Density of States Guided Møller-Plesset Perturbation Theory.

An integral formalism using a density-of-state framework has been developed for Møller-Plesset perturbation theory. This method is designed to compute the correlation energy correction for large systems with high density of states, such as polymers and nanostructures. The framework has the potential to lower the computational cost of perturbation theory, and such perspectives are discussed in this paper. This method has been implemented for the second- and third-order perturbation theory. Applications of the new methods to test cases of conjugated molecules show very good accuracy and significant savings in computational cost.

Oscillator Strength: How Does TDDFT Compare to EOM-CCSD?

In this work, we compare a large variety of density functionals against the equation of motion coupled cluster singles and doubles (EOM-CCSD) method for the calculation of oscillator strengths. Valence and Rydberg states are considered for a test set composed of 11 small organic molecules. In our previous work, the same systems and methods were tested against experimental results for the excitation energies. The results from this investigation confirm our previous findings, i.e., that there is a large difference between the functionals. For the oscillator strength, the average best agreement with EOM-CCSD is provided by CAM-B3LYP followed by LC-ωPBE and, to a lesser extent, B3P86 and LC-BLYP.

Oscillator Strengths in ONIOM Excited State Calculations.

We compute oscillator strengths with the ONIOM (Our own N-layer Integrated molecular Orbital molecular Mechanics) hybrid method between ground and valence excited states and compare the results with the high level of theory equation of motion coupled cluster singles and doubles (EOM-CCSD). This work follows our previous studies in which we validated the ability of ONIOM to compute accurate transition energies compared to EOM-CCSD. We test various levels of theory and molecular systems, as well as the effect of the link atom bond length. Our results show that oscillator strengths can be accurately computed with ONIOM, provided that a sensible choice of the partitioning and of the low level method is made. Being able to calculate both the transition energy and the oscillator strength, ONIOM represents a promising approach to completely characterize valence excited states of molecules that are too large to be studied with a conventional high-accuracy method.

Projected Coupled Cluster Amplitudes from a Different Basis Set As Initial Guess.

Many model chemistry schemes require a sequence of high level calculations, often at the coupled cluster (CC) level, with increasingly larger basis sets. The CC equations are solved iteratively, and the rate of convergence strongly depends on the quality of the initial guess. Here, we propose a strategy to define a better guess from a previous CC calculation with a different basis set by employing the concept of corresponding orbitals. (1, 2) Only the part of the converged amplitudes from the previous calculation that has a large correspondence to the space spanned by the new basis set is projected and used as a new starting point. The computational time for the projection is negligible and significantly reduces the number of cycles necessary for convergence in comparison to the standard guess based on the first order wave function. Numerical results are presented for ground and excited state calculations with the CC singles and doubles (CCSD) and the equation of motion CCSD (EOM-CCSD) methods with the restricted and unrestricted Hartree-Fock (HF) reference functions. However, this approach is more general and can be applied to any truncation of the cluster expansion and reference function.

Link atom bond length effect in ONIOM excited state calculations.

We investigate how the choice of the link atom bond length affects an electronic transition energy calculation with the so-called our own N-layer integrated molecular orbital molecular mechanics (ONIOM) hybrid method. This follows our previous paper [M. Caricato et al., J. Chem. Phys. 131, 134105 (2009)], where we showed that ONIOM is able to accurately approximate electronic transition energies computed at a high level of theory such as the equation of motion coupled cluster singles and doubles (EOM-CCSD) method. In this study we show that the same guidelines used in ONIOM ground state calculations can also be followed in excited state calculations, and that the link atom bond length has little effect on the ONIOM energy when a sensible model system is chosen. We also suggest further guidelines for excited state calculations which can help in checking the effectiveness of the definition of the model system and controlling the noise in the calculation.

Electronic excitation energies in solution at equation of motion CCSD level within a state specific polarizable continuum model approach.

