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A general formulation of the strong coupling between photons confined in a cavity and molecular electronic states is developed for the state-interaction state-average spin-restricted ensemble-referenced Kohn–Sham method. The light–matter interaction is included in the Jaynes–Cummings model, which requires the derivation and implementation of the analytical derivatives of the transition dipole moments between the molecular electronic states. The developed formalism is tested in the simulations of the nonadiabatic dynamics in the polaritonic states resulting from the strong coupling between the cavity photon mode and the ground and excited states of the penta-2,4-dieniminium cation, also known as PSB3. Comparison with the field-free simulations of the excited-state decay dynamics in PSB3 reveals that the light–matter coupling can considerably alter the decay dynamics by increasing the excited state lifetime and hindering photochemically induced torsion about the C=C double bonds of PSB3. The necessity of obtaining analytical transition dipole gradients for the accurate propagation of the dynamics is underlined. [ABSTRACT FROM AUTHOR]

The photophysical properties of a series of recently synthesized single benzene fluorophores were investigated using ensemble density functional theory calculations. The energetic stability of the ground and excited state species were counterposed against the aromaticity index derived from local vibrational modes. It was found that the large Stokes shift of the fluorophores (up to ca. 5800 cm −1) originates from the effect of electron donating and electron withdrawing substituents rather than π‐delocalization and related (anti‐)aromaticity. On the basis of nonadiabatic molecular dynamics simulations, the absence of fluorescence from one of the regioisomers was explained by the occurrence of easily accessible S 1/S 0 conical intersections below the vertical excitation energy level. It is demonstrated in the manuscript that the analysis of local mode force constants and the related aromaticity index represent a useful tool for the characterization of π‐delocalization effects in π‐conjugated compounds. [ABSTRACT FROM AUTHOR]

Conical intersections control excited state reactivity, and thus, elucidating and predicting their geometric and energetic characteristics are crucial for understanding photochemistry. Locating these intersections requires accurate and efficient electronic structure methods. Unfortunately, the most accurate methods (e.g., multireference perturbation theories such as XMS-CASPT2) are computationally challenging for large molecules. The state-interaction state-averaged restricted ensemble referenced Kohn–Sham (SI-SA-REKS) method is a computationally efficient alternative. The application of SI-SA-REKS to photochemistry was previously hampered by a lack of analytical nuclear gradients and nonadiabatic coupling matrix elements. We have recently derived analytical energy derivatives for the SI-SA-REKS method and implemented the method effectively on graphical processing units. We demonstrate that our implementation gives the correct conical intersection topography and energetics for several examples. Furthermore, our implementation of SI-SA-REKS is computationally efficient, with observed sub-quadratic scaling as a function of molecular size. This demonstrates the promise of SI-SA-REKS for excited state dynamics of large molecular systems. [ABSTRACT FROM AUTHOR]

The use of the mixed reference (MR) reduced density matrix, which combines reduced density matrices of the MS = +1 and -1 triplet-ground states, is proposed in the context of the collinear spin-fliptime-dependent density functional theory (SF-TDDFT) methodology. The time-dependent Kohn-Sham equation with the mixed state is solved by the use of spinor-like open-shell orbitals within the linear response formalism, which enables to generate additional configurations in the realm of TD-DFT. The resulting MR-SF-TDDFT computational scheme has several advantages before the conventional collinear SF-TDDFT. The spin-contamination of the response states of SF-TDDFT is nearly removed. This considerably simplifies the identification of the excited states, especially in the "black-box" type applications, such as the automatic geometry optimization, reaction path following, or molecular dynamics simulations. With the new methodology, the accuracy of the description of the excited states is improved as compared to the collinear SF-TDDFT. Several test examples, which include systems typified by strong non-dynamic correlation, orbital (near) degeneracy, and conical intersections, are given to illustrate the performance of the new method. [ABSTRACT FROM AUTHOR]

An extended variant of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, the REKS(4,4) method, designed to describe the ground electronic states of strongly multireference systems is modified to enable calculation of excited states within the time-independent variational formalism. The new method, the state-interaction state-averaged REKS(4,4), i.e., SI-SA-REKS(4,4), is capable of describing several excited states of a molecule involving double bond cleavage, polyradical character, or multiple chromophoric units. We demonstrate that the newmethod correctly describes the ground and the lowest singlet excited states of a molecule (ethylene) undergoing double bond cleavage. The applicability of the new method for excitonic states is illustrated with π stacked ethylene and tetracene dimers. We conclude that the new method can describe a wide range of multireference phenomena. [ABSTRACT FROM AUTHOR]

The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham(REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. In this work, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirely in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. The implementation and benchmarking of the derived formalism will be described in a subsequent article of this series. [ABSTRACT FROM AUTHOR]

