocyclohexan-1-ol has been prepared as a potential candidate species. Vibrational circular dichroism revealed a chiral environment surrounding the rhenium atom, even though the rhenium is not a stereogenic center itself, and enabled to assign the (1S,2S)-(-) and (1R,2R)-(+) absolute configuration for 5. For both compound 5 and complex 4, previously studied by us and bearing a propane-2-olato-3-thiolato ligand, relativistic calculations predict parity violating vibrational frequency differences of a few hundreds of millihertz, above the expected sensitivity attainable by a molecular beam Ramsey interferometer that we are constructing.

Relativistic Polarizable Embedding.

Most chemistry, including chemistry where relativistic effects are important, occurs in an environment, and in many cases, this environment has a significant effect on the chemistry. In nonrelativistic quantum chemistry, a lot of progress has been achieved with respect to including environments such as a solvent or protein in the calculations, and now is the time to extend the possibilities for also doing this in relativistic quantum chemistry. The polarizable embedding (PE) model efficiently incorporates electrostatic effects of the environment by describing it as a collection of localized electric multipoles and polarizabilities obtained through quantum chemical calculations. In this article, we present the theory and implementation of four- and exact two-component Hamiltonians within a PE framework. We denote the methods the PE-4c-DFT and PE-X2C-DFT models. The models include a linear response formalism to calculate time-dependent (TD) properties: PE-TD-4c-DFT and PE-TD-X2C-DFT. With this first implementation, we calculate the PE-TD-4c-PBE0 excitation energies of the TcO4- and ReO4- ions in an explicit water solvent. This initial investigation focuses on the relative size of relativistic and solvent contributions to the excitation energies. The solvent effect is divided into an indirect solvent effect due to the structural perturbation of the XO4- ion and a direct electrostatic effect. The relativistic effects as well as both types of solvent effects are found to contribute to a shift in the excitation energies, but they do so to different extents depending on the ion and the electronic transition in question.

On the calculation of second-order magnetic properties using subsystem approaches in a relativistic framework.

We report an implementation of nuclear magnetic resonance (NMR) shielding (σ), isotope-independent indirect spin-spin coupling (K) and the magnetizability (ξ) tensors in a frozen density embedding scheme using the four-component (4c) relativistic Dirac-Coulomb (DC) Hamiltonian and non-collinear spin density functional theory. The formalism takes into account the magnetic balance between the large and the small components of molecular spinors and assures the gauge-origin independence of the NMR shielding and magnetizability results. This implementation has been applied to hydrogen-bonded HXHOH2 complexes (X = Se, Te, Po) and compared with supermolecular calculations and with an approach based on the integration of the magnetically induced current density vector. A comparison with the approximate zeroth-order regular approximation (ZORA) Hamiltonian indicates non-negligible differences in σ and K in the HPoHOH2 complex, and calls for a thorough comparison of ZORA and DC Hamiltonians in the description of environment effects on NMR parameters for molecular systems with heavy elements.

Five-Photon Absorption and Selective Enhancement of Multiphoton Absorption Processes.

We study one-, two-, three-, four-, and five-photon absorption of three centrosymmetric molecules using density functional theory. These calculations are the first ab initio calculations of five-photon absorption. Even- and odd-order absorption processes show different trends in the absorption cross sections. The behavior of all even- and odd-photon absorption properties shows a semiquantitative similarity, which can be explained using few-state models. This analysis shows that odd-photon absorption processes are largely determined by the one-photon absorption strength, whereas all even-photon absorption strengths are largely dominated by the two-photon absorption strength, in both cases modulated by powers of the polarizability of the final excited state. We demonstrate how to selectively enhance a specific multiphoton absorption process.

Four-component relativistic calculations in solution with the polarizable continuum model of solvation: theory, implementation, and application to the group 16 dihydrides H2X (X = O, S, Se, Te, Po).

