Internally contracted multiconfiguration-reference configuration interaction calculations for excited states

Summary The calculation of electronically excited states with the internally contracted multiconfiguration-reference configuration interaction (CMRCI) method is discussed. A straightforward method, in which contracted functions for all states are included in the basis, is shown to be very accurate and stable even in cases of narrow avoided crossings. However, the expense strongly increases with the number of states. A new method is proposed, which employs different contracted basis sets for each state, and in which eigensolutions of the Hamiltonian are found using an approximate projection operator technique. The computational effort for this method scales only linearly with the number of states. The two methods are compared for various applications.Dedicated in honor of Prof. Klaus Ruedenberg     

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.     

Ab initio calculations of electronically excited states of cyano-substituted polyacetylene cations

The transition energies for the lowest energy pi --> pi* electronic excitations are calculated with the complete active space self-consistent field method (CASSCF) and with the complete active space second-order perturbation theory method (CASPT2) for the linear cyano-substituted polyacetylene cations, H-Cn-CN+, n = 4-11, and NC-Cn-CN+, n = 2-10. These systems are models for an important class of interstellar species. We demonstrate the utility of the theoretical calculations in assigning the experimental spectra.     

Semiempirical calculations of the electronic spectra of organometallic compounds: Estimation of solvent and counterion effects

The electronic spectra of the [Ru(NH₃)₅pz]²⁺, [Ru(NH₃)₅pz]³⁺, and [Ru(CN)₅pz]³⁻ complexes are calculated by the CI INDO method. The effect of solvation on the spectra is considered in a point charge approximation and in terms of the parametric model of a charged sphere enveloping the metal fragment. Interrelation of these approaches is discussed. Data on the molecular electrostatic potentials created by the complexes are presented to substantiate the models. St. Petersburg State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 4, pp. 603–618, July–August, 1996. Translated by I. Izvekova     

Benchmarks of electronically excited states: basis set effects on CASPT2 results

Vertical excitation energies and one-electron properties are computed for the valence excited states of 28 medium-sized organic benchmark molecules using multistate multiconfigurational second-order perturbation theory (MS-CASPT2) and the augmented correlation-consistent aug-cc-pVTZ basis set. They are compared with previously reported MS-CASPT2 results obtained with the smaller TZVP basis. The basis set extension from TZVP to aug-cc-pVTZ causes rather minor and systematic shifts in the vertical excitation energies that are normally slightly reduced (on average by 0.11 eV for the singlets and by 0.09 eV for the triplets), whereas the changes in the calculated oscillator strengths and dipole moments are somewhat more pronounced on a relative scale. These basis set effects at the MS-CASPT2 level are qualitatively and quantitatively similar to those found at the coupled cluster level for the same set of benchmark molecules. The previously proposed theoretical best estimates (TBE-1) for the vertical excitation energies for 104 singlet and 63 triplet excited states of the benchmark molecules are upgraded by replacing TZVP with aug-cc-pVTZ data that yields a new reference set (TBE-2). Statistical evaluations of the performance of density functional theory (DFT) and semiempirical methods lead to the same ranking and very similar quantitative results for TBE-1 and TBE-2, with slightly better performance measures with respect to TBE-2. DFT/MRCI is most accurate among the investigated DFT-based approaches, while the OMx methods with orthogonalization corrections perform best at the semiempirical level.     

Semiempirical configuration interaction calculations for ru‐centered dyes*

Computational investigation of the photochemical properties of transition‐metal‐centered dyes typically involves optimization of the molecular structure followed by calculation of the UV/visible spectrum. At present, these steps are usually carried out using density functional theory (DFT) and time‐dependent DFT calculations. Recently, we demonstrated that semiempirical methods with appropriate parameterization could yield geometries that were in very good agreement with DFT calculations, allowing large sets of molecules to be screened quickly and efficiently. In this article, we modify a configuration interaction (CI) method based on a semiempirical PM6 Hamiltonian to determine the UV/visible absorption spectra of Ru‐centered complexes. Our modification to the CI method is based on a scaling of the two‐center, two‐electron Coulomb integrals. This modified, PM6‐based method shows a significantly better match to the experimental absorption spectra versus the default configuration interaction method (in MOPAC) on a training set of 13 molecules. In particular, the modified PM6 method blue‐shifts the location of the metal‐to‐ligand charge‐transfer (MLCT) peaks, in better agreement with experimental and DFT‐based computational results, correcting a significant deficiency of the unmodified method. Published 2018. This article is a U.S. Government work and is in the public domain in the USA     