The spin-restricted ensemble-referenced Kohn-Sham (REKS) method is based on an ensemble representation of the density and is capable of correctly describing the non-dynamic electron correlation stemming from (near-)degeneracy of several electronic configurations. The existing REKS methodology describes systems with two electrons in two fractionally occupied orbitals. In thiswork, the REKS methodology is extended to treat systems with four fractionally occupied orbitals accommodating four electrons and self-consistent implementation of the REKS(4,4) method with simultaneous optimization of the orbitals and their fractional occupation numbers is reported. The new method is applied to a number of molecular systems where simultaneous dissociation of several chemical bonds takes place, as well as to the singlet ground states of organic tetraradicals 2,4-didehydrometaxylylene and 1,4,6,9-spiro[4.4]nonatetrayl. [ABSTRACT FROM AUTHOR]

The analytical gradient for the two-component Normalized Elimination of the Small Component (2c-NESC) method is presented. The 2c-NESC is a Dirac-exact method that employs the exact two-component one-electron Hamiltonian and thus leads to exact Dirac spin-orbit (SO) splittings for one-electron atoms. For many-electron atoms and molecules, the effect of the two-electron SO interaction is modeled by a screened nucleus potential using effective nuclear charges as proposed by Boettger [Phys. Rev. B 62, 7809 (2000)]. The effect of spin-orbit coupling (SOC) on molecular geometries is analyzed utilizing the properties of the frontier orbitals and calculated SO couplings. It is shown that bond lengths can either be lengthened or shortened under the impact of SOC where in the first case the influence of low lying excited states with occupied antibonding orbitals plays a role and in the second case the j j-coupling between occupied antibonding and unoccupied bonding orbitals dominates. In general, the effect of SOC on bond lengths is relatively small (=5% of the scalar relativistic changes in the bond length). However, large effects are found for van der Waals complexes Hg2 and Cn2, which are due to the admixture of more bonding character to the highest occupied spinors. [ABSTRACT FROM AUTHOR]

State-averaged (SA) variants of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, SA-REKS and state-interaction (SI)-SA-REKS, implement ensemble density functional theory for variationally obtaining excitation energies of molecular systems. In this work, the currently existing version of the SA-REKS method, which included only one excited state into the ensemble averaging, is extended by adding more excited states to the averaged energy functional. A general strategy for extension of the REKS-type methods to larger ensembles of ground and excited states is outlined and implemented in extended versions of the SA-REKS and SI-SA-REKS methods. The newly developed methods are tested in the calculation of several excited states of ground-state multi-reference systems, such as dissociating hydrogen molecule, and excited states of donor-acceptor molecular systems. For hydrogen molecule, the new method correctly reproduces the distance dependence of the lowest excited state energies and describes an avoided crossing between the doubly excited and singly excited states. For bithiophene-perylenediimide stacked complex, the SI-SA-REKS method correctly describes crossing between the locally excited state and the charge transfer excited state and yields vertical excitation energies in good agreement with the ab initio wavefunction methods. [ABSTRACT FROM AUTHOR]

Electron transfer in the ground and excited states of a model donor-acceptor (D-A) system is investigated using the single-reference and multi-reference density functional theory (DFT) methods. To analyze the results of the calculations, a simple two-site multi-reference model was derived that predicts a stepwise electron transfer in the S0 state and a wave-like dependence of the S1 electron transfer on the external stimulus. The standard single-reference Kohn-Sham (KS) DFT approach and the time-dependent DFT (TDDFT) method failed to describe the correct dependence of the S0 and S1 electron transfer on the external electric field applied along the donor-acceptor system. The multi-reference DFT approach, the spin-restricted ensemble-referenced KS (REKS) method, was able to successfully reproduce the correct behavior of the S0 and S1 electron transfer on the applied field. The REKS method was benchmarked against experimentally measured gas phase charge transfer excitations in a series of organic donor-acceptor complexes and displayed its ability to describe this type of electronic transitions with a very high accuracy, mean absolute error of 0.05 eV with the use of the standard range separated density functionals. On the basis of the calculations undertaken in this work, it is suggested that the non-adiabatic coupling between the S0 and S1 states may interfere with the electron transfer in a weakly coupled donor-acceptor system. It is also suggested that the electronic excitation of a D+-A- system may play a dual role by assisting the further electron transfer at certain magnitudes of the applied electric field and causing the backward transfer at lower electric field strengths. [ABSTRACT FROM AUTHOR]

Computational investigation of the longest wavelength excitations in a series of cyanines and linear n-acenes is undertaken with the use of standard spin-conserving linear response time-dependent density functional theory (TD-DFT) as well as its spin-flip variant and a ΔSCF method based on the ensemble DFT. The spin-conserving linear response TD-DFT fails to accurately reproduce the lowest excitation energy in these π-conjugated systems by strongly overestimating the excitation energies of cyanines and underestimating the excitation energies of n-acenes. The spin-flip TD-DFT is capable of correcting the underestimation of excitation energies of n-acenes by bringing in the non-dynamic electron correlation into the ground state; however, it does not fully correct for the overestimation of the excitation energies of cyanines, for which the non-dynamic correlation does not seem to play a role. The ensemble DFT method employed in this work is capable of correcting for the effect of missing non-dynamic correlation in the ground state of n-acenes and for the deficient description of differential correlation effects between the ground and excited states of cyanines and yields the excitation energies of both types of extended π-conjugated systems with the accuracy matching high-level ab initio multireference calculations. [ABSTRACT FROM AUTHOR]