We present a formulation of four-component relativistic self-consistent field (SCF) theory for a molecular solute described within the framework of the polarizable continuum model (PCM) for solvation. The linear response function for a four-component PCM-SCF state is also derived, as well as the explicit form of the additional contributions to the first-order response equations. The implementation of such a four-component PCM-SCF model, as carried out in a development version of the DIRAC program package, is documented. In particular, we present the newly developed application programming interface PCMSolver used in the actual implementation with DIRAC. To demonstrate the applicability of the approach, we present and analyze calculations of solvation effects on the geometries, electric dipole moments, and static electric dipole polarizabilities for the group 16 dihydrides H2X (X = O, S, Se, Te, Po).

Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients.

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.

The Dalton quantum chemistry program system.

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Analytic density functional theory calculations of pure vibrational hyperpolarizabilities: the first dipole hyperpolarizability of retinal and related molecules.

We present a general approach for the analytic calculation of pure vibrational contributions to the molecular (hyper)polarizabilities at the density functional level of theory. The analytic approach allows us to study large molecules, and we apply the new code to the study of the first dipole hyperpolarizabilities of retinal and related molecules. We investigate the importance of electron correlation as described by the B3LYP exchange-correlation functional on the pure vibrational and electronic hyperpolarizabilities and compare the computed hyperpolarizabilities with available experimental data. The effects of electron correlation on the pure vibrational corrections vary signficantly even between these structurally very similar molecules, making it difficult to estimate these effects without explicit calculations at the density functional theory level. As expected, the frequency-dependent first hyperpolarizability, which determines the experimentally observed second-harmonic generation, is dominated by the electronic term, whereas for the static hyperpolarizability, the vibrational contribution is equally important. As a consequence, frequency extrapolation of the measured optical hyperpolarizabilities can only provide an estimate for the electronic contribution to the static hyperpolarizability, not its total value. The relative values of the hyperpolarizabilities for different molecules, obtained from the calculations, are in reasonable agreement with experimental data.

Analytic cubic and quartic force fields using density-functional theory.

We present the first analytic implementation of cubic and quartic force constants at the level of Kohn-Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange-correlation kernels. We use generalized second-order vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree-Fock results. The Hartree-Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants.

A chiral rhenium complex with predicted high parity violation effects: synthesis, stereochemical characterization by VCD spectroscopy and quantum chemical calculations.

With their rich electronic, vibrational, rotational and hyperfine structure, molecular systems have the potential to play a decisive role in precision tests of fundamental physics. For example, electroweak nuclear interactions should cause small energy differences between the two enantiomers of chiral molecules, a signature of parity symmetry breaking. Enantioenriched oxorhenium(VII) complexes S-(-)- and R-(+)-3 bearing a chiral 2-methyl-1-thio-propanol ligand have been prepared as potential candidates for probing molecular parity violation effects via high resolution laser spectroscopy of the Re=O stretching. Although the rhenium atom is not a stereogenic centre in itself, experimental vibrational circular dichroism (VCD) spectra revealed a surrounding chiral environment, evidenced by the Re=O bond stretching mode signal. The calculated VCD spectrum of the R enantiomer confirmed the position of the sulfur atom cis to the methyl, as observed in the solid-state X-ray crystallographic structure, and showed the presence of two conformers of comparable stability. Relativistic quantum chemistry calculations indicate that the vibrational shift between enantiomers due to parity violation is above the target sensitivity of an ultra-high resolution infrared spectroscopy experiment under active preparation.

All-Metal Aromaticity: Revisiting the Ring Current Model among Transition Metal Clusters.

