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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]

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]

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]

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 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]

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]

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 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]

In this paper it is argued that the use of density functional theory (DFT) to solve the exact, non-relativistic, many-electron problem, for magnetic systems requires imposing space and spin symmetry constraints exactly in the same way as it is currently done in ab initio wave function theory. This strong statement is supported on pertinent calculations for selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids. These calculations include several wave function methods of increasing accuracy and different forms of the exchange- correlation functional. The comparisons of numerical results carried out always within the same standard Gaussian Type Orbital atomic basis set show that imposing or not the spin and space constraints (restricted or unrestricted formalisms) leads to contradictory results. Therefore, it appears that, in the case of the Heisenberg magnetic constant, the present exchange-correlation functionals may provide reasonable numerical results although for the wrong physical reasons thus evidencing the failure of the current DFT methods to properly describe magnetic systems. [ABSTRACT FROM AUTHOR]

Next‐generation quantum theory of atoms in molecules was applied to analyze, along an entire bond path, intramolecular interactions known to influence the photoisomerization dynamics of a light‐driven rotary molecular motor. The 3D bond‐path framework set B0,1 constructed from the least and most preferred directions of electronic motion, provided new insights into the bonding leading to different S1 state lifetimes including the first quantification of covalent character of a closed‐shell intramolecular bond path. We undertook the first use of the stress tensor trajectory Tσ(s) analysis on selected nonadiabatic molecular dynamics trajectories with the electron densities obtained using the ensemble density functional theory method. The stress tensor Tσ(s) analysis was found to be well suited to follow the dynamics trajectories that included the S0 and S1 electronic states through the conical intersection and also provided to a new measure to assess the degree of purity of the axial bond rotation for the design of rotary molecular motors. [ABSTRACT FROM AUTHOR]