CI Wavefunctions Research Articles

PyBEST: Improved functionality and enhanced performance

PyBEST: Improved functionality and enhanced performance

Photodissociation and formation of an ion-pair in CH2 FCl (HCFC-31).

Although CH2 FCl (HCFC-31) recently became of great atmospheric importance, studies concerning its excited states are almost nonexistent. Several excited singlet states were studied (valence nσ* and Rydberg n3s, n3p, σ3s, and σ3p) through highly correlated multireference configuration interaction with singles and doubles, including extensivity correction. Comparison with the states of CH3 Cl indicates a strong influence of the F atom. Potential energy curves suggest formation of an electrostatically bound complex that relaxes to a hydrogen-bonded contact ion-pair (HBCIP) which can decay yielding CH2 F + Cl or to the ground state minimum of CH2 FCl. The HBCIP has a dipole moment of 9.57 D, a CI wavefunction described as 0.65ionic + 0.20biradical and it is strongly bonded by 4.72 eV. Its H bond has characteristics of moderate and strong H bonds. The simulated absorption spectrum confirms the nσ* assignment for the first and suggests the n3s + n3pσ assignment for the second band.

Ground and low-lying excited states of DyCl studied by the four-component relativistic configuration interaction methods

The ground and low-lying excited states of the DyCl molecule are investigated by the four-component relativistic CI methods. Electronic states are classified into so-called families by applying the f-shell Omega decomposition method to the CI wavefunctions, and the characters of the states are clarified. The X7.5 ground state may be described as Dy+[(4f)9(6s)2]Cl−, but at large nuclear distance (R > 4.80 au), beyond the equilibrium nuclear distance (4.724 au), the dominant configuration changes to Dy+[(4f)10(6s)1]Cl−. The dominant configuration of Dy+[(4f)9(6s)2]F− is retained in DyF, but the dominant configuration in DyCl changes drastically as R increases. The calculated value (231 cm−1) of the vibrational frequency (ωe) agrees well with the value of 233 cm−1 observed by Linton et al. (J Mol Spectrosc 232:30–39, 2005). This low frequency reflects the weakness of the Cl− ligand compared to F−. The Y[0.15]8.5, Z[0.85]7.5, and [0.97] states observed by Linton et al. are found to have a dominant configuration of [(4f)10(6s)1], and the A[16.4]8.5 and B[15.4]Ω states observed both have (4f)10([6p1/2,1/2])1, belonging to different families. (The number in square brackets denotes the excitation energy in unit of k cm−1, and the number after a right square bracket denotes an Ω value.) The Ω value of the B[15.4]Ω state, which has not been determined experimentally, is calculated to be 6.5.

The role of the CI expansion length in time-dependent studies.

With the recent advances in experimental attosecond science, theoretical predictions of electron dynamics can now be validated against experiment. Time-dependent studies of the electron motion in molecules can be used to obtain information about electronic transitions and the interaction of the electrons with electromagnetic fields. Often, these approaches rely on single-excited wave functions. Presented here is a first attempt to evaluate the accuracy of the time-dependent configuration interaction method so that the optimal representation of the electronic wave function for time-dependent studies can be assessed. A quantifier is determined that can aid in finding this optimal representation. The approach is demonstrated on a variety of molecules that include both localized and intramolecular charge transfer electron excitations. Observables including excitation energies, dipole moments, strengths, and static polarizabilities are obtained from time-independent and time-dependent calculations and are compared to experimental data. In this way, a rigorous routine is developed by which the reliability and accuracy of the CI wave function can be assessed and which represents a first step to a more quantitative description of electron dynamics in molecules.

Non-orthogonal internally contracted multi-configurational perturbation theory (NICPT): Dynamic electron correlation for large, compact active spaces.

A computational method is presented for systems that require high-level treatments of static and dynamic electron correlation but cannot be treated using conventional complete active space self-consistent field-based methods due to the required size of the active space. Our method introduces an efficient algorithm for perturbative dynamic correlation corrections for compact non-orthogonal MCSCF calculations. In the algorithm, biorthonormal expansions of orbitals and CI-wave functions are used to reduce the scaling of the performance determining step from quadratic to linear in the number of configurations. We describe a hierarchy of configuration spaces that can be chosen for the active space. Potential curves for the nitrogen molecule and the chromium dimer are compared for different configuration spaces. Already the most compact spaces yield qualitatively correct potentials that with increasing size of configuration spaces systematically approach complete active space results.

