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Within the self-consistent field approximation, computationally tractable expressions for the isotropic second-order hyperpolarizability have been derived and implemented for the calculation of two-photon absorption cross sections. The novel tensor average formulation presented in this work allows for the evaluation of isotropic damped cubic response functions using only ∼3.3% (one-photon off-resonance regions) and ∼10% (one-photon resonance regions) of the number of auxiliary Fock matrices required when explicitly calculating all the needed individual tensor components. Numerical examples of the two-photon absorption cross section in the one-photon off-resonance and resonance regions are provided for alanine–tryptophan and 2,5-dibromo-1,4-bis(2-(4-diphenylaminophenyl)vinyl)-benzene. Furthermore, a benchmark set of 22 additional small- and medium-sized organic molecules is considered. In all these calculations, a quantitative assessment is made of the reduced and approximate forms of the cubic response function in the one-photon off-resonance regions and results demonstrate a relative error of less than ∼5% when using the reduced expression as compared to the full form of the isotropic cubic response function. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A computational approach to the calculation of excited state electronic circular dichroism (ESECD) spectra of chiral molecules is discussed. Frequency dependent quadratic response theory is employed to compute the rotatory strength for transitions between excited electronic states, by employing both a magnetic gauge dependent and a (velocity-based) magnetic gauge independent approach. Application is made to the lowest excited states of two prototypical chiral molecules, propylene oxide, also known as 1,2-epoxypropane or methyl oxirane, and R-(+)-1,1′-bi(2-naphthol), or BINOL. The dependence of the rotatory strength for transitions between the lowest three excited states of methyl oxirane upon the quality and extension of the basis set is analyzed, by employing a hierarchy of correlation consistent basis sets. Once established that basis sets of at least triple zeta quality, and at least doubly augmented, are sufficient to ensure sufficiently converged results, at least at the Hartree-Fock self-consistent field (HF-SCF) level, the rotatory strengths for all transitions between the lowest excited electronic states of methyl oxirane are computed and analyzed, employing HF-SCF, and density functional theory (DFT) electronic structure models. For DFT, both the popular B3LYP and its recently highly successful CAM-B3LYP extension are exploited. The strong dependence of the spectra upon electron correlation is highlighted. A HF-SCF and DFT study is carried out also for BINOL, a system where excited states show the typical pairing structure arising from the interaction of the two monomeric moieties, and whose conformational changes following photoexcitation were studied recently with via time-resolved CD. [ABSTRACT FROM AUTHOR]

We analyze the ability of spin-flip time dependent density functional theory (TD-DFT) to uniformly describe excited states of single, double, and mixed excitation character in closed-shell molecular systems, using the polyene oligomers as a primary test case. The results of comparison between conventional and spin-flip TD-DFT and with correlated ab initio methods indicate that spin-flip TD-DFT provides a more consistent description of the ordering and relative positions of the excited states than conventional TD-DFT provided a suitable exchange-correlation functional is used in the calculations. It is found that spin-flip TD-DFT provides a physically appealing picture of excitation processes which involve one or two electrons, as it captures their most important features and facilitates a more uniform description of excited states with different character. This makes spin-flip TD-DFT a promising approach for general modeling of excited states and spectra of medium and large size molecules, which exhibit low-lying excited states with strong double excitation character. [ABSTRACT FROM AUTHOR]

The density functional restricted-unrestricted approach for treatments of spin polarization effects in molecular properties using spin restricted Kohn–Sham theory has been extended from linear to nonlinear properties. It is shown that the spin polarization contribution to a nonlinear property has the form of a quadratic response function that includes the zero-order Kohn–Sham operator, in analogy to the lower order case where the spin polarization correction to an expectation value has the form of a linear response function. The developed approach is used to formulate new schemes for computation of electronic g-tensors and hyperfine coupling constants, which include spin polarization effects within the framework of spin restricted Kohn–Sham theory. The proposed computational schemes are in the present work employed to study the spin polarization effects on electron paramagnetic resonance spin Hamiltonian parameters of square planar copper complexes. The obtained results indicate that spin polarization gives rise to sizable contributions to the hyperfine coupling tensor of copper in all investigated complexes, while the electronic g-tensors of these complexes are only marginally affected by spin polarization and other factors, such as choice of exchange-correlation functional or molecular structures, will have more pronounced impact on the accuracy of the results. [ABSTRACT FROM AUTHOR]

