Local CC2 response method for triplet states based on Laplace transform: excitation energies and first-order properties

A new multistate local CC2 response method for calculating excitation energies and first-order properties of excited triplet states in extended molecular systems is presented. The Laplace transform technique is employed to partition the left/right local CC2 eigenvalue problems as well as the linear equations determining the Lagrange multipliers needed for the properties. The doubles part in the equations can then be inverted on-the-fly and only effective equations for the singles part must be solved iteratively. The local approximation presented here is adaptive and state-specific. The density-fitting method is utilized to approximate the electron-repulsion integrals. The accuracy of the new method is tested by comparison to canonical reference values for a set of 12 test molecules and 62 excited triplet states. As an illustrative application example, the lowest four triplet states of 3-(5-(5-(4-(bis(4-(hexyloxy)phenyl)amino)phenyl)thiophene-2-yl)thiophene-2-yl)-2-cyanoacrylic acid, an organic sensitizer for solar-cell applications, are computed in the present work. No triplet charge-transfer states are detected among these states. This situation contrasts with the singlet states of this molecule, where the lowest singlet state has been recently found to correspond to an excited state with a pronounced charge-transfer character having a large transition strength.     

Local CC2 electronic excitation energies for large molecules with density fitting

A new local method for the computation of electronic excitation energies of singlet states in extended molecular systems is presented. It is based on the CC2 model and local approximations to the wave functions. In the proposed method the singles excitations are treated nonlocally and local restrictions are imposed on doubles amplitudes only. The accuracy of the new method was tested by calculating several lowest excited states for 14 molecules and comparing them with canonical CC2 values. Deviations of the local excitation energies from the canonical reference values do not exceed 0.05 eV for all test molecules and all states in the lower energy range investigated in this work. The method uses the density-fitting approximation for all two-electron integrals, which considerably simplifies the computational complexity of the individual diagrams. A combination of the local approximations and the powerful density-fitting technique leads to a low-scaling method, capable to treat molecular systems comprised of 100 atoms and more in a basis of a polarized double zeta quality. A test calculation for a system consisting of 127 atoms and 370 active electrons without symmetry is presented to show the efficiency of the new method.     

Fock space multi-reference coupled cluster study of transition moment and oscillator strength

Summary A method of calculating transition moment and oscillator strength within the framework of the Fock space multi-reference coupled cluster method is described. Diagrammatic technique is used to obtain coupled cluster equations. The general form of equations for the transition moment betweenN-electron ground and excited states is obtained. MBPT analysis of the final equations is done. The excitation energies, dipole transition moments and oscillator strengths for theCH ⁺ molecule are calculated.     

Semiempirical NDDO/MC calculations of the excited states of the chromate ion

A new semiempirical method of calculating the excited states of transition metal complexes is developed. This technique uses the configuration interaction and semiempirical NDDO/MC methods to obtain the ground state of a set of Slater type valence spd-orbitals chosen from the optical spectra of transition metals together with the corresponding core integrals. The method is tested in calculations of the electronically excited states of the chromate ion. Good agreement with the experimental energies of vertical transitions and the results of ab initio calculations is achieved.     

Note on the ab initio PUHF treatment of open-shell systems

Ab initio projected-unrestricted Hartree-Fock calculations have been carried out on a number of excited and ionic states of the water molecule. Results have been compared with large-scale CI calculations, with IVO calculations, and with those of Mrozek and Golebiewski obtained by the 2 × 2 rotation method applied to orbitals. It is concluded that the PUHF method may provide the most useful alternative to large-scale CI for calculating properties of open-shell systems. But it will not be generally useful for calculating spectral transition energies.     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Calculation of excitation energies of open-shell molecules with spatially degenerate ground states. I. Transformed reference via an intermediate configuration Kohn-Sham density-functional theory and applications to d1 and d2 systems with octahedral and tetrahedral symmetries

A method for calculating the UV-vis spectra of molecules with spatially degenerate ground states using time-dependent density-functional theory (TDDFT) is proposed. The new transformed reference via an intermediate configuration Kohn-Sham TDDFT (TRICKS-TDDFT) method avoids the difficulties caused by the multireference nature of spatially degenerate states by rather than utilizing the ground state instead taking a nondegenerate excited state with desirable properties as the reference for the TDDFT calculation. The scope and practical application of the method are discussed. Like all open-shell TDDFT calculations this method at times suffers from the inability to produce transitions to states that are eigenfunctions of the total spin operator. A technique for alleviating this difficulty to some extent is proposed. The applicability and accuracy of the TRICKS-TDDFT method is demonstrated through example calculations of several d(1) and d(2) transition metal complexes with tetrahedral and octahedral symmetries. For the most part, the results of these calculations are similar in quality to to those obtained from standard TDDFT calculations.     