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation.

We propose a size-consistent generalization of the recently developed spin-extended configuration interaction with singles and doubles (ECISD), where a CI wave function is explicitly spin-projected. The size-consistent effect is effectively incorporated by treating quadruples within the formulation of coupled electron pair approximation. As in coupled-cluster theory, quadruple excitations are approximated by a disconnected product of double excitations. Despite its conceptual similarity to the standard single-reference and multireference analogues, such a generalization requires careful derivation, as the spin-projected CI space is nonorthogonal and overcomplete. Although our methods generally yield better results than ECISD, size-consistency is only approximately retained because the action of a symmetry-projection operator is size-inconsistent. In this work, we focus on simple models where exclusion-principle-violating terms, which eliminate undesired contributions to the correlation effects, are either completely neglected or averaged. These models possess an orbital-invariant energy functional that is to be minimized by diagonalizing an energy-shifted effective Hamiltonian within the singles and doubles manifold. This allows for a straightforward generalization of the ECISD analytical gradients needed to determine molecular properties and geometric optimization. Given the multireference nature of the spin-projected Hartree-Fock method, the proposed approaches are expected to handle static correlation, unlike single-reference analogues. We critically assess the performance of our methods using dissociation curves of molecules, singlet-triplet splitting gaps, hyperfine coupling constants, and the chromium dimer. The size-consistency and size-extensivity of the methods are also discussed.

Dynamical correlation within the Interacting Quantum Atoms method through coupled cluster theory

The Interacting Quantum Atoms (IQA) approach is an energy partition of an electronic system which has provided new understandings and insightful information about diverse chemical systems and processes from Hartree–Fock, CASSCF as well as truncated and full CI wavefunctions. Nonetheless, the unavailability of an implementation of IQA relying on size extensive correlated methods such as coupled cluster or Møller–Plesset perturbation theory, has prevented the application of this procedure to the study of molecular systems in which these models of electronic structure are necessary to obtain accurate results. This paper uses first and second-order density matrices consistent with a closed shell coupled cluster energy to carry out the IQA splitting. The presented developments are tested and discussed using H2, N2, H2O and CO as representative examples. It is our hope that the implementations discussed in this paper would give new insights in the study of chemical bonding, intermolecular interactions and other important phenomena in chemistry for which the consideration of electron correlation is critical.

Lossless compression of wave function information using matrix factorization: A “gzip” for quantum chemistry

We propose the use of the singular value decomposition to decrease the storage required for wave function information. The specific case considered is determinantal full configuration interaction, but the same technique is readily applicable to truncated configuration interaction and coupled-cluster calculations of various types; as we discuss this is a reformulation of approximate methods that have been in use for some time, but our approach eliminates those approximations. Numerical examples support the contention that considerable compression of the wave function is possible without significant loss of accuracy: as expected a considerable amount of the information contained in the full CI wave function is redundant.

Fragment-based configuration interaction wave function to calculate environmental effect on excited states in proteins and solutions

• Coarse-grained analysis to figure out excited-state w.f. including environments. • A fragment-based truncated CIS for the excited-state w.f. including environments. • CTs between environmental fragments give negligible contributions. Solvatochromic effect in proteins and solutions was described by a configuration interaction singles (CIS) wave function with fragment-localized molecular orbitals. Coarse-grained analysis indicated that the CI wave function can be described by local excitations and charge-transfer (CT) excitations between the chromophore and the environment. We developed an atomic-orbital direct runcated CIS code and applied the excited states of retinal chromophore in bacteriorhodopsin and MeOH environments, and those of s -trans-acrolein in water. Number of excitation operators was significantly reduced by eliminating the CT excitations between the environmental fragments. The truncated CIS wave functions reproduced the original excitation energies very well.