Analytic second derivatives of the relativistic energy for the calculation of electric response properties are derived utilizing the normalized elimination of the small component (NESC) method. Explicit formulas are given for electric static dipole polarizabilities and infrared intensities by starting at the NESC representation of electric dipole moments. The analytic derivatives are implemented in an existing NESC program and applied to calculate dipole moments, polarizabilities, and the infrared spectra of gold- and mercury-containing molecules as well as some actinide molecules. Comparison with experiment reveals the accuracy of NESC second order electric response properties. [ABSTRACT FROM AUTHOR]

Based on the analytic derivatives formalism for the spin-free normalized elimination of the small component method, a new computational scheme for the calculation of the electric field gradient at the atomic nuclei was developed and presented. The new computational scheme was tested by the calculation of the electric field gradient at the mercury nucleus in a series of Hg-containing inorganic and organometallic compounds. The benchmark calculations demonstrate that the new formalism is capable of reproducing experimental and theoretical reference data with high accuracy. The method developed can be routinely applied to the calculation of large and very large molecules and holds considerable promise for the interpretation of the experimental data of biologically relevant compounds containing heavy elements. [ABSTRACT FROM AUTHOR]

The analytical energy gradient of the normalized elimination of the small component (NESC) method is derived for the first time and implemented for the routine calculation of NESC geometries and other first order molecular properties. Essential for the derivation is the correct calculation of the transformation matrix U relating the small component to the pseudolarge component of the wavefunction. The exact form of ∂U/∂λ is derived and its contribution to the analytical energy gradient is investigated. The influence of a finite nucleus model and that of the picture change is determined. Different ways of speeding up the calculation of the NESC gradient are tested. It is shown that first order properties can routinely be calculated in combination with Hartree-Fock, density functional theory (DFT), coupled cluster theory, or any electron correlation corrected quantum chemical method, provided the NESC Hamiltonian is determined in an efficient, but nevertheless accurate way. The general applicability of the analytical NESC gradient is demonstrated by benchmark calculations for NESC/CCSD (coupled cluster with all single and double excitation) and NESC/DFT involving up to 800 basis functions. [ABSTRACT FROM AUTHOR]

The isomer shift for the 23.87 keV M1 resonant transition in the 119Sn nucleus is calibrated with the help of ab initio calculations. The calibration constant α(119Sn) obtained from Hartree–Fock (HF) calculations (αHF(119Sn)=(0.081±0.002)a0-3 mm/s) and from second-order Mo\ller–Plesset (MP2) calculations (αMP2(119Sn)=(0.091±0.002)a0-3 mm/s) are in good agreement with the previously obtained values. The importance of a proper treatment of electron correlation effects is demonstrated on the basis of a statistical analysis of the results of the calibration. The approach used in the calibration is applied to study the 119Sn isomer shift in CaSnO3 perovskite under pressure. Comparison with the experimental results for the pressure range of 0–36 GPa shows that the current methodology is capable of describing tiny variations of isomer shift with reasonable accuracy. [ABSTRACT FROM AUTHOR]

The orbital products of occupied and virtual orbitals are employed as an expansion basis for the charge density generating the local potential in the optimized effective potential method thus avoiding the use of auxiliary basis sets. The high computational cost arising from the quadratic increase of the dimension of this product basis with system size can be greatly reduced by elimination of the linearly dependent products according to a procedure suggested by Beebe and Linderberg [Int. J. Quantum Chem. 12, 683 (1977)]. Numerical results from this approach show a very good agreement with those obtained from balancing the auxiliary basis for the expansion of the local potential with the orbital basis set. [ABSTRACT FROM AUTHOR]

The optimized effective potential (OEP) equations are solved in a matrix representation using the orbital products of occupied and virtual orbitals for the representation of both the local potential and the response function. This results in a direct relationship between the matrix elements of local and nonlocal operators for the exchange-correlation potential. The effect of the truncation of the number of such products in the case of finite orbital basis sets on the OEP orbital and total energies and on the spectrum of eigenvalues of the response function is examined. Test calculations for Ar and Ne show that rather large AO basis sets are needed to obtain an accurate representation of the response function. [ABSTRACT FROM AUTHOR]