New algorithms for iterative matrix‐free eigensolvers in quantum chemistry

New algorithms for iterative diagonalization procedures that solve for a small set of eigen‐states of a large matrix are described. The performance of the algorithms is illustrated by calculations of low and high‐lying ionized and electronically excited states using equation‐of‐motion coupled‐cluster methods with single and double substitutions (EOM‐IP‐CCSD and EOM‐EE‐CCSD). We present two algorithms suitable for calculating excited states that are close to a specified energy shift (interior eigenvalues). One solver is based on the Davidson algorithm, a diagonalization procedure commonly used in quantum‐chemical calculations. The second is a recently developed solver, called the “Generalized Preconditioned Locally Harmonic Residual (GPLHR) method.” We also present a modification of the Davidson procedure that allows one to solve for a specific transition. The details of the algorithms, their computational scaling, and memory requirements are described. The new algorithms are implemented within the EOM‐CC suite of methods in the Q‐Chem electronic structure program. © 2014 Wiley Periodicals, Inc.     

Ab initio and quantum-defect calculations for the Rydberg states of ArH

Potential energy curves were evaluated for the ground and thirteen low-lying excited electronic states of the ArH molecule over a wide range of internuclear distances by the multi-reference averaged quadratic coupled cluster method. The ab initio energy differences and transition dipole moments were used to estimate Einstein emission coefficients, absorption oscillator strengths and radiative lifetimes. Diagonal and off-diagonal quantum defects, as functions of internuclear distance, were extracted from ab initio potentials of the lowest Rydberg states of the neutral ArH molecule by taking account of configuration interaction between Rydberg series converging to the ground and two electronic excited states of the ArH(+) cation. The derived quantum-defect functions were used to generate manifolds of higher excited Rydberg states. The agreement between experimental and calculated energies and radiative transition probabilities was found to be as good as or better than that obtained by earlier calculations.     

Locally correlated equation-of-motion coupled cluster theory for the excited states of large molecules

We report an extension of the local correlation concept to electronically excited states via the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method. We apply the same orbital domain structure used successfully for ground-state CCSD by Werner and co-workers and find that the resulting localized excitation energies are in error generally by less than 0.2 eV relative to their canonical EOM-CCSD counterparts, provided the basis set is flexible and includes Rydberg-like functions. In addition, we account for weak-pair contributions efficiently using a correction to local-EOM-CCSD transition energies based on the perturbative (D) correction used with configuration interaction singles (CIS).     

Role of doubly excited states in calculations of optical activity

It is shown that doubly excited states play an important role in calculations of the optical activity of molecules with well-conjugated electron systems, such as the DNA bases. In some significant cases it is necessary to include a large number of excited states in the configuration interaction (CI ) to obtain a reliable, converging result. A new version of the CNDO/OPTIC method, which includes doubly excited states in the CI , is proposed. As an application, the electric transition moments in different pyrimidines are considered. The calculated results agree with experimental data and results obtained from ab initio calculations and INDO calculations using doubly excited states in the CI .     

CASSCF and CASPT2 studies on the structures, transition energies, and dipole moments of ground and excited states for azulene

The electronic structure of azulene molecule has been studied. We have obtained the optimized structures of ground and singlet excited states by using the complete active space self-consistent-field (CASSCF) method, and calculated vertical and 0-0 transition energies between the ground and excited states with second-order M?ller-Plesset perturbation theory (CASPT2). The CASPT2 calculations indicate that the bond-equalized C(2v) structure is more stable than the bond-alternating C(s) structure in the ground state. For a physical understanding of electronic structure change from C(2v) to C(s), we have performed the CASSCF calculations of Duschinsky matrix describing mixing of the b(2) vibrational mode between the ground (1A(1)) and the first excited (1B(2)) states based on the Kekule-crossing model. The CASPT2 0-0 transition energies are in fairly good agreement with experimental results within 0.1-0.3 eV. The CASSCF oscillator strengths between the ground and excited states are calculated and compared with experimental data. Furthermore, we have calculated the CASPT2 dipole moments of ground and excited states, which show good agreement with experimental values.     

Potential--energy surfaces for excited states in extended systems

With a simple and physically intuitive method, first-principles calculations of potential-energy surfaces are performed for excited states in a number of illustrative systems, including dimers (H(2) and NaCl) and gas-surface systems [Cl-Na(100) and Cl(2)-Na(100)]. It is based on density-functional theory and is a generalization of the Delta self-consistent field (DeltaSCF) method, where electron-hole pairs are introduced in order to model excited states, corresponding to internal electron transfers in the considered system. The desired excitations are identified by analysis of calculated electron orbitals, local densities of states, and charge densities. For extended systems, where reliable first-principles methods to account for electronically excited states have so far been scarce, our method is very promising. Calculated results, such as the chemiluminescence of halogen molecules impinging on a alkali-metal surface, and the vertical (5 sigma-->2 pi(*)) excitation within the adsorbed CO molecule on the Pd(111) surface, are in working agreement with those of other studies and experiments.     