On the formulation of a density matrix functional for Van der Waals interaction of like- and opposite-spin electrons in the helium dimer

Whereas a density functional that incorporates dispersion interaction has remained elusive to date, we demonstrate that in principle the dispersion energy can be obtained from a density matrix functional. In density matrix functional theory one tries to find suitable approximations to the two-particle reduced density matrix (2RDM) in terms of natural orbitals (NOs) and natural orbital occupation numbers (ONs). The total energy is then given as a function(al) of the NOs and ONs, i.e., as an implicit functional of the 1RDM. The left-right correlation in a (dissociating) bond, as well as various types of dynamical correlation, can be described accurately with a NO functional employing only J and K integrals (JK-only functional). We give a detailed analysis of the full CI wavefunction of the He(2) dimer, from which the dispersion part of the two-particle density matrix is obtained. It emerges that the entirely different physics embodied in the dispersion interaction leads to an essentially different type of exchange-correlation orbital functional for the dispersion energy (non-JK). The distinct NO functionals for the different types of correlation imply that they can be used in conjunction without problems of double counting. Requirements on the (primitive) basis set for Van der Waals bonding appear to be more modest than for other types of correlation.

A Configuration Interaction Picture for a Molecular Environment Using Localized Molecular Orbitals: The Excited States of Retinal Proteins

Electronic excitations of chromophores in proteins and solutions are associated with the electronic response of the molecular environment. The underlying interactions are important origins of solvatochromism. We performed large-scale configuration interaction singles (CIS) calculations (up to 1000 atoms) for retinal chromophores in proteins and methanol solution, in which one-electron processes (polarization and charge-transfer effects of the environment) are included. The present approach also improved the electrostatic potential, as compared to that described by a molecular mechanics (MM) force field. The CIS results were combined with the symmetry adapted cluster (SAC)-CI result using our own N-layer integrated molecular orbital molecular mechanics (ONIOM) method. As compared to the MM description, the CIS reduces the calculated excitation energy by 0.1-0.3 eV and also improves the relative excitation energies among retinal proteins. We applied our localized molecular orbital (LMO) transformation scheme to analyze the CI wave functions. The result clarified the contributions of the amino acids. In bacteriorhodopsin, Tyr185 contributes intermolecular CT excitations. The radial distribution of amino acids' contributions to the CI wave function was also analyzed. The results of the analysis are useful not only for understanding the molecular interactions and the role of amino acids in color tuning, but also for providing insight into the structure of the excited-state wave function for the molecular environment. An excitation-energy decomposition analysis also supported the results of the excited-state wave functions.

LARGE-SCALE FIRST PRINCIPLES CONFIGURATION INTERACTION CALCULATIONS OF OPTICAL ABSORPTION IN BORON CLUSTERS

We have performed systematic large-scale all-electron correlated calculations on boron clusters B n(n = 2 - 5), to study their linear optical absorption spectra. Several possible isomers of each cluster were considered, and their geometries were optimized at the coupled-cluster singles doubles (CCSD) level of theory. Using the optimized ground-state geometries, the excited states of different clusters were computed using the multi-reference singles-doubles configuration–interaction (MRSDCI) approach, which includes electron correlation effects at a sophisticated level. These CI wave functions were used to compute the transition dipole matrix elements connecting the ground and various excited states of different clusters, eventually leading to their linear absorption spectra. The convergence of our results with respect to the basis sets, and the size of the CI expansion were carefully examined. The contribution of configurations to many body wave-function of various excited states suggests that the excitations involved are collective, plasmonic type.

Natural hybrid orbitals: Ab initio SCF and CI results for CO and NiCO

The natural hybrid orbital (NHO) procedure of Foster and Weinhold is generalized to treat ab initio SCF or CI wavefunctions in minimal or extended basis sets. The first applications of the ab initio NHO analysis to a series of wavefunctions for carbon monoxide and the NiCO complex are presented. Numerical and graphical comparisons of NHOs for these systems exhibit the effects of basis-set augmentation and electron correlation on the details of the natural “Lewis diagrams”. Hybrid p-character and bond polarization are found to be persistent features of the NHO description, well represented even at the minimal basis level. Extension of the basis set allows the natural lone pairs to delocalize somewhat, while the principal effect of electron correlation is to shift occupancy somewhat into the π*CO orbitals. The effect of coordination of CO to a Ni atom, as conventional chemical intuition would suggest, is to polarize the carbon lone pair more toward the metal atom and the πCO bond more toward the oxygen.