A quantum chemical computational scheme for the calculation of isomer shift in Mössbauer spectroscopy is suggested. Within the described scheme, the isomer shift is treated as a derivative of the total electronic energy with respect to the radius of a finite nucleus. The explicit use of a finite nucleus model in the calculations enables one to incorporate straightforwardly the effects of relativity and electron correlation. The results of benchmark calculations carried out for several iron complexes as well as for a number of atoms and atomic ions are presented and compared with the available experimental and theoretical data. [ABSTRACT FROM AUTHOR]

It is demonstrated that the LYP correlation functional is not suited to be used for the calculation of electron spin resonance hyperfine structure (HFS) constants, nuclear magnetic resonance spin-spin coupling constants, magnetic, shieldings and other properties that require a balanced account of opposite- and equal-spin correlation, especially in the core region. In the case of the HFS constants of alkali atoms, LYP exaggerates opposite-spin correlation effects thus invoking too strong in-out correlation effects, an exaggerated spin-polarization pattern in the core shells of the atoms, and, consequently, too large HFS constants. Any correlation functional that provides a balanced account of opposite- and equal-spin correlation leads to improved HFS constants, which is proven by comparing results obtained with the LYP and the PW91 correlation functional. It is suggested that specific response properties are calculated with the PW91 rather than the LYP correlation functional. [ABSTRACT FROM AUTHOR]

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas–Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac–Hartree–Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5×10-9 hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change. [ABSTRACT FROM AUTHOR]

A simple modification of the zeroth-order regular approximation (ZORA) in relativistic theory is suggested to suppress its erroneous gauge dependence to a high level of approximation. The method, coined gauge-independent ZORA (ZORA-GI), can be easily installed in any existing nonrelativistic quantum chemical package by programming simple one-electron matrix elements for the quasirelativistic Hamiltonian. Results of benchmark calculations obtained with ZORA-GI at the Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory (MP2) level for dihalogens X2 (X=F,Cl,Br,I,At) are in good agreement with the results of four-component relativistic calculations (HF level) and experimental data (MP2 level). ZORA-GI calculations based on MP2 or coupled-cluster theory with single and double perturbations and a perturbative inclusion of triple excitations [CCSD(T)] lead to accurate atomization energies and molecular geometries for the tetroxides of group VIII elements. With ZORA-GI/CCSD(T), an improved estimate for the atomization energy of hassium (Z=108) tetroxide is obtained. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The infinite-order regular approximation (IORA) and IORA with modified metric (IORAmm) is used to develop an algorithm for calculating relativistically corrected isotropic hyperfine structure (HFS) constants. The new method is applied to the calculation of alkali atoms Li–Fr, coinage metal atoms Cu, Ag, and Au, the Hg+ radical ion, and the mercury containing radicals HgH, HgCH3, HgCN, and HgF. By stepwise improvement of the level of theory from Hartree–Fock to second-order Møller–Plesset theory and to quadratic configuration interaction theory with single and double excitations, isotropic HFS constants of high accuracy were obtained for atoms and for molecular radicals. The importance of relativistic corrections is demonstrated. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A new method for calculating the indirect nuclear spin–spin coupling constant within the regular approximation to the exact relativistic Hamiltonian is presented. The method is completely analytic in the sense that it does not employ numeric integration for the evaluation of relativistic corrections to the molecular Hamiltonian. It can be applied at the level of conventional wave function theory or density functional theory. In the latter case, both pure and hybrid density functionals can be used for the calculation of the quasirelativistic spin–spin coupling constants. The new method is used in connection with the infinite-order regular approximation with modified metric (IORAmm) to calculate the spin–spin coupling constants for molecules containing heavy elements. The importance of including exact exchange into the density functional calculations is demonstrated. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c[sup -20]. Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Analytic expressions for the derivatives of the total molecular energy with respect to external electric field are derived within the regular approximation to the full four-component relativistic Hamiltonian and presented in matrix form suitable for implementation in standard quantum-chemical codes. Results of benchmark calculations using the infinite-order regular approximation with modified metric method are presented and discussed. The static electric dipole polarizabilities of group VIII metal tetroxides MO[SUB4] for M = Ru, Os, Hs (Z5108) are studied with the help of second-order Møller-Plesset perturbation theory using the infinite-order regular approximation with modified metric Hamiltonian. The polarizabilities obtained vary in the sequence RuO[SUB4] > OsO[SUB4] > HsO[SUB4], which is different from those obtained in other studies. However, it is in line with calculated [SUP1]T[SUB2] ← [SUP1]A[SUB1] excitation energies of the group VIII tetroxides, which provide a measure for the magnitude of their polarizabilities. [ABSTRACT FROM AUTHOR]

