Joanna Kauczor

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)].

A simple polyol-free synthesis route to Gd2O3 nanoparticles for MRI applications: an experimental and theoretical study

Chelated gadolinium ions, e.g., Gd-DTPA, are today used clinically as contrast agents for magnetic resonance imaging (MRI). An attractive alternative contrast agent is composed of gadolinium oxide nanoparticles as they have shown to provide enhanced contrast and, in principle, more straightforward molecular capping possibilities. In this study, we report a new, simple, and polyol-free way of synthesizing 4–5-nm-sized Gd2O3 nanoparticles at room temperature, with high stability and water solubility. The nanoparticles induce high-proton relaxivity compared to Gd-DTPA showing r1 and r2 values almost as high as those for free Gd3+ ions in water. The Gd2O3 nanoparticles are capped with acetate and carbonate groups, as shown with infrared spectroscopy, near-edge X-ray absorption spectroscopy, X-ray photoelectron spectroscopy and combined thermogravimetric and mass spectroscopy analysis. Interpretation of infrared spectroscopy data is corroborated by extensive quantum chemical calculations. This nanomaterial is easily prepared and has promising properties to function as a core in a future contrast agent for MRI.

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.

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.

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.

The magnetic circular dichroism spectrum of the C-60 fullerene

The magnetic circular dichroism spectrum of the C60 fullerene has been determined with the use of Kohn–Sham density functional theory in conjunction with the CAM-B3LYP exchange-correlation functional. The experimental spectrum of Gasyna et al. [Chem. Phys. Lett. 183, 283 (1991)] covering the wavelength region above 200 nm is explained by the signal responses from the three lowest singlet states of T 1u symmetry.

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.

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.