A complex-polarization-propagator protocol for magneto-chiral axial dichroism and birefringence dispersion.

A computational protocol for magneto-chiral dichroism and magneto-chiral birefringence dispersion is presented within the framework of damped response theory, also known as complex polarization propagator theory, at the level of time-dependent Hartree-Fock and time-dependent density functional theory. Magneto-chiral dichroism and magneto-chiral birefringence spectra in the (resonant) frequency region below the first ionization threshold of R-methyloxirane and l-alanine are presented and compared with the corresponding results obtained for both the electronic circular dichroism and the magnetic circular dichroism. The additional information content yielded by the magneto-chiral phenomena, as well as their potential experimental detectability for the selected species, is discussed.

Beyond the electric-dipole approximation: A formulation and implementation of molecular response theory for the description of absorption of electromagnetic field radiation.

We present a formulation of molecular response theory for the description of a quantum mechanical molecular system in the presence of a weak, monochromatic, linearly polarized electromagnetic field without introducing truncated multipolar expansions. The presentation focuses on a description of linear absorption by adopting the energy-loss approach in combination with the complex polarization propagator formulation of response theory. Going beyond the electric-dipole approximation is essential whenever studying electric-dipole-forbidden transitions, and in general, non-dipolar effects become increasingly important when addressing spectroscopies involving higher-energy photons. These two aspects are examined by our study of the near K-edge X-ray absorption fine structure of the alkaline earth metals (Mg, Ca, Sr, Ba, and Ra) as well as the trans-polyenes. In following the series of alkaline earth metals, the sizes of non-dipolar effects are probed with respect to increasing photon energies and a detailed assessment of results is made in terms of studying the pertinent transition electron densities and in particular their spatial extension in comparison with the photon wavelength. Along the series of trans-polyenes, the sizes of non-dipolar effects are probed for X-ray spectroscopies on organic molecules with respect to the spatial extension of the chromophore.

TD-DFT investigation of the magnetic circular dichroism spectra of some purine and pyrimidine bases of nucleic acids.

We present a computational study of the magnetic circular dichroism (MCD) spectra in the 200-300 nm wavelength region of purine and its derivative hypoxanthine, as well as of the pyrimidine bases of nucleic acids uracil, thymine, and cytosine, using the B3LYP and CAM-B3LYP functionals. Solvent effects are investigated within the polarizable continuum model and by inclusion of explicit water molecules. In general, the computed spectra are found to be in good agreement with the experimental ones, apart from some overall blue shifts. Both the pseudo-A term shape of the MCD spectra of the purines and the B term shape of the spectra of pyrimidine bases are reproduced. Our calculations also correctly reproduce the reversed phase of the MCD bands in purine compared to that of its derivatives present in nucleic acids. Solvent effects are sizable and system specific, but they do not in general alter the qualitative shape of the spectra. The bands are dominated by the bright π → π* transitions, and our calculations in solution nicely reproduce their energy differences, improving the estimates obtained in the gas phase. Shoulders are predicted for purine and uracil due to n → π* excitations, but they are too weak to be observed in the experiment.

The Dalton quantum chemistry program system.

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

Nuclear spin circular dichroism.

Recent years have witnessed a growing interest in magneto-optic spectroscopy techniques that use nuclear magnetization as the source of the magnetic field. Here we present a formulation of magnetic circular dichroism (CD) due to magnetically polarized nuclei, nuclear spin-induced CD (NSCD), in molecules. The NSCD ellipticity and nuclear spin-induced optical rotation (NSOR) angle correspond to the real and imaginary parts, respectively, of (complex) quadratic response functions involving the dynamic second-order interaction of the electron system with the linearly polarized light beam, as well as the static magnetic hyperfine interaction. Using the complex polarization propagator framework, NSCD and NSOR signals are obtained at frequencies in the vicinity of optical excitations. Hartree-Fock and density-functional theory calculations on relatively small model systems, ethene, benzene, and 1,4-benzoquinone, demonstrate the feasibility of the method for obtaining relatively strong nuclear spin-induced ellipticity and optical rotation signals. Comparison of the proton and carbon-13 signals of ethanol reveals that these resonant phenomena facilitate chemical resolution between non-equivalent nuclei in magneto-optic spectra.