A new method for relativistically corrected nuclear magnetic resonance (NMR) chemical shifts is developed by combining the individual gauge for the localized orbital approach for density functional theory with the normalized elimination of a small component using an effective potential. The new method is used for the calculation of the NMR chemical shifts of [SUP95]Mo and [SUP183]W in various molybdenum and tungsten compounds. It is shown that quasirelativistic corrections lead to an average improvement of calculated NMR chemical shift values by 300 and 120 ppm in the case of [SUP95]Mo and [SUP183]W, respectively, which is mainly due to improvements in the paramagnetic contributions. The relationship between electronic structure of a molecule and the relativistic paramagnetic corrections is discussed. Relativistic effects for the diamagnetic part of the magnetic shielding caused by a relativistic contraction of the s,p orbitals in the core region concern only the shielding values, however, have little consequence for the shift values because of the large independence from electronic structure and a cancellation of these effects in the shift values. It is shown that the relativistic corrections can be improved by level shift operators and a B3LYP hybrid functional, for which Hartree-Fock exchange is reduced to 15%. [ABSTRACT FROM AUTHOR]

Analytic expressions are derived for the evaluation of derivatives of the total molecular energy with respect to external parameters (nuclear coordinates, external electric fields, etc.) within the relativistic regular approximation. The presented formalism employs the spectral resolution of the identity avoiding, however, the explicit use of an auxiliary basis set in the calculation of the matrix elements of the regular relativistic Hamiltonian. The final formulas for the total energy and energy derivatives are presented in matrix form suitable for implementation into standard quantum chemical packages. Results of benchmark calculations for gold containing diatomic molecules and for xenone hexafluoride performed at the Hartree-Fock and various correlation corrected levels of theory are presented and discussed. [ABSTRACT FROM AUTHOR]

Investigates various atomic and molecular multiplet states using a proposed spin-restricted open-shell Kohn-Sham (ROKS) method. Range of multiplets considered; ROKS equations; States of atomic species; Angular momentum states of linear molecules; Diradicaloid states of perpendicular ethylene and of square cyclobutadiene.

A new family of light driven molecular rotary motors, which can be synthesized from easily available precursor compounds and which are capable of completing a full 360° revolution by two photoisomerization steps only, is proposed. The non-adiabatic molecular dynamic simulations show that the photoisomerization steps of the motor's working cycle occur on an ultrafast time scale (ca. 200–300 fs), have a very high quantum yield of isomerization (0.91–0.97), and display high selectivity of torsion in the same direction. It is expected that the new motor should remain operational at lower temperatures than the currently existing motors. [ABSTRACT FROM AUTHOR]

Utilizing the analytic derivative formalism for the Mössbauer isomer shift in connection with the Dirac-exact two-component Normalized Elimination of the Small Component (2c-NESC) method a new approach to the analytic calculation of the contact densities at the nuclei has been developed and implemented in the general purpose NESC programme. The new approach is applied to the calculation of the contact densities as well as contact density differences in several iodine-, gold-, and mercury-containing molecules. Substantial differences between the contact densities obtained by the spin-free 1c-NESC method and the 2c-NESC method are found, which demonstrate the importance of spin-orbit coupling. However, the influence of spin-orbit coupling on the contact density differences between the sample and the reference nuclei is found to be modest. This result suggests that a low-cost determination of accurate contact densities at the nuclei can be achieved by combining the 1c-NESC densities obtained at the correlated wavefunction level of theory with the contact density differences obtained at the 2c-NESC/DFT level. [ABSTRACT FROM AUTHOR]

The dynamics of the ring opening in the state of cyclohexa-1,3-diene (CHD) is studied by a new direct mixed quantum-classical non-adiabatic dynamics approach which employs the decoherence-induced surface hopping based on the exact factorisation (DISH-XF) molecular dynamics method in connection with the state-interaction state-averaged spin-restricted ensemble-referenced Kohn–Sham (SI-SA-REKS, or SSR) electronic structure method. The critical species on the and PESs of CHD were studied using the SSR method and the minimum energy pathways (MEPs) were optimised. The obtained vertical excitation energies are in good agreement (within ca. 5–6 kcal/mol) with the experimental values. The optimised geometry of the / minimum energy conical intersection (MECI) agrees well with the previously obtained MSPT2 geometry. The DISH-XF/SSR non-adiabatic molecular dynamics (NAMD) simulations of ring opening in CHD predict the exponential decay constant fs in a reasonable agreement with an experimental estimate (230±30 fs). The calculated product branching ratio (CHD:HT = 64:36) is in agreement with the recent experimental measurement (70:30). The NAMD trajectories are analysed in terms of the vibrational normal modes and the obtained branching ratio is explained by persistent stretching of the fissile bond when the trajectories propagate on the PES. [ABSTRACT FROM AUTHOR]

It is estimated that 72% of the worldwide primary energy consumption is lost as waste heat. Thermoelectric Generators (TEGs) are a possible solution to convert a part of this energy into electricity and heat for space heating. However, for their deployment a proven long-term operation is required. Therefore, this research investigates the long-term stability of TEGs on system level in air and argon atmosphere under thermal cycling up to 543 K. The layout of the examined test objects resembles a TEG in stack design. The results show that the maximal output power of the test object in air reaches a plateau at 57% of the initial power after 50 cycles caused by an increased electrical resistance of the system. Whereas the test object in argon atmosphere shows no significant degradation of electrical power or resistance. The findings represent a step towards the understanding of the long-term stability of TEGs and can be used as a guideline for design decisions. [ABSTRACT FROM AUTHOR]

