A combined freeze-and-cut strategy for the description of large molecular systems using a localized orbitals approach

A technique to reduce the computational effort in calculating ab initio energies using a localized orbitals approach is presented. By exploiting freeze strategy at the self-consistent field (SCF) level and a cut of the unneeded atomic orbitals, it is possible to perform a localized complete active space (CAS-SCF) calculation on a reduced system. This will open the possibility to perform ab initio treatments on very large molecular systems, provided that the chemically important phenomena happen in a localized zone of the molecule. Two test cases are discussed, to illustrate the performance of the method: the cis-trans interconversion curves for the (7Z)-13 ammoniotridec-7-enoate, which demonstrates the ability of the method to reproduce the interactions between charged groups; and the cisoid-transoid energy barrier for the aldehydic group in the C13 polyenal molecule.     

Localized virtual and occupied molecular orbitals

This report describes the generation of localized from canonical molecular orbitals such that the method (1) be consistently applicable to occupied bond, lone pair and unoccupied orbitals and (2) permit symmetry related orbitals in molecules of two-fold or higher symmetry. Minimization of populations completely external to each local pair region effectively meets these criteria. Finally, conventional strategy for finding the global extremization point is costly in time and memory to implement; a much more efficient numerical search procedure for the global extremum is described. Results for ethylene, butadiene and benzene are presented to clarify the difficulties and their resolution.     

Theoretical study of the vertical excited states of benzene, pyrimidine, and pyrazine by the symmetry adapted cluster--configuration interaction method

The ground state and the excited states of benzene, pyrimidine, and pyrazine have been examined by using the symmetry adapted cluster-configuration interaction (SAC-CI) method. Detailed characterizations and the structures of the absorption peaks in the vacuum ultraviolet (VUV), low energy electron impact (LEEI), and electron energy loss (EEL) spectra were theoretically clarified by calculating the excitation energy and the oscillator strength for each excited state. We show that SAC-CI has the power to well reproduce the electronic excitation spectra (VUV, LEEI, and EEL) simultaneously to an accuracy for both the singlet and the triplet excited states originated from the low-lying pi --> pi*, n --> pi*, pi --> sigma* and n --> sigma* excited states of the titled compounds. The present results are compared with those of the previous theoretical studies by methods, such as EOM-CCSD(T), STEOM-CCSD, CASPT2 and TD-B3LYP, etc.     

Molecular electric properties in electronic excited states: multipole moments and polarizabilities of H2O in the lowest1 B 1 and3 B 1 excited states

Summary The dipole and quadrupole moments and the dipole polarizability tensor components are calculated for the¹ B ₁ and³ B ₁ excited states of the water molecule by using the complete active space (CAS) SCF method and an extended basis set of atomic natural orbitals. The dipole moment in the lowest¹ B ₁ (0.640 a.u.) and³ B ₁ (0.416 a.u.) states is found to be antiparallel to that in the ground electronic state of H₂O. The shape of the quadrupole moment ellipsoid is significantly modified by the electronic excitation to both states investigated in this paper. All components of the excited state dipole polarizability tensor increase by about an order of magnitude compared to their values in the ground electronic state. The present results are used to discuss some aspects of intermolecular interactions involving molecules in their excited electronic states.     

Localized orbitals for optimal decomposition of molecular properties

We present the procedure for transforming delocalized molecular orbitals into the localized property-optimized orbitals (LPOs) designed for building the most accurate, in the Frobenius norm sense, approximation to the first-order reduced density matrix in form of the sum of localized monoatomic and diatomic terms. In this way, a decomposition of molecular properties into contributions associated with individual atoms and the pairs of atoms is obtained with the a priori known upper bound for the decomposition accuracy. Additional algorithm is proposed for obtaining the set of “the Chemist's LPOs” (CLPOs) containing a single localized orbital, with nearly double occupancy, per a pair of electrons. CLPOs form an idealized Lewis structure optimized for the closest possible reproduction of one-electron properties derived from the original many-electron wavefunction. The computational algorithms for constructing LPOs and CLPOs from a general wavefunction are presented and their implementation within the open-source freeware program JANPA ( http://janpa.sourceforge.net /) is discussed. The performance of the proposed procedures is assessed using the test set of density matrices of 33 432 small molecules obtained at both Hartree-Fock and second-order Moller-Plesset theory levels and excellent agreement with the chemist's Lewis-structure picture is found.     

Molecular orbitals for excited states of atoms and molecules

A method is described for calculating SCF wavefunctions for excited electronic states of atoms and molecules. The orthogonality conditions with the ground state wavefunction and the underlying excited states wavefunctions are introduced in the SCF process in a simplified form.     

Theoretical calculation about the valence and Rydberg excited states of hydrogen cyanide

The singlet and triplet excited states of hydrogen cyanide have been computed by using the complete active space self-consistent field and completed active space second order perturbation methods with the atomic natural orbital (ANO-L) basis set. Through calculations of vertical excitation energies, we have probed the transitions from ground state to valence excited states, and further extensions to the Rydberg states are achieved by adding 1s1p1d Rydberg orbitals into the ANO-L basis set. Four singlet and nine triplet excited states have been optimized. The computed adiabatic energies and the vertical transition energies agree well with the available experimental data and the inconsistencies with the available theoretical reports are discussed in detail.     