Relative Stability of the La and Lb Excited States in Adenine and Guanine: Direct Evidence from TD-DFT Calculations of MCD Spectra.

The relative position of La and Lb ππ* electronic states in purine nucleobases is a much debated topic, since it can strongly affect our understanding of their photoexcited dynamics. To assess this point, we calculated the absorption and magnetic circular dichroism (MCD) spectra of adenine, guanine, and their nucleosides in gas-phase and aqueous solution, exploiting recent developments in MCD computational technology within time-dependent density functional theory. MCD spectroscopy allows us to resolve the intense S0→ La transition from the weak S0→ Lb transition. The spectra obtained in water solution, by using B3LYP and CAM-B3LYP functionals and describing solvent effect by cluster models and by the polarizable continuum model (PCM), are in very good agreement with the experimental counterparts, thus providing direct and unambiguous evidence that the energy ordering predicted by TD-DFT, La < Lb, is the correct one.

Damped Response Theory in Combination with Polarizable Environments: The Polarizable Embedding Complex Polarization Propagator Method.

We present a combination of the polarizable embedding (PE) scheme with the complex polarization propagator (CPP) method with the aim of calculating response properties including relaxation for large and complex systems. This new approach, termed PE-CPP, will benefit from the highly advanced description of the environmental electrostatic potential and polarization in the PE method as well as the treatment of near-resonant effects in the CPP approach. The PE-CPP model has been implemented in a Kohn-Sham density functional theory approach, and we present pilot calculations exemplifying the implementation for the UV/vis and carbon K-edge X-ray absorption spectra of the protein plastocyanin. Furthermore, technical details associated with a PE-CPP calculation are discussed.

Efficient Calculations of Molecular Linear Response Properties for Spectral Regions.

Molecular spectra can be determined from molecular response functions, by solving the so-called damped response equations using the complex polarization propagator approach. The overall structure of response equations is identical for variational wave functions such as the Hartree-Fock, multiconfiguration self-consistent field, and Kohn-Sham density functional theory, and the key program module is the linear response equation solver. We present an implementation of the solver using the algorithm with symmetrized vectors, optimized for addressing spectral regions of a width of some 5-10 eV and a resolution below 0.1 eV. The work is illustrated by the consideration of UV-vis as well as near carbon K -edge absorption spectra of the C60 fullerene. We demonstrate that it is possible to converge tightly response equations for hundreds of optical frequencies in resonance regions of the spectrum at a cost not much exceeding the solution of a single response equation in the nonresonant region. Our work is implemented in the molecular orbital based module of the Dalton program and serves as a documentation of the code distributed in the Dalton2013 release version.

Communication: A reduced-space algorithm for the solution of the complex linear response equations used in coupled cluster damped response theory.

We present a reduced-space algorithm for solving the complex (damped) linear response equations required to compute the complex linear response function for the hierarchy of methods: coupled cluster singles, coupled cluster singles and iterative approximate doubles, and coupled cluster singles and doubles. The solver is the keystone element for the development of damped coupled cluster response methods for linear and nonlinear effects in resonant frequency regions.

Non-additivity of polarizabilities and van der Waals C6 coefficients of fullerenes.

We present frequency-dependent polarizabilities and C6 dipole-dipole dispersion coefficients for a wide range of fullerene molecules including C60, C70, C78, C80, C82, and C84. The static and dynamic polarizabilities at imaginary frequencies are computed using time-dependent Hartree-Fock, B3LYP, and CAM-B3LYP ab initio methods by employing the complex linear polarization propagator and are subsequently utilized to determine the C6 coefficients using the Casimir-Polder relation. Overall, the C60 and C70 average static polarizabilities α(0) agree to better than 2% with linear-response coupled-cluster single double and experimental benchmark results, and the C6 coefficient of C60 agrees to better than 1% with the best accepted value. B3LYP provides the best agreement with benchmark results with deviations less than 0.1% in α(0) and C6. We find that the static polarizabilities and the C6 coefficients are non-additive, and scale, respectively, as N(1.2) and N(2.2) with the number of carbon atoms in the fullerene molecule. The exponent for C6 power-dependence on N is much smaller than the value predicted recently based on a classical-metallic spherical-shell approximation of the fullerenes.

