Single-reference Configuration Interaction Research Articles

State-specific solvation for restricted active space spin-flip (RAS-SF) wave functions based on the polarizable continuum formalism.

The restricted active space spin-flip (RAS-SF) formalism is a particular form of single-reference configuration interaction that can describe some forms of strong correlation at a relatively low cost and which has recently been formulated for the description of charge-transfer excited states. Here, we introduce both equilibrium and nonequilibrium versions of a state-specific solvation correction for vertical transition energies computed using RAS-SF wave functions, based on the framework of a polarizable continuum model (PCM). Ground-state polarization is described using the solvent's static dielectric constant and in the nonequilibrium solvation approach that polarization is modified upon vertical excitation using the solvent's optical dielectric constant. Benchmark calculations are reported for well-studied models of photo-induced charge transfer, including naphthalene dimer, C2H4⋯C2F4, pentacene dimer, and perylene diimide (PDI) dimer, several of which are important in organic photovoltaic applications. For the PDI dimer, we demonstrate that the charge-transfer character of the excited states is enhanced in the presence of a low-dielectric medium (static dielectric constant ɛ0 = 3) as compared to a gas-phase calculation (ɛ0 = 1). This stabilizes mechanistic traps for singlet fission and helps to explain experimental singlet fission rates. We also examine the effects of nonequilibrium solvation on charge-separated states in an intramolecular singlet fission chromophore, where we demonstrate that the energetic ordering of the states changes as a function of solvent polarity. The RAS-SF + PCM methodology that is reported here provides a framework to study charge-separated states in solution and in photovoltaic materials.

Toward Molecular-Level Characterization of Photoinduced Decarboxylation of the Green Fluorescent Protein: Accessibility of the Charge-Transfer States.

Irradiation of the green fluorescent protein (GFP) by intense violet or UV light leads to decarboxylation of the Glu222 side chain in the vicinity of the chromophore (Chro). This phenomenon is utilized in optical highlighters, such as photoactivatable GFP (PA-GFP). Using state-of-the-art quantum chemical calculations, we investigate the feasibility of the mechanism proposed in the experimental studies [van Thor et al. Nature Struct. Biol.2002, 9, 37-41; Bell et al. J. Am. Chem. Soc.2003, 125, 37-41]. It was hypothesized that a primary event of this photoconversion involves population of a charge-transfer (CT) state via either the first excited state S1 when using longer wavelength (404 and 476 nm) or a higher excited state when using higher energy radiation (254 and 280 nm). Based on the results of electronic structure calculations, we identify these critical CT states (produced by electron transfer from Glu to electronically excited Chro) and show that they are accessible via different routes, i.e., either directly, by one-photon absorption, or through a two-step excitation via S1. The calculations are performed for model systems representing the chromophore and the key nearby residues using two complementary approaches: (i) the multiconfigurational quasidegenerate perturbation theory of second order with the occupation restricted multiple active space scheme for configuration selection in the multiconfigurational self-consistent field reference; and (ii) the single-reference configuration interaction singles method with perturbative doubles that does not involve active space selection. We examined electronic transitions with nonzero oscillator strengths in the UV and visible range between the electronic states involving the Chro and Glu residues. Both methods predict the existence of CT states with nonzero oscillator strength in the UV range and a local excited state of the chromophore accessible via S1 that may lead to the target CT state. The results suggest several possible scenarios for the primary photoconversion event. We also demonstrate that the point mutation Thr203His exploited in PA-GFP results in shifting the light wavelength to access the CT up to 20 nm, which suggests a possibility of a rational design of photoactivatable proteins in silico.

Orbital invariance issue in multireference methods

AbstractThe orbital invariance problem is analyzed from the tensor theory point of view, with an emphasis on multireference coupled cluster methods. Using the transformation properties of second‐quantized operators, we discuss the orbital invariance properties of various methods by examining the tensor properties of the residual equations. A simple self‐consistency‐checking algorithm is proposed. We first establish the orbital invariance properties for the Hartree–Fock, single reference configuration interaction, single reference coupled cluster, complete‐active‐space self‐consistent‐field, and multireference configuration interaction methods, and then discuss the invariance properties of the complete‐active‐space coupled cluster and CCSDt methods. Finally, we demonstrate theoretically the lack of orbital invariance for Jeziorski–Monkhorst ansatz based methods. It appears necessary to modify the ansatz to achieve orbital invariance, and internal contraction serves as one possible solution. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Hyperfine coupling constants and electron-spin g-factors of B2+, Al2+, Ga2+, BAl+, BGa+, and AlGa+: An ab initio study