We propose a simple self-interaction correction to Kohn-Sham orbital energies in order to apply ground state Kohn-Sham density functional theory to accurate predictions of core electron binding energies and chemical shifts. The proposition is explored through a series of calculations of organic compounds of different sizes and types. Comparison is made versus experiment and the “ΔKohn-Sham” method employing separate state optimizations of the ground and core hole states, with the use of the B3LYP functional and different basis sets. A parameter α is introduced for a best fitting of computed and experimental ionization potentials. It is found that internal parametrizations in terms of basis set expansions can be well controlled. With a unique α=0.72 and basis set larger than 6-31G, the core ionization energies (IPs) of the self-interaction corrected Kohn-Sham calculations fit quite well to the experimental values. Hence, self-interaction corrected Kohn-Sham calculations seem to provide a promising tool for core IPs that combines accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds. [ABSTRACT FROM AUTHOR]

A general framework within time-dependent density functional theory is presented for the calculation of excitations to states of arbitrary multiplicity in molecular systems with a non-singlet ground state. The proposed approach combines generalized orbital excitation operators designed to generate excited states which have well-defined multiplicities and the noncollinear formulation of density functional theory and it can be straightforwardly implemented in currently existing density functional programs. [ABSTRACT FROM AUTHOR]

This work presents the derivation, implementation, and first applications of the generalized restricted-unrestricted method based on the density functional Kohn-Sham formalism. By using a spin-restricted Kohn-Sham representation for the reference state the well-known spin contamination problem is avoided, while the unrestricted representation of the perturbation response retains a proper description of spin polarization. The formulation is a generalization of our previous implementation of the restricted-unrestricted method [Z. Rinkevicius et al., J. Chem. Phys. 121, 7614 (2004)], as it accounts for the full unrestricted response instead of describing the spin polarization in terms of triplet operators only. The purpose of this paper is to investigate the role of the generalization employed and demonstrate its numerical performance. For this purpose we focus on isotropic hyperfine coupling constants of a set of organic radicals and transition metal compounds. For both classes of molecules we observe that the effect of neglecting singlet excitation operators in the response part of restricted-unrestricted formalism changes the calculated hyperfine coupling parameters by a few MHz. The obtained results confirm the validity of the approximation used in the simplified restricted-unrestricted approach, i.e. spin polarization can, in most cases, be adequately described by an account of only triplet operators in the response term. [ABSTRACT FROM AUTHOR]

This work outlines the calculation of indirect nuclear spin-spin coupling constants with spin-orbit corrections using density functional response theory. The nonrelativistic indirect nuclear spin-spin couplings are evaluated using the linear response method, whereas the relativistic spin-orbit corrections are computed using quadratic response theory. The formalism is applied to the homologous systems H2X (X=O,S,Se,Te) and XH4 (X=C,Si,Ge,Sn,Pb) to calculate the indirect nuclear spin-spin coupling constants between the protons. The results confirm that spin-orbit corrections are important for compounds of the H2X series, for which the electronic structure allows for an efficient coupling between the nuclei mediated by the spin-orbit interaction, whereas in the case of the XH4 series the opposite situation is encountered and the spin-orbit corrections are negligible for all compounds of this series. In addition we analyze the performance of the density functional theory in the calculations of nonrelativistic indirect nuclear spin-spin coupling constants. [ABSTRACT FROM AUTHOR]