Comparison of standard and damped response formulations of magnetic circular dichroism.

We apply damped response theory to the phenomenon of magnetic circular dichroism (MCD), and we investigate how the numerical instability associated with the simulation of the MCD spectrum from individually calculated A and B terms for close lying states can be remedied by the use of damped response theory. We also present a method for calculating the Faraday A term, formulated as a double residue of the quadratic response function.

Damped response theory description of two-photon absorption.

Damped response theory is applied to the calculation of two-photon absorption (TPA) spectra, which are determined directly, at each frequency, from a modified damped cubic response function. The TPA spectrum may therefore be evaluated for selected frequency ranges, making the damped TPA approach attractive for calculations on large molecules with a high density of states, where the calculation of TPA using standard theory is more problematic. Damped response theory can also be applied to the case of intermediate state resonances, where the standard TPA expression is divergent. Both exact damped response theory and its application within density functional theory are discussed. The latter is implemented using an atomic-orbital based density matrix formulation, which makes the approach especially suitable for studies on large systems. A test preliminary study is presented for the TPA spectrum of R-(+)-1,1'-bi(2-naphtol).

On the Efficiency of Algorithms for Solving Hartree-Fock and Kohn-Sham Response Equations.

The response equations as occurring in the Hartree-Fock, multiconfigurational self-consistent field, and Kohn-Sham density functional theory have identical matrix structures. The algorithms that are used for solving these equations are discussed, and new algorithms are proposed where trial vectors are split into symmetric and antisymmetric components. Numerical examples are given to compare the performance of the algorithms. The calculations show that the standard response equation for frequencies smaller than the highest occupied molecular orbital-lowest unoccupied molecular orbital gap is best solved using the preconditioned conjugate gradient or conjugate residual algorithms where trial vectors are split into symmetric and antisymmetric components. For larger frequencies in the standard response equation as well as in the damped response equation in general, the preconditioned iterative subspace approach with symmetrized trial vectors should be used. For the response eigenvalue equation, the Davidson algorithm with either paired or symmetrized trial vectors constitutes equally good options.

Quasienergy formulation of damped response theory.

We present a quasienergy-based formulation of damped response theory where a common effective lifetime parameter has been introduced for all excited states in terms of complex excitation energies. The introduction of finite excited state lifetimes leads to a set of (complex) damped response equations, which have the same form to all orders in the perturbation. An algorithm is presented for solving the damped response equations in Hartree-Fock theory and Kohn-Sham density functional theory. The use of the quasienergy formulation allows us to obtain directly the computationally simplest expressions for damped response functions by applying a set of response parameter elimination rules, which minimize the total number of damped response equations to be solved. In standard response theory broadened absorption spectra are obtained by ad hoc superimposing lineshape functions onto the absorption stick spectra, whereas an empirical lineshape function common to all excitations is an integrated part of damped response theory. By superimposing the lineshape functions inherent in damped response theory onto the stick spectra of standard response theory, we show that the absorption spectra obtained in standard and damped response theory calculations are identical. We demonstrate that damped response theory may be applied to obtain absorption spectra in all frequency ranges, also those that are not readily addressed using standard response theory. This makes damped response theory an effective tool, e.g., for determining absorption spectra for large molecules, where the density of the excited states may be very high, and where standard response theory therefore is not applicable in practice. A thorough comparison is given between our formulation of damped response theory and the formulation by Norman et al. [J. Chem. Phys. 123, 194103 (2005)].