An extension of koopmans' theorem III. ionization energies of the open-shell atoms Li and B

Extended Koopmans' theorem orbital energies are calculated using unsymmetrized hole states for the Li 2S and B 2P states. These orbital energies are compared with ionization energies obtained from Δci calculations in the same basis sets as well as with experimental ionization energies. The extended Koopmans' orbital energies over unsymmetrized hole states for the outer shell orbital 2sα of Li and for the two outer shell orbitals 2pα and 2sβ of B agree well with Δci ionization energies and with experimental ionization energies. The overlap of the 2sα hole state of Li with a ci wave function of Li+ is 0.999983. The corresponding overlaps of the 2pα and 2sβ hole states of B with ci wave functions are 0.996588 and 0.999258, respectively. The unsymmetrized hole states for inner shell orbitals are strong mixtures of different symmetry types and yield increasingly poorer ionization energies.

The measurement of charge densities by diffraction techniques

A brief review of the field of the determination of information on atomic and molecular charge densities by electron scattering is presented. The connection between this work and x-ray scattering is pointed out. Recent calculations on atomic charge densities for the neon atom are reviewed and compared with new experimental data. It is shown that current experimental techniques are on a par with a CI wave function for Ne, giving 86% of the electronic correlation energy, for deducing information about detailed shapes of the charge distribution in small atoms and molecules. Recent calculations of scattered molecular intensities with molecular wave functions are reviewed and compared with existing experimental data. It is pointed out that effects of correlation and chemical binding on charge densities can probably be investigated currently with greater accuracy by experimental techniques than with presently available numerical theoretical procedures in the case of many molecules.

Calculation of transition matrix elements by nonsingular orbital transformations

A general strategy is described for the evaluation of transition matrix elements between pairs of full class CI wave functions built up from mutually nonorthogonal molecular orbitals. A new method is proposed for the counter-transformation of the linear expansion coefficients of a full CI wave function under a nonsingular transformation of the molecular-orbital basis. The method, which consists in a straightforward application of the Cauchy–Binet formula to the definition of a Slater determinant, is shown to be simple and suitable for efficient implementation on current high-performance computers. The new method appears mainly beneficial to the calculation of miscellaneous transition matrix elements among individually optimized CASSCF states and to the re-evaluation of the CASCI expansion coefficients in Slater-determinant bases formed from arbitrarily rotated (e.g., localized or, conversely, delocalized) active molecular orbitals. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Möbius and twisted graphene nanoribbons: Stability, geometry, and electronic properties

Results of classical force field geometry optimizations for twisted graphene nanoribbons with a number of twists N(t) varying from 0 to 7 (the case N(t)=1 corresponds to a half-twist Möbius nanoribbon) are presented in this work. Their structural stability was investigated using the Brenner reactive force field. The best classical molecular geometries were used as input for semiempirical calculations, from which the electronic properties (energy levels, HOMO, LUMO orbitals) were computed for each structure. CI wavefunctions were also calculated in the complete active space framework taking into account eigenstates from HOMO-4 to LUMO+4, as well as the oscillator strengths corresponding to the first optical transitions in the UV-VIS range. The lowest energy molecules were found less symmetric than initial configurations, and the HOMO-LUMO energy gaps are larger than the value found for the nanographene used to build them due to electronic localization effects created by the twisting. A high number of twists leads to a sharp increase of the HOMO-->LUMO transition energy. We suggest that some twisted nanoribbons could form crystals stabilized by dipolar interactions.