The normalized elimination of the small component method is a first principles two-component relativistic approach that leads to the Dirac-exact description of one-electron systems. Therefore, it is an ideal starting point for developing procedures, by which first- and second-order response properties can be routinely calculated. We present algorithms and methods for the calculation of molecular response properties such as geometries, dipole moments, hyperfine structure constants, vibrational frequencies and force constants, electric polarizabilities, infrared intensities and so forth. The described formalisms are applied to molecules containing mercury and other heavy elements, which require a relativistic treatment. Perspectives for the future development and application of Dirac-exact methods are outlined. © 2013 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

In the past, the design of light-driven single molecule rotary motors has been mainly guided by the modification of their ground-state conformational properties. Further progress in this field is thus likely to be achieved through a detailed understanding of light-induced dynamics of the system and the ways of modulating it by introducing chemical modifications. In the present theoretical work, the analysis of model organic chromophores and synthesized rotary motors is used for rationalizing the effect of electron-withdrawing heteroatoms (such as a cationic nitrogen) on the topography and branching plane of mechanistically relevant conical intersections. Such an analysis reveals how the character of rotary motion could be changed from a precessional motion to an axial rotational motion. These concepts are then used to design and build quantum chemical models of three distinct types of Schiff base rotary motors. One of these models, featuring the synthetically viable indanylidenepyrroline framework, has conical intersection structures consistent with an axial rotation not hindered by ground-state conformational barriers. It is expected that this type of motor should be capable of funneling the photon energy into specific rotary modes, thus achieving photoisomerization quantum efficiencies comparable to those seen in visual pigments. [ABSTRACT FROM AUTHOR]

1,3-Benzenediamidoethanethiolatemercury [BDT-Hg or BD(S)-Hg] and its derivatives are investigated utilizing the Dirac exact relativistic normalized elimination of the small component method in connection with B3LYP, CCSD(T), and polarizable continuum calculations. It is shown that die chelating energy of BDT-Hg can be significantly increased by replacing sulfur with selenium or tellurium, thus leading to BD(Se)-Hg or BD(Te)-Hg. In this particular case, the chalcogenophilicity of mercury increases from S to Te because increasing the E--Hg bond lengths leads to a reduction of ring strain. Various possibilities of increasing die metal (M) chelating strength in BDT-M complexes are investigated, and suggestions for new chelating agents based on the BDT-M template are made. [ABSTRACT FROM AUTHOR]

Multireference averaged quadratic coupled cluster (MRAQCC) (4,5)/cc-pVTZ calculations predict that bond pseudorotation (BPR) in the first excited singlet state of the cyclopentadienyl cation (CPC) proceeds with a barrier of just 0.35 kcal/mol, where five dienylic forms present the minima and five allylic forms the transition states of the pseudorotation process. Vibrational and entropic corrections revert the order of stabilities and lead to a Δ G(298) of just 0.05 kcal/mol indicating that BPR is unhindered at room temperature. The description of the CPC ring in terms of curvilinear deformation coordinates (seven for C5, seven for X5, and three coupling coordinates) make it possible to explore both the six-dimensional (6D) Jahn-Teller and the 8D pseudo-Jahn-Teller space and assess the importance of Jahn-Teller and pseudo-Jahn-Teller deformations of the CPC ring. The latter dominate the ring deformations along the BPR path. The only somewhat larger Jahn-Teller contribution results from a E [ABSTRACT FROM AUTHOR]

In this tutorial review, we discuss the utilization of chemical shift information as well as ab initiocalculations of nuclear shieldings for protein structure determination. Both the empirical and computational aspects of the chemical shift are reviewed and the role of molecular dynamics and the accuracy of different computational methods are discussed. It is anticipated that incorporating theoretical information on chemical shifts will increase the accuracy of protein structures, in the solid and liquid state alike, and extend the applicability of NMR spectroscopy to ever larger systems. [ABSTRACT FROM AUTHOR]

Abstract: Mössbauer spectroscopy is a widely used analytic tool which provides information about local electronic structure of solid materials on an atomic scale. The isomer shift of resonance nuclear transition is a sensitive parameter which depends on the charge and spin state of the resonating atom as well as on its chemical environment. Theory underlying the isomer shift is reviewed and its connection to the local electronic structure is discussed. A review of advances made in the ab initio calculation of isomer shift is presented. The importance of careful calibration of the parameters of nuclear transitions on the basis of high-level quantum chemical calculations with the inclusion of both relativistic effects and electron correlation is underlined. With the help of accurate theoretical calculations of the isomer shift over a wide range of chemical environments deeper understanding of a relationship between the observed spectroscopic parameters and the electronic structure of materials will be gained. [Copyright &y& Elsevier]