We present a study of excitation energies in solution at the equation of motion coupled cluster singles and doubles (EOM-CCSD) level of theory. The solvent effect is introduced with a state specific polarizable continuum model (PCM), where the solute-solvent interaction is specific for the state of interest. Three definitions of the excited state one-particle density matrix (1PDM) are tested in order to gain information for the development of an integrated EOM-CCSD/PCM method. The calculations show the accuracy of this approach for the computation of such property in solution. Solvent shifts between nonpolar and polar solvents are in good agreement with experiment for the test cases. The completely unrelaxed 1PDM is shown to be a balanced choice between computational effort and accuracy for vertical excitation energies, whereas the response of the ground state CCSD amplitudes and of the molecular orbitals is important for other properties, as for instance the dipole moment.

A Comparison of Three Variants of the Generalized Davidson Algorithm for the Partial Diagonalization of Large Non-Hermitian Matrices.

The solution of the equation of motion coupled cluster singles and doubles problem, that is finding the lowest lying electronic transition energies and properties, is fundamentally a large non-Hermitian matrix diagonalization problem. We implemented and compared three variants of the widely diffuse generalized Davidson algorithm, which iteratively finds the lowest eigenvalues and eigenvectors of such a matrix. Our numerical tests, based on different molecular systems, basis sets, state symmetries, and reference functions, demonstrate that the separate evaluation of the left- and right-hand eigenvectors is the most efficient strategy to solve this problem considering storage, numerical stability, and convergence rate.

Electronic Transition Energies: A Study of the Performance of a Large Range of Single Reference Density Functional and Wave Function Methods on Valence and Rydberg States Compared to Experiment.

This work reports a comparison among wave function and DFT single reference methods for vertical electronic transition energy calculations toward singlet states, valence and Rydberg in nature. A series of 11 small organic molecules are used as test cases, where accurate experimental data in gas phase are available. We compared CIS, RPA, CIS(D), EOM-CCSD, and 28 multipurpose density functionals of the type LSDA, GGA, M-GGA, H-GGA, HM-GGA and with separated short and long-range exchange. The list of functionals is obviously not complete, but it spans more than 20 years of DFT development and includes functionals which are commonly used in the computation of a variety of molecular properties. Large differences in the results were found between the various functionals. The aim of this work is therefore to shed some light on the performance of the plethora of functionals available and compare them with some traditional wave function based methods on a molecular property of large interest as the transition energy.

On the difference between the transition properties calculated with linear response- and equation of motion-CCSD approaches.

In this work, we quantitatively investigate the difference between the linear response (LR) and the equation of motion (EOM) coupled cluster (CC) approaches in the calculation of transition properties, namely, dipole and oscillator strengths, for the most widely used truncated CC wave function, which includes single and double excitation operators. We compare systems of increasing size, where the size-extensivity may be important. Our results suggest that, for small molecules, the difference is small even with large basis sets. The difference increases with the size of the system, but it is numerically small until hundreds of electron pairs are correlated. Although these calculations may be possible in a few years, at present the EOM approach is more advantageous, albeit more approximate, because it is computationally less demanding.

Using the ONIOM hybrid method to apply equation of motion CCSD to larger systems: benchmarking and comparison with time-dependent density functional theory, configuration interaction singles, and time-dependent Hartree-Fock.

Equation of motion coupled-cluster singles and doubles (EOM-CCSD) is one of the most accurate computational methods for the description of one-electron vertical transitions. However, its O(N(6)) scaling, where N is the number of basis functions, often makes the study of molecules larger than 10-15 heavy atoms prohibitive. In this work we investigate how accurately less expensive methods can approximate the EOM-CCSD results. We focus on our own N-layer integrated molecular orbital molecular mechanics (ONIOM) hybrid scheme, where the system is partitioned into regions which are treated with different levels of theory. For our set of benchmark calculations, the comparison of conventional configuration interaction singles (CIS), time-dependent Hartree-Fock (TDHF), and time-dependent density functional theory (TDDFT) methods and ONIOM (with different low level methods) showed that the best accuracy-computational time combination is obtained with ONIOM(EOM:TDDFT), which has a rms of the error with respect to the conventional EOM-CCSD of 0.06 eV, compared with 0.47 eV of the conventional TDDFT.