Variational problem for ground and excited rovibronic states on the basis of a molecular Hamiltonian in the principal central axes

A general scheme of realization of nonempirical methods for calculation of the ground and excited rovibronic states of flexible molecules is proposed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Quantum Monte Carlo calculations for ground and excited states

A brief overview of the diffusion quantum Monte Carlo method is given. We illustrate the application to ground‐state calculations by a study of the relative stability of carbon clusters near the crossover to fullerene stability, thereby determining the smallest stable fullerene. The application to excited states is illustrated via a study of excitonic states in small hydrogenated silicon clusters. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Further investigations about the zwitterionic excited states of twisted conjugated molecules

For twisted zwitterionic excited states, the single-determinant closed-shell SCF approach favours one of the two possibly resonant structures A⁺B^– or A^–B⁺, but gives a very low energy by allowing reorganization and polarization under the field. This effect is very difficult to include in CI developments using neutral symmetry adapted MO's. The closed-shell SCF approach is always relevant for energy, and only fails for the wavefunction in the (near) degeneracy region between A^–B⁺ and A⁺ B^–, where the Born-Oppenheimer approximation, anyway, breaks down. The process is applied in nonempirical (minimal + diffuse AO basis set) calculations of butadiene. The role of geometry optimization and of further electron correlation is illustrated. The extent of polarization is shown in ethylene, suggesting a neutral two carbene limit picture of this excited state.     

Low‐lying singlet excited states of isocyanogen

Recent photofragment fluorescence excitation (PHOFEX) spectroscopy experiments have observed the ùA″ singlet excited state of isocyanogen (CNCN) for the first time. The observed spectrum is not completely assigned and significant questions remain about the excited states of this system. To provide insight into the energetically accessible excited states of CNCN, optimized geometries, harmonic vibrational frequencies, and excitation energies for the first three singlet excited states are determined using equation‐of‐motion coupled‐cluster theory with singles and doubles (EOM‐CCSD) and correlation‐consistent basis sets. Additionally, excited state coupled‐cluster methods which approximate the contributions from triples (CC3) are utilized to estimate the effect of higher‐order correlation on the energy of each excited state. For the ùA″ state, our best estimate for T₀ is about 42,200 cm^?1, in agreement with the experimentally estimated upper limit for the zero‐point level of 42,523 cm^?1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Direct INDO/SCI method for excited state calculations

Intermediate neglect of differential overlap (INDO) is the most commonly utilized semiempirical technique for performing excited state calculations on large organic systems such as organic semiconductors and fluorescent dyes. The calculations are typically done at the singles-configuration interaction (SCI) level. Direct methods provide a more efficient means of performing configuration interaction (CI) calculations, and the computational trade offs associated with various approaches to direct-CI theory have been well characterized for ab initio Hamiltonians and high-order CI. However, the INDO and SCI approximations lead to a new set of trade offs. In particular, application of the electron-electron interactions in the atomic basis leads to savings in computational time that scale as the number of atomic orbitals, which for a large organic system can be two to three orders of magnitude. These savings are largest when only a few low-lying excited states are generated and when a full SCI basis, which includes excitations between all filled and empty molecular orbitals, is used. In addition, substantial memory savings are achieved in the direct method by avoiding the evaluation of the two electron integrals in the molecular orbital basis. The method is demonstrated by calculating the absorption spectrum of a poly(paraphenylenevinylene) oligomer containing 16 phenyl rings.     

Calculation and properties of non-orthogonal,strictly local molecular orbitals

A general procedure to calculate non-orthogonal, strictly local molecular orbitals (NOLMOs) expanded using only a subset of the total basis set is presented. The energy of a single determinant wave function is minimised using a Newton-Raphson approach. Total energies and barriers to internal rotation for CH₄, NH₃, H₂O, CH₃CH₃, CH₃NH₂, CH₃OH, NH₂NH₂, NH₂OH and HOOH, and certain properties of the NOLMOs present in these molecules, are investigated using the 4-31G basis set.     

A theoretical investigation of the excited states of OCLO radical, cation, and anion using the CASSCF/CASPT2 method

Using the complete active space self-consistent field method with a large atomic natural orbital basis set, 10, 13, and 9 electronic states of the OClO radical, OClO(+) cation, and OClO(-) anion were calculated, respectively. Taking the further correlation effects into account, the second-order perturbation (CASPT2) calculations were carried out for the energetic calibration. The photoelectron spectroscopy of the OClO radical and OClO(-) anion were extensively studied in the both case of the adiabatic and vertical ionization energies. The calculated results presented the relatively complete assignment of the photoelectron bands of the experiments for OClO and its anion. Furthermore, the Rydberg states of the OClO radical were investigated by using multiconfigurational CASPT2 (MS-CASPT2) theory under the basis set of large atomic natural orbital functions augmented with an adapted 1s1p1d Rydberg functions that have specially been built for this study. Sixteen Rydberg states were obtained and the results were consistent with the experimental results.     

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.     

The valence and Rydberg excited states of CH2: A theoretical exploration

Using the completed active space second‐order perturbation (CASPT2) method, valence and Rydberg excited states of CH₂ molecule are probed with the large atomic natural orbital (ANO‐L) basis set. Five states are optimized and the geometric parameters are in good agreement with the available data in literatures, furthermore, the state of 2¹B₁ is obtained for the first time. Valence and Rydberg excited states of CH₂ are also calculated for the vertical transitions with the ANO‐L+ basis set that is constructed by adding a set of 1s1p1d Rydberg orbitals into the ANO‐L basis set. Two Rydberg states of the p?³A₂ and r?³B₁ at 9.88 and 10.50 eV are obtained for the first time, and the 3a₁ → 3d_yz nature of the state p?³A₂ and the 3a₁ → d_x2?y2 nature of the state r?³B₁ are confirmed. © 2012 Wiley Periodicals, Inc.