Nine AuX molecules (X = H, O, S, Se, Te, F, Cl, Br, I), their isoelectronic HgX+ analogues, and the corresponding neutral HgX diatomics have been investigated using NESC (Normalized Elimination of the Small Component) and B3LYP theory to determine relativistic effects for bond dissociation energies (BDEs), bond lengths, dipole moments, and charge distributions. Relativistic effects are substantially larger for AuX than HgX molecules. AuX bonding has been contrasted with HgX bonding considering the effects of relativity, charge transfer and ionic bonding, 3-electron versus 2-electron bonding, residual π- bonding, lone pair repulsion, and the d-block effect. The interplay of the various electronic effects leads to strongly differing trends in calculated BDEs, which can be rationalized with a simple MO model based on electronegativity differences, atomic orbital energies, and their change due to scalar relativity. A relativistic increase or decrease in the BDE is directly related to relativistic changes in the 6s orbital energy and electron density. [ABSTRACT FROM AUTHOR]

The convergence behavior of the iterative solution of the normalized elimination of the small component (NESC) method is investigated. A simple and efficient computational protocol for obtaining the exact positive-energy eigenvalues of the relativistic Hamiltonian starting from the energies obtained within the regular approximation is suggested. The protocol is based on the analysis of the relationship between the eigenvalues of the quasi-relativistic Hamiltonian in the regular approximation and the positive-energy eigenvalues of the exact relativistic Hamiltonian which was derived in the course of this work. [ABSTRACT FROM AUTHOR]

By expanding the Foldy-Wouthuysen representation of the Dirac equation near the free- particle solution it is shown that the Hamiltonian of the zeroth-order regular approximation (ZORA) leads to an infinite summation of the leading relativistic corrections to the free- particle, non-relativistic energy. The analysis of the perturbation expansion of the ZORA Hamiltonian reveals that the ZORA Hamiltonian recovers all terms of the Breit-Pauli theory to second order. This result is general and applies not only to hydrogen-like atomic ions (as was demonstrated before) but also to a wide variety of physical problems. ZORA is analogous to the random phase approximation in many-body theory in the sense that both methods include an infinite-order summation of the asymptotically non-vanishing terms. This highlights the difference between ZORA and the Douglas-Kroll method, with the latter being analogous to finite-order many-body perturbation theory. On the basis of this analysis the performance of ZORA when calculating various molecular properties is discussed. [ABSTRACT FROM AUTHOR]

All-electron CCSD(T), QCISD(T) and MP4(SDQ) calculations including relativistic effects via the use of the IORAmm Hamiltonian have been performed for PdCO. The optimized molecular geometry is in nice agreement with the recently obtained experimental data. The Pd–CO bond dissociation energy is estimated to be 38.8 kcal/mol. The vibrational spectrum of PdCO is calculated and a reassessment of the experimental datum for the frequency of bending mode is suggested. [Copyright &y& Elsevier]

For the quasi-relativistic normalized elimination of small component using an effective potential (NESC-EP) method, analytical energy gradients were developed, programmed, and implemented in a standard quantum chemical program package. NESC-EP with analytical gradients was applied to determine geometry, vibrational frequencies, and dissociation enthalpies of ferrocene, tungsten hexafluoride, and tungsten hexacarbonyle. Contrary to non-relativistic calculations and calculations carried out with RECPs for the same compounds, NESC-EP provided reliable molecular properties in good agreement with experiment. The computational power of NESC-EP results from the fact that reliable relativistic corrections are obtained at a cost level only slightly larger than that of a non-relativistic calculation. [Copyright &y& Elsevier]

With the help of resolution of the identity (RI) a compact representation for the zeroth-order (ZORA) and infinite-order (IORA) regular approximation Hamiltonians in matrix form is developed. The new representation does not require calculation of any additional molecular integrals, which involve an auxiliary basis set used in the RI. The IORA computational scheme is modified in such a way that the erroneous gauge dependence of the total energy is reduced by an order of magnitude. The new quasi-relativistic method, dubbed IORAmm, is tested along with the ZORA and IORA methods in atomic and molecular calculations performed at the SCF and MP2 level. [Copyright &y& Elsevier]

A recently developed variationally stable quasi-relativistic method, which is based on the low-order approximation to the method of normalized elimination of the small component, was incorporated into density functional theory (DFT). The new method was tested for diatomic molecules involving Ag, Cd, Au, and Hg by calculating equilibrium bond lengths, vibrational frequencies, and dissociation energies. The method is easy to implement into standard quantum chemical programs and leads to accurate results for the benchmark systems studied. [Copyright &y& Elsevier]