The quest for best suited references for configuration interaction singles calculations of core excited states

Near edge X‐ray absorption fine structure (NEXAFS) simulations based on the conventional configuration interaction singles (CIS) lead to excitation energies, which are systematically blue shifted. Using a (restricted) open shell core hole reference instead of the Hartree Fock (HF) ground state orbitals improves (Decleva et al., Chem. Phys., 1992, 168, 51) excitation energies and the shape of the spectra significantly. In this work, we systematically vary the underlying SCF approaches, that is, based on HF or density functional theory, to identify best suited reference orbitals using a series of small test molecules. We compare the energies of the K edges and NEXAFS spectra to experimental data. The main improvement compared to conventional CIS, that is, using HF ground state orbitals, is due to the electrostatic influence of the core hole. Different SCF approaches, density functionals, or the use of fractional occupations lead only to comparably small changes. Furthermore, to account for bigger systems, we adapt the core‐valence separation for our approach. We demonstrate that the good quality of the spectrum is not influenced by this approximation when used together with the non‐separated ground state wave function. Simultaneously, the computational demands are reduced remarkably. © 2016 Wiley Periodicals, Inc.     

On the electronically excited states of uracil

Vertical excitation energies in uracil in the gas phase and in water solution are investigated by the equation-of-motion coupled-cluster and multireference configuration interaction methods. Basis set effects are found to be important for converged results. The analysis of electronic wave functions reveals that the lowest singlet states are predominantly of a singly excited character and are therefore well described by single-reference equation-of-motion methods augmented by a perturbative triples correction to account for dynamical correlation.Our best estimates for the vertical excitation energies for the lowest singlet n --> pi* and pi --> pi* are 5.0 +/- 0.1 eV and 5.3 +/- 0.1 eV, respectively. The solvent effects for these states are estimated to be +0.5 eV and +/- 0.1 eV, respectively. We attribute the difference between the computed vertical excitations and the maximum of the experimental absorption to strong vibronic interaction between the lowest A" and A' states leading to intensity borrowing by the forbidden transition.     

Minimal basis sets in calculations of intermolecular interaction energies

Several minimal (7, 3/3) Gaussian basis sets have been used to calculate the energies and some other properties of CH₄ and H₂O. Improved basis sets developed for these molecules have been extended to NH₃ and HF and employed to H₂CO and CH₃OH. Interaction energies between XH_n molecules have been calculated using the old and the new minimal basis sets. The results obtained with the new basis sets are comparable in accuracy to those calculated with significantly more extended basis sets involving polarization functions. Binding energies calculated using the counterpoise method are not much different for the new and the old minimal basis sets, and are likely to be more accurate than the results of much more extended calculations.     

Semiempirical NDDO calculations with STO-3G and 4-31G basis sets

Possible refinements of semiempirical methods include the use of larger basis sets and of correlated wave functions. These possibilities are investigated in semiempirical NDDO SCF calculations with the STO-3G and 4-31G basis sets, and in correlated calculations at the STO-3G level. The present approach is characterized by the analytical evaluation of all one-center terms and two-electron integrals, and the semiempirical adjustment of the remaining one-electron integrals and the nuclear repulsions. The NDDO SCF results tend to reproduce the correspondingab initio results more closely than experimental data, even if they are parametrized with respect to experiment. The explicit inclusion of electron correlation at the STO-3G level improves the calculated results only slightly.     

Semiempirical andab initio calculations of the full configuration interaction using iterated Krylov’s spaces

The algorithm proposed previously for calculating the full configuration interaction using the variation matrix of the wave operator involves the numerical solution of the corresponding incomplete eigenvalue problem based on iterated Krylov’s subspaces. In practice, that means using the multistep gradient method as a special version of the Lanczos method. The high efficiency of this algorithm, which can readily be used in personal computer calculations, is proved by particular ab initio calculations of the full configuration interaction for the helium and beryllium atoms as well as by semiempirical calculations of π-shells for naphthalene and diphenylene. The algorithm is of particular assistance in obtaining numerous excited states, which are used for determining various spectral sums (polarizability, van der Waals interaction constants, and photoionization cross sections). Translated fromZhumal Struktumoi Khimii, Vol. 38, No. 1, pp. 14–22, January–February, 1997.     