Linear dependence in Hylleraas configuration-interaction calculations of He atom

The explicitly-correlated basis sets are much easier to be linearly dependent than the product type bases constructed by one-electron orbitals due to the explicit inclusion of interelectronic coordinates in system wave functions. In this work, we apply Löwdin's canonical orthogonalization method to study the linearly dependent problems arising from the variational calculations based on Hylleraas configuration-interaction (Hy-CI) basis functions. Both the ground and excited states of He atom are calculated with increasingly large basis sets. Our results show that the linear dependence in Hy-CI basis sets can be successfully overcome by employing Löwdin's canonical orthogonalization method, yet without using extended higher-precision arithmetic in numerical implementations. Therefore, the computational effort can be reduced considerably. It is expected that the present method can be applied to other types of explicitly correlated basis functions.     

S1 and S2 excited states of gas-phase Schiff-base retinal chromophores: a time-dependent density functional theoretical investigation

In concert with the recent photoabsorption experiments of gas-phase Schiff-base retinal chromophores (Nielsen et al. Phys. Rev. Lett. 2006, 96, 018304), quantum chemical calculations using time-dependent density functional theory coupled with different functionals and under the Tamm-Dancoff approximation were made on the first two excited states (S1 and S2) of two retinal chromophores: 11-cis and all-trans protonated Schiff bases. The calculated vertical excitation energies (Tv) and oscillator strengths (f) are consistent with the experimental absorption bands. The experimentally observed phenomenon that the transition dipole moment (mu) of S2 is much smaller that of S1 was interpreted by 3D representation of transition densities. The different optical behaviors (linear and nonlinear optical responds) of the excited states were investigated by considering different strengths of external electric fields.     

Accurate estimation of the density of states from Monte Carlo transition probability data

This study develops an efficient approach for calculating the density of states from energy transition probability matrices generated from extended sampling Monte Carlo simulations. Direct and iterative variants of the method are shown to achieve high accuracy when applied to the two-dimensional Ising model for which the density of states function can be determined exactly. They are also used to calculate the density of states of lattice protein and Lennard-Jones models which generate more complex nonzero matrix structures. Whereas the protein simulations test the method on a system exhibiting a rugged free energy landscape, the Lennard-Jones calculations highlight implementation details that arise in applications to continuous energy systems. Density of states results for these two systems agree with estimates from multiple histogram reweighting, demonstrating that the new method provides an alternative approach for computing the thermodynamic properties of complex systems.     

State-selective optimization of local excited electronic states in extended systems

Standard implementations of time-dependent density-functional theory (TDDFT) for the calculation of excitation energies give access to a number of the lowest-lying electronic excitations of a molecule under study. For extended systems, this can become cumbersome if a particular excited state is sought-after because many electronic transitions may be present. This often means that even for systems of moderate size, a multitude of excited states needs to be calculated to cover a certain energy range. Here, we present an algorithm for the selective determination of predefined excited electronic states in an extended system. A guess transition density in terms of orbital transitions has to be provided for the excitation that shall be optimized. The approach employs root-homing techniques together with iterative subspace diagonalization methods to optimize the electronic transition. We illustrate the advantages of this method for solvated molecules, core-excitations of metal complexes, and adsorbates at cluster surfaces. In particular, we study the local π→π(?) excitation of a pyridine molecule adsorbed at a silver cluster. It is shown that the method works very efficiently even for high-lying excited states. We demonstrate that the assumption of a single, well-defined local excitation is, in general, not justified for extended systems, which can lead to root-switching during optimization. In those cases, the method can give important information about the spectral distribution of the orbital transition employed as a guess.     

A new fragment-based approach for calculating electronic excitation energies of large systems

We present a new fragment-based scheme to calculate the excited states of large systems without necessity of a Hartree-Fock (HF) solution of the whole system. This method is based on the implementation of the renormalized excitonic method [M. A. Hajj et al., Phys. Rev. B 72, 224412 (2005)] at ab initio level, which assumes that the excitation of the whole system can be expressed by a linear combination of various local excitations. We decomposed the whole system into several blocks and then constructed the effective Hamiltonians for the intra- and inter-block interactions with block canonical molecular orbitals instead of widely used localized molecular orbitals. Accordingly, we avoided the prerequisite HF solution and the localization procedure of the molecular orbitals in the popular local correlation methods. Test calculations were implemented for hydrogen molecule chains at the full configuration interaction, symmetry adapted cluster/symmetry adapted cluster configuration interaction, HF/configuration interaction singles (CIS) levels and more realistic polyene systems at the HF/CIS level. The calculated vertical excitation energies for lowest excited states are in reasonable accordance with those determined by the calculations of the whole systems with traditional methods, showing that our new fragment-based method can give good estimates for low-lying energy spectra of both weak and moderate interaction systems with economic computational costs.