The connection between the exact quasirelativistic approach developed in the title reference [W. Kutzelnigg and W. Liu, J. Chem. Phys. 123, 241102 (2005)] and the method of elimination of the small component in matrix form developed previously by Dyall is explicitly worked out. An equation that links Hermitian and non-Hermitian formulations of the exact quasirelativistic theory is derived. Besides establishing a kinship between the existing formulations, the proposed equation can be employed for the derivation of new formulations of the exact quasirelativistic theory. [ABSTRACT FROM AUTHOR]

[Display omitted] • Ehrenfest Force F (r) applied to the two C-O ring-opening photo-reactions of oxirane. • Ehrenfest Force trajectories and hybrid stress tensor trajectory calculated with the F (r) BCP s. • Torsion of the CH 2 group facilitated the photo-reaction pathway towards the CI. • Torsion of CH 2 group induced symmetry breaking evident from S 0 and S 1 F (r) trajectories. • Agreement found between the Ehrenfest Force and hybrid stress tensor trajectories. Ehrenfest Force F (r) trajectories were constructed for the C-O ring-opening photo-reactions of oxirane. The F (r) trajectories were constructed in an eigenvector-space corresponding to bond-flexing, bond-twist and bond-anharmonicity associated with the least and most preferred directions of charge density accumulation and bond critical point (BCP) sliding respectively. The presence of the torsion of a CH 2 group for one of the photo-reactions led to greater symmetry breaking and greater reaction pathway preference. Consistency was found from hybrid Ehrenfest Force F (r) trajectories that were constructed using the Ehrenfest Force F (r) BCP s and the stress tensor eigenvectors. [ABSTRACT FROM AUTHOR]

The non-adiabatic dynamics of furan excited in the ππ* state (S2 in the Franck–Condon geometry) was studied using non-adiabatic molecular dynamics simulations in connection with an ensemble density functional method. The time-resolved photoelectron spectra were theoretically simulated in a wide range of electron binding energies that covered the valence as well as the core electrons. The dynamics of the decay (rise) of the photoelectron signal were compared with the excited-state population dynamics. It was observed that the photoelectron signal decay parameters at certain electron binding energies displayed a good correlation with the events occurring during the excited-state dynamics. Thus, the time profile of the photoelectron intensity of the K-shell electrons of oxygen (decay constant of 34 ± 3 fs) showed a reasonable correlation with the time of passage through conical intersections with the ground state (47 ± 2 fs). The ground-state recovery constant of the photoelectron signal (121 ± 30 fs) was in good agreement with the theoretically obtained excited-state lifetime (93 ± 9 fs), as well as with the experimentally estimated recovery time constant (ca. 110 fs). Hence, it is proposed to complement the traditional TRPES observations with the trXPS (or trNEXAFS) measurements to obtain more reliable estimates of the most mechanistically important events during the excited-state dynamics. [ABSTRACT FROM AUTHOR]

An exchange functional is proposed which is conceptually similar to the established Becke functional and satisfies the same asymptotic properties. The one-parameter variant A of this new functional yields atomic exchange energies which are very close to those from the optimized potential model (OPM) for the light elements (up to Ne), whereas the three-parameter variant B reproduces the OPM reference values for all elements (H to Xe) more accurately than other established exchange functionals. For molecular applications, the new exchange functional is combined with a new non-local correlation functional based on a Coulomb hole model. Detailed results are reported for the molecules from the G2 data base. For each of the four basis sets considered, variants A and B yield essentially the same atomization energies, ionization potentials, proton affinities and molecular geometries. The mean absolute deviation between the calculated and experimental atomization energies for the G2 reference molecules is 3 kcalmol-1 . In an overall assessment, the present results seem comparable in quality with those from the B3LYP hybrid functional, even though our new functional does not include any Hartree-Fock exchange. Some illustrative results for transition-metal compounds are also given. [ABSTRACT FROM AUTHOR]

A new algorithm for the two-component Normalized Elimination of the Small Component (2cNESC) method is presented and tested in the calculation of spin-orbit (SO) splittings for a series of heavy atoms and their molecules. The 2cNESC is a Dirac-exact method that employs the exact two-component one-electron Hamiltonian and thus leads to exact Dirac SO splittings for one-electron atoms. For many-electron atoms and molecules, the effect of the two-electron SO interaction is modeled by a screened nucleus potential using effective nuclear charges as proposed by Boettger [Phys. Rev. B 62, 7809 (2000)]. The use of the screened nucleus potential for the two-electron SO interaction leads to accurate spinor energy splittings, for which the deviations from the accurate Dirac Fock-Coulomb values are on the average far below the deviations observed for other effective one-electron SO operators. For hydrogen halides HX (X = F, Cl, Br, I, At, and Uus) and mercury dihalides HgX2 (X = F, Cl, Br, I) trends in spinor energies and SO splittings as obtained with the 2cNESC method are analyzed and discussed on the basis of coupling schemes and the electronegativity of X. [ABSTRACT FROM AUTHOR]