Molecular one‐electron properties using the multireference Hartree–Fock CI method

AbstractThe recently introduced multireference Hartree–Fock configuration interaction (MRHFCI) method has been applied to the calculation of the dipole moment of the LiH, BH, FH, CO, and H2O molecules. The results obtained indicate that MRHFCI wave functions, much more compact but of the same quality of the orthogonal full CI ones, can provide better dipole moments than the corresponding full CI wave functions. The value of the dipole moments obtained with the MRHFCI wave functions is quite insensitive to the choice of the HF references but the same is not true for the electronic energy. Therefore, further studies are necessary to develop a criterion for selecting a set of HF references which could provide the best values of energy and dipole moment. Also, it would be important to verify if other one‐electron properties can be computed with the same degree of accuracy obtained for the dipole moments. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Theoretical Studies on Dications and Trications of FH, ClH, and BrH. Properties of the Bound 15Σ- States. Electron-Spin g-Factors and Fine/Hyperfine Constants of the Metastable X3Σ- States of ClH2+ and BrH2+

This theoretical study reports calculations on the fine and hyperfine structure parameters of the metastable X(3)Sigma(-)(sigma(2)pi(2)) state of ClH(2+) and BrH(2+). Data on the repulsive FH(2+) system are also included for comparison purposes. The hyperfine structure (hfs) coupling constants for magnetic (A(iso), A(dip)) and quadrupole (eQq) interactions are evaluated using B3LYP, MP4SDQ, CCSD, and QCISD methods and several basis sets. The fine structure (fs) constants (zero-field splitting lambda and spin-rotation coupling gamma) and electron-spin magnetic moments (g-factor) are evaluated in 2nd-order perturbation theory using multireference CI (MRCI) wave functions. Our calculations find for (35)Cl of ClH(2+) A(iso)/A(dip) = 110/-86 MHz; eQq(0) = -59 MHz; 2lambda = 20.4 cm(-1); g( perpendicular)(v = 0) = 2.02217; and gamma = -0.31 cm(-1) (to be compared with the available experimental A(iso)/A(dip)= 162/-30 MHz). For (79)BrH(2+), the corresponding values are 300/-400 MHz; 368 MHz; 362.6 cm(-1); 2.07302; and -0.98 cm(-1) (experimental 2lambda = 445(+/-80) cm(-1)). We find g( perpendicular)(ClH(2+)) to increase by about 0.0054 between v = 0 and 2, whereas the experimental effective g( perpendicular) changes drastically with vibrational excitation. Nuclear quadrupole coupling constants for halogen atoms X are found to be as large as corresponding A(dip)(X)'s, indicating that both terms may have to be included in the Hamiltonian used to interpret XH(2+) hyperfine spectra. A novel finding relates to the bound character of the 1(5)Sigma(-)(sigmapi(2)sigma) state in FH(2+), as already known for ClH(2+) and BrH(2+), but having a deeper potential well D(e) approximately 4,000 cm(-1) (versus 1,000 cm(-1) in the heavier radicals). Vertical ionization potentials for formation of XH(3+) trications are also discussed.

Electronic Spectroscopy of the AlSb Molecule: A Theoretical Study

Relativistic configuration interaction calculations are carried out to study the electronic spectrum of the AlSb molecule. Potential energy curves of 44 electronic states within 6 eV of energy are constructed. Spectroscopic constants (re, ωe, Te, De, μe) of the low-lying Λ-S states are computed. The equilibrium bond length and vibrational frequency of the ground state (X3Σ-) of AlSb are estimated to be 2.79 Å and 249 cm-1, respectively. Effects of the spin−orbit coupling on the spectroscopic properties and potential energy curves of states that correlate with the lowest two dissociation limits are investigated. The computed dissociation energy of the ground-state spin component (X3 ) is 1.44 eV. Transition moments of several electric dipole-allowed and spin-forbidden transitions are computed from CI wave functions. Radiative lifetimes of the low-lying excited states of AlSb at the lowest three vibrational levels (v‘ = 0, 1, 2) are estimated. Transitions from the 33Π0+ component to all lower states with ΔΩ = 0, ±1 are predicted. At v‘ = 0, the 33Π0+ component has a lifetime of about 1.26 μs. The electronic states of AlSb are also compared with those of isovalent AlP, GaAs, GaSb, and InSb molecules.