We present density-functional theory for time-dependent response functions up to and including cubic response. The working expressions are derived from an explicit exponential parametrization of the density operator and the Ehrenfest principle, alternatively, the quasienergy ansatz. While the theory retains the adiabatic approximation, implying that the time-dependency of the functional is obtained only implicitly—through the time dependence of the density itself rather than through the form of the exchange-correlation functionals—it generalizes previous time-dependent implementations in that arbitrary functionals can be chosen for the perturbed densities (energy derivatives or response functions). In particular, general density functionals beyond the local density approximation can be applied, such as hybrid functionals with exchange correlation at the generalized-gradient approximation level and fractional exact Hartree–Fock exchange. With our implementation the response of the density can always be obtained using the stated density functional, or optionally different functionals can be applied for the unperturbed and perturbed densities, even different functionals for different response order. As illustration we explore the use of various combinations of functionals for applications of nonlinear optical hyperpolarizabilities of a few centrosymmetric systems; molecular nitrogen, benzene, and the C60 fullerene. Considering that vibrational, solvent, and local field factors effects are left out, we find in general that very good experimental agreement can be obtained for the second dynamic hyperpolarizability of these systems. It is shown that a treatment of the response of the density beyond the local density approximation gives a significant effect. The use of different functional combinations are motivated and discussed, and it is concluded that the choice of higher order kernels can be of similar importance as the choice of the potential which governs the Kohn–Sham orbitals. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This work presents derivation, implementation, and the first applications of the restricted-unrestricted approach based on restricted Kohn-Sham formalism for evaluation of hyperfine coupling constants. By using the spin-restricted Kohn-Sham method the well-known spin contamination problem existing in the unrestricted Kohn-Sham formalism is avoided and a proper description of spin polarization is achieved via the restricted-unrestricted approach without introducing spin contamination into the evaluation of the hyperfine coupling constants. The performance of the proposed formalism is evaluated for a set of organic radicals and transition metal compounds. The results of this investigation indicate promising accuracy of the restricted-unrestricted approach for calculation of the isotropic hyperfine coupling constants in organic radicals as well as transition metal compounds. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present the implementation of density functional response theory combined with the polarizable continuum model (PCM), enabling first principles calculations of molecular g-tensors of solvated molecules. The calculated g-tensor shifts are compared with experimental g-tensor shifts obtained from electron paramagnetic resonance spectra for a few solvated species. The results indicate qualitative agreement between the calculations and the experimental data for aprotic solvents, whereas PCM fails to reproduce the electronic g-tensor behavior for protic solvents. This failure of PCM for protic solvents can be resolved by including into the model those solvent molecules which are involved in hydrogen bonding with the solute. The results for the protic solvents show that the explicit inclusion of the solvent molecules of the first solvation sphere is not sufficient in order to reproduce the behavior of the electronic g-tensor in protic solvents, and that better agreement with experimental data can be obtained by including the long-range electrostatic effects accounted for by the PCM approach on top of the explicit hydrogen-bonded complexes. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present density functional response theory generalized to triplet excitations. A method based on an exponential parametrization of the spin-dependent density operator is derived for the evaluation of linear and quadratic response functions for spin-dependent perturbations. The developed methodology is applicable to commonly available functionals, also hybrid functionals including exchange–correlation functionals at the general gradient-approximation level and fractional exact Hartree–Fock exchange. Illustrative calculations are presented for singlet–triplet transition moments and phosphorescence lifetimes, providing numerical data on these quantities for the first time using time-dependent density functional theory. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A method for calculations of electronic g-tensors based on a spin-restricted open-shell Kohn–Sham formalism and linear response theory is described. Test calculations for main group organic radicals and transition metal compounds have been carried out using two different spin–orbit approximations: Scaled spin–orbit and atomic mean-field spin–orbit operators. The results indicate slightly better performance of the proposed spin-restricted approach compared to previous methods based on the unrestricted Kohn–Sham formalism. An exception to this general improvement are the anions, as they show considerable spin-polarization. The results also show the superiority of the atomic mean field spin–orbit approximation of the spin–orbit operator with respect to the scaled approximation. For main group radicals, quantitative agreement with high level ab initio as well as experimental data are achieved, whereas for transition metal compounds the results systematically underestimate experimental values, showing also a considerable dependency on the employed exchange correlation functional, similarly to previous reports on calculations using unrestricted density functional theory. From this work we conclude that these problems are not primarily associated with the spin-contamination problem, and that they must be referred to the current time-dependent density functional theories as such. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Nonhomogeneous broadening of phosphorescence lines and microwave signals in optical detection of magnetic resonance (ODMR) has been calculated using multiconfigurational self-consistent field wave functions and the polarized continuum model. The solvent effects on the zero-field splitting (ZFS) parameters in the low-lying triplet states of aza-aromatic molecules are found to be linearly dependent on the solvent-induced shifts in the phosphorescence frequency in agreement with experimental data. The main contribution to the ZFS originates in the dipolar interaction of the two electron spins, the spin-spin coupling. The spin-orbit coupling (SOC) contribution to the ZFS parameter is much larger for the [SUP3]nπ* state of pyrazine compared to the [SUP3]ππ* states of quinoline. The second-order SOC contribution to the splitting of the [SUP3]nπ* state in the pyrazine molecule does not show any appreciable dependence on the dielectric constant of the solvent. This raises doubts about earlier theories for explaining the inhomogeneous broadening in triplet-state spectra based exclusively on the SOC-induced mixing of the singlet and triplet states. We complete the interpretation of the ODMR spectrum of pyrazine by calculating the hyperfine coupling (HFC) tensors in the lowest triplet state using the UB3LYP hybrid functional. An appreciable solvent-induced rotation of the anisotropic HFC tensor axes has been obtained for the [SUP3]nπ* state of pyrazine, in particular for [SUP13]C and [SUP14]N nuclei. This produces additional nonhomogeneous broadening not only in electron-nuclear double resonance spectra, but also in electron paramagnetic resonance signals because the anisotropic HFC perturbation results in intensity redistribution among the magnetic transitions between the spin sublevels. A small in-plane rotation of the ZFS tensor axes upon solvation has been predicted for quinoline. Rotation of the magnetic axes induced by the interaction with isotropic... [ABSTRACT FROM AUTHOR]