We present new insight into the nature of aromaticity in metal clusters. We give computational arguments in favor of using the ring-current model over local indices, such as nucleus independent chemical shifts, for the determination of the magnetic aromaticity. Two approaches for estimating magnetically induced ring currents are employed for this purpose, one based on the quantum theory of atoms in molecules (QTAIM) and the other where magnetically induced current densities (MICD) are explicitly calculated. We show that the two-zone aromaticity/antiaromaticity of a number of 3d metallic clusters (Sc3(-), Cu3(+), and Cu4(2-)) can be explained using the QTAIM-based magnetizabilities. The reliability of the calculated atomic and bond magnetizabilities of the metallic clusters are verified by comparison with MICD computed at the multiconfiguration self-consistent field (MCSCF) and density functional levels of theory. Integrated MCSCF current strength susceptibilities as well as a visual analysis of the calculated current densities confirm the interpretations based on the QTAIM magnetizabilities. In view of the new findings, we suggest a simple explanation based on classical electromagnetic theory to explain the anomalous magnetic shielding in different transition metal clusters. Our results suggest that the nature of magnetic aromaticity/antiaromaticity in transition-metal clusters should be assessed more carefully based on global indices.

Multiconfigurational Self-Consistent Field Calculations of the Magnetically Induced Current Density Using Gauge-Including Atomic Orbitals.

Nondynamical electron correlation based on a genuine multiconfigurational theory is of considerable importance for a balanced ab initio calculation of aromatic and antiaromatic molecules either with open-shell character or quasi-degeneracy in the electronic states. Among the various aromaticity indices, the calculation of magnetically induced ring current densities (MICD) has emerged as a strong contender, providing both a qualitative and a quantitative description of the effect. We report here the first implementation of MICD at the multiconfigurational self-consistent field (MCSCF) level of theory together with example calculations. This extension makes the method applicable to systems that cannot be appropriately handled with earlier implementations based on a single-reference starting function. We present the formulation of the MCSCF MICD theory along with applications to a prototypical antiaromatic (cyclobutadiene) and an aromatic (benzyne) system, both systems that require a multiconfigurational description. We compare the MCSCF results to those obtained using Hartree-Fock and Kohn-Sham density functional theory and discuss the effects of static correlation on the aromaticity.

Charge-transfer excitations in uranyl tetrachloride ([UO2Cl4]2-): how reliable are electronic spectra from relativistic time-dependent density functional theory?

Four-component relativistic time-dependent density functional theory (TD-DFT) is used to study charge-transfer (CT) excitation energies of the uranyl molecule as well as the uranyl tetrachloride complex. Adiabatic excitation energies and vibrational frequencies of the excited states are calculated for the lower energy range of the spectrum. The results for TD-DFT with the CAM-B3LYP exchange-correlation functional for the [UO(2)Cl(4)](2-) system are in good agreement with the experimentally observed spectrum of this species and agree also rather well with other theoretical data. Use of the global hybrid B3LYP gives qualitatively correct results, while use of the BLYP functional yields results that are qualitatively wrong due to the too low CT states calculated with this functional. The applicability of the overlap diagnostic of Peach et al. (J. Chem. Phys.2008, 128, 044118) to identify such CT excitations is investigated for a wide range of vertical transitions using results obtained with three different approximate exchange-correlation functionals: BLYP, B3LYP, and CAM-B3LYP.

A simple scheme for magnetic balance in four-component relativistic Kohn-Sham calculations of nuclear magnetic resonance shielding constants in a Gaussian basis.

We report the implementation of nuclear magnetic resonance (NMR) shielding tensors within the four-component relativistic Kohn-Sham density functional theory including non-collinear spin magnetization and employing London atomic orbitals to ensure gauge origin independent results, together with a new and efficient scheme for assuring correct balance between the large and small components of a molecular four-component spinor in the presence of an external magnetic field (simple magnetic balance). To test our formalism we have carried out calculations of NMR shielding tensors for the HX series (X = F, Cl, Br, I, At), the Xe atom, and the Xe dimer. The advantage of simple magnetic balance scheme combined with the use of London atomic orbitals is the fast convergence of results (when compared with restricted kinetic balance) and elimination of linear dependencies in the basis set (when compared to unrestricted kinetic balance). The effect of including spin magnetization in the description of NMR shielding tensor has been found important for hydrogen atoms in heavy HX molecules, causing an increase of isotropic values of 10%, but negligible for heavy atoms.