Large-scale configuration interaction calculations on the π-electron states of benzene

Ab initio extensive configuration interaction calculations were carried out on the π-electron states of benzene. Among the three π → π^*(e_1g → e_2u) singlet states, ¹B_2u(S₁). ¹B_1u(S₂), and ¹E_1u(S₃), the π^* orbital was found to be velence-like in S₁ and S₂, but diffuse in S₃. All three corresponding triplet states, ³B_1u(T₁) and ³B_2u(T₃), were found to be valence-like. The valence-like ¹E_2g(S₄) and ³E_2g(T₄) states were found to have significant double-excitation character, and were estimated to lie somewhat above S₃ and T₃, respectively. No low-lying S₅ and T₅ states were found. Several low-lying Rydberg states were identified.     

Semiempirical configuration interaction calculations of XPS shake-up satellites in Ni(CO)4

INDO/CI calculations were used to analyze the C1s and O1s shake-up spectra of nickel tetracarbonyl, Ni(CO)₄. The satellite structure in both cases is dominated by excitations from metal–ligand bonding (2Π_b) to metal–ligand antibonding (2Π_a) orbitals and by excitations within the core-ionized CO molecule, Π_CO—Π*_CO. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 649–657, 1998     

Full spin-orbit configuration interaction calculations on electronic states of LiBe

Ab initio calculations are reported for the simplest heteronuclear metal cluster, LiBe. Full spin-orbit configuration interaction calculations in the context of relativistic effective core potentials lead to accurate potential energy curves for low-lying states. Results are compared with recent experimental observations and with all electron multi-reference configuration interaction calculations.     

Full configuration interaction calculation of singlet excited states of Be3

The full configuration interaction (FCI) study of the singlets vertical spectrum of the neutral beryllium trimer has been performed using atomic natural orbitals [3s2p1d] basis set. The FCI triangular equilibrium structure of the ground state has been used to calculate the FCI vertical excitation energies up to 4.8 eV. The FCI vertical ionization potential for the same geometry and basis set amounts to 7.6292 eV. The FCI dipole and quadrupole transition moments from the ground state are reported as well. The FCI electric quadrupole moment of the X (3)A(1) (') ground state has been also calculated with the same basis set (Theta(zz)=-2.6461 a.u., Theta(xx)=Theta(yy)=-1/2Theta(zz)). Twelve of the 19 calculated excited singlets are doubly excited states. Most of the states have large multiconfigurational character. These results provide benchmark values for electronic correlation multireference methods. (4ex6MO)CAS-SDCI values for the same energies and properties are also reported.     

Correlated molecular and multicenter multipole moments in ground and excited states from multiple reference double-excitation configuration interaction calculations

Correlated molecular mulitpole moments and compact correlated cumulative atomic multipole moment (CCAMM) representation of molecular charge distribution in ground as well as in excited states have been derived directly from multiple reference double-excitation configuration interaction (MRD-CI) wave functions for BH and H₂CO molecules using several extended basis sets with multiple polarization functions. This approach extends previously introduced uncorrelated and correlated CAMMs, and allows obtaining inexpensive modeling of electrostatic effects involving molecules in excited electronic states. © 1992 by John Wiley & Sons, Inc.     

Hydrogen bonding in electronically excited states of molecules

Theoretical Chemistry Accounts - CNDO/2 calculations show that hydrogen bonds in the electronically excited states of +H2O and +HOCH3 systems are slightly weaker than in the ground states. The...     

Semiempirical valence-electron calculations of excited state geometries and vibrational frequencies

Summary The use of finite differences and finite second differences in order to approximate gradients and second derivatives of the energy for geometry optimization and determination of normal modes of vibration on the CI level of computation is discussed in connection with the semiempirical MNDOC-CI valence electron method. Results are given for ground and excited states of ethylene, acetylene, formaldehyde, acetaldehyde, acetone, formamide and acetamide and are compared with experimental andab initio data. Mean absolute errors for bond lengths, bond angles, excitation energies and vibrational frequencies indicate that the MNDOC-CI method is well suited to describe ground and excited states of organic molecules on the same level of approximation and with comparable accuracy.     

Theoretical investigation of the electronically excited states of chlorine hydrate

As a step toward a first principles characterization of the optical properties of chlorine hydrate, we have calculated the electronic absorption spectrum of a chlorine molecule trapped in dodecahedral (H2O)20 and hexakaidodecahedral (H2O)24 cages. For comparison, spectra were also calculated for an isolated Cl2 molecule as well as for selected Cl2(H2O)n, n < or =8, clusters cut out of the Cl2(H2O)20 cluster, allowing us to follow the evolution of the low-lying excited states with increasing number of surrounding water molecules. Although encapsulation of a chlorine molecule within the water cages has relatively little effect on its low-lying valence transitions, it does result in a large number of solvent-to-solute charge-transfer transitions at energies starting near 48,000 cm(-1).