In this paper we report the derivation and the performance of a spin-restricted density functional formalism for linear time-dependent properties in open-shell molecules. The formalism is based on an exponential parameterization of the density operator with the response functions defined through Ehrenfest's principle. In addition to the derivation of formulas, details of implementation are given as well as a discussion of numerical results for excitation energies and dynamic polarizabilities for a selected set of radicals. [ABSTRACT FROM AUTHOR]

We propose and evaluate first principles methods for calculating the nuclear shielding tensor in open-shell, paramagnetic molecules, dealing with the case of small spin-orbit coupling that, in turn, implies the best applicability to light, organic compounds. The formalism is consistent up to second order in the fine structure constant, and includes orbital, fully anisotropic dipolar, and isotropic contact contributions to the tensor. The proposed method is implemented within the ab initio singleand multiconfiguration self-consistent field as well as density functional theory frameworks. The applications include small main-group radicals and larger nitroxide radicals. The analysis of the results and comparison with the experimental nuclear magnetic resonance data, which are available for the latter compounds, indicate promising accuracy and applicability of the density functional theory method to chemically interesting problems. [ABSTRACT FROM AUTHOR]

We present density-functional theory for linear and nonlinear response functions using an explicit exponential parametrization of the density operator. The response functions are derived using two alternative variation principles, namely, the Ehrenfest principle and the quasienergy principle, giving different but numerically equivalent formulas. We present, for the first time, calculations of dynamical hyperpolarizabilities for hybrid functionals including exchange-correlation functionals at the general gradient-approximation level and fractional exact Hartree-Fock exchange. Sample calculations are presented of the first hyperpolarizability of the para-nitroaniline molecule and of a porphyrin derived push-pull molecule, showing good agreement with available experimental data. [ABSTRACT FROM AUTHOR]

Presents analytical calculations of the electronic spin-orbit interaction contribution to nuclear magnetic shielding tensors using linear and quadratic response theory. Effects of the Fermi contact and the spin-dipole interactions; Nonrelativistic multiconfiguration self-consistent field reference states.

We outline a method for the calculation of nonlinear properties such as dynamic hyperpolarizabilities for self-consistent-field (SCF) wave functions. In this method, two-electron integrals are only addressed in the evaluation of Fock matrices and Fock matrices with one-index transformed integrals. These matrices are determined directly in terms of integrals evaluated in the atomic orbital basis, avoiding expensive integral transformations between atomic and molecular orbital bases as well as storing and retrieving the two-electron integrals. The method is double direct—direct in the sense of constructing Fock matrices from atomic integrals, and direct in the sense of solving the response equations iteratively using direct linear transformations of a generating matrix times trial vectors. Applications can be performed on species of the same size as in direct SCF. The cost of evaluating a single nonlinear molecular property is comparable to that of optimizing the wave function. Additional properties can be obtained at little extra cost by solving all response equations simultaneously. As a demonstration, we calculate the static and dynamic hyperpolarizabilities of para-nitroaniline. [ABSTRACT FROM AUTHOR]

A formalism is presented for the calculation of quadratic response functions of multiconfigurational self-consistent field reference wave functions. The formalism is general in the sense that it applies equally well to singlet and triplet perturbations and it does not assume any permutational symmetry in the integrals of the perturbational operators. This formalism can be used to derive expressions for various properties related to singlet or triplet quadratic response functions and their residues. We focus on the spin-forbidden dipole transitions between singlet and triplet electronic states responsible for the long lifetime of phosphorescent states. The singlet–triplet transition moments are evaluated as the residues of quadratic response functions. Sample calculations are presented for the formaldehyde molecule. [ABSTRACT FROM AUTHOR]

We have used multiconfiguration self-consistent-field theory to determine indirect nuclear spin–spin coupling constants. The Fermi contact, spin dipole, and paramagnetic spin–orbit contributions are evaluated as multiconfiguration linear response functions at zero frequency and the diamagnetic spin–orbit contribution as an average value of the multiconfiguration wave function. Sample calculations on HD and CH4 demonstrate that most of the correlation contributions can be recovered in relatively small complete active space (CAS) reference state calculations. [ABSTRACT FROM AUTHOR]

Spin–orbit coupling constants between singlet and triplet states are evaluated as residues of multiconfiguration linear response functions. In this approach, the spin–orbit coupling constants are automatically determined between orthogonal and noninteracting states. Sample calculations are presented for the X 3Σ-g–b 1Σ+g transition in O2 and the 1A1–3B1 transition in CH2. The convergence of the coupling constants is examined as a function of basis set and level of correlation. An exotic behavior is observed in the correlation of the 1A1 state for CH2 when increasing the active space, demonstrating an intricate coupling between the dynamic and static correlation. In general, the results indicate that reliable spin–orbit coupling constants between valence states may be obtained with a 4s3p2d1f basis set for first row atoms and a modest active orbital space. [ABSTRACT FROM AUTHOR]

Focuses on the computation of the hypermagnetizability and the hypermagnetizability anisotropy of the oxygen molecule. Cubic response theory applied to multi-configurational self-consistent field wave functions; Effects of basis set, electron correlation, frequency dispersion, zero point vibrational averaging and pure vibrational contributions.

Using OH adsorbed on the copper(111) surface as model system we demonstrate the feasibility of calculations of NEXAFS spectra of chemisorbed species. We employ a static exchange method that is implemented for large systems through direct atomic orbital techniques. The general cluster convergence of the spectra ranging up to 49 cluster atoms is investigated and found to be satisfactory. The special character of the strong metal to adsorbate charge transfer involving occupied OH orbitals and of the OH–metal ionic bond are shown to have particular consequences for both the analysis and the computation of the NEXAFS spectra. For the larger clusters the discrete spectra are dominated by adsorbate to cluster transitions, which can be understood from the similarity of electronic structure of the adsorbed OH moiety with that of free OH- for which all transitions end up in the continuum. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present calculations on near-edge x-ray absorption fine structures (NEXAFS) in polyenes based on a newly derived direct, atomic orbital, static exchange method. The trends of different NEXAFS features with respect to the site of ionization and with respect to the number of ethylene subunits in the oligomer chain are studied. The trends for energies and intensities are found to be regular and alternant. A substantial reduction of the π to σ intensity ratios with the number of ethylene subunits is predicted, indicating delocalization of the screening π electrons. In contrast to NEXAFS spectra of a heterogeneous group attached to hydrocarbon chains, the NEXAFS spectra of oligomer sequences, here the polyenes, converge slowly. The building block principle is less appropriate than the final state rule for rationalizing the present findings. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Static and frequency-dependent dipole polarizabilities α and first hyperpolarizabilities β are calculated for H2O using self-consistent field (SCF) and multiconfigurational self-consistent- field (MCSCF) linear and quadratic response theory. With an active orbital space where one correlating orbital is included for each occupied valence orbital excellent agreement is obtained with the experimental hyperpolarizability. Basis set dependency has been investigated and a detailed vibrational analysis has been carried out. [ABSTRACT FROM AUTHOR]

We propose a simple self-interaction correction to Kohn-Sham orbital energies in order to apply ground state Kohn-Sham density functional theory to accurate predictions of core electron binding energies and chemical shifts. The proposition is explored through a series of calculations of organic compounds of different sizes and types. Comparison is made versus experiment and the "DeltaKohn-Sham" method employing separate state optimizations of the ground and core hole states, with the use of the B3LYP functional and different basis sets. A parameter alpha is introduced for a best fitting of computed and experimental ionization potentials. It is found that internal parametrizations in terms of basis set expansions can be well controlled. With a unique alpha=0.72 and basis set larger than 6-31G, the core ionization energies (IPs) of the self-interaction corrected Kohn-Sham calculations fit quite well to the experimental values. Hence, self-interaction corrected Kohn-Sham calculations seem to provide a promising tool for core IPs that combines accuracy and efficiency.