The hyperfine coupling constants (hfcc) and electron-spin g-factors (magnetic moments) calculated for B2+, Al2+, Ga2+, BAl+, BGa+, and AlGa+ are reported. The hfcc’s are obtained with single-reference configuration interaction, second-order Møller–Plesset, density functional (B3LYP, PW91PW91) methods, and 6-311+G(2df ) basis sets. The 2σg/3σ SOMOs of X 2Σg+(1σg21σu22σg)/X 2Σ+(1σ22σ23σ) mainly have a pσ–pσ composition, leading in most cases to similar values of Adip and Aiso. As a result, |A∥| is up two orders of magnitude larger than |A⊥|. The A⊥’s are slightly negative (ca. −10 MHz) for Al2+, Ga2+, and AlGa+. The g-shifts (Δg=g−ge) are evaluated with multireference CI wave functions, perturbation expansions up to second-order, and 6-311+G(2d) basis sets. Both Δg∥ and Δg⊥ are negative, but Δg∥ lies close to zero. The Δg⊥’s of B2+, Al2+, Ga2+ are about −1 300, −12 800, −97 300 ppm, respectively, while for BGa+, BAl+, AlGa+, they are much smaller (−800, −2 800, −47 400 ppm). The reduced Δg⊥’s for XY+ result from the mutual cancellation between a positive contribution from the 1 2Π(3σ→1π) state but a negative one from 2 2Π(3σ→2π). The positive contribution is at variance with the rule-of-thumb stating that SOMO→virtual MO excitations should contribute negatively. The variation of the hfcc’s with bond distance is analyzed for all systems, and that of the Δg⊥ component for B2+ and BAl+. Experimental or previous theoretical electron-spin resonance data are not available for comparison.

Bk approximation applied to the multireference configuration interaction method

The single-reference configuration interaction through quadrupoles CI SDTQ-Bk method has been extended to the general multireference CI method in the Bk approximation (MR CI-Bk). The computer code is based on the traditional graphical unitary group approach (GUGA)-CI technique, and it processes only the loops (coupling coefficients) that are necessary for the MR CI-Bk Hamiltonian matrix evaluation. The number of processed loops, and therefore also the cost of calculation, is considerably lower than in the case of the respective complete MR CI calculation. The method was tested on the ground-state potential curves of the N2, F2, and HF molecules, by comparing the calculated MR CI-Bk energies with the available literature data obtained by complete MR CI and full CI calculations. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 185–196, 2000

Static structure factor and electron correlation effects studied by inelastic x-ray scattering spectroscopy

Inelastic x-ray scattering spectra of methanol, acetonitrile, benzene, and cyclohexane have been measured with 2 eV resolution for momentum transfer q between 0.69 and 2.77 a.u. using synchrotron radiation from the photon factory (PF) storage ring. By utilizing the Bethe sum rule, the spectra were brought onto an absolute scale, so that the static structure factor S(q) has been obtained. S(q) of these molecules has also been calculated at the single reference configuration interaction (CI) with several types of basis sets. A new formula is proposed to carry out spherical averaging accurately. It is concluded that the CI singles and doubles (CISD) treatment is necessary to predict correct S(q), and that an inclusion of polarization function influences S(q) significantly at this level. An addition of f functions also improves the agreement with the experiments. S(q)’s based on CISD wave functions are in good agreement with the experimental ones, in particular at large q.

The chemistry of the superheavy elements. I. Pseudopotentials for 111 and 112 and relativistic coupled cluster calculations for (112)H+, (112)F2, and (112)F4

One- and two-component (spin–orbit coupled) relativistic and nonrelativistic energy adjusted pseudopotentials and basis sets for the elements 111 and 112 are presented. Calculations on the positively charged monohydride of the recently discovered superheavy element 112 are reported. Electron correlation is treated at the multireference configuration interaction and coupled cluster level and fine structure effects are derived from a single-reference configuration interaction treatment. Relativistic effects decrease the (112)H+ bond distance by 0.41 Å. This bond contraction is similar to the one calculated recently for (111)H [Chem. Phys. Lett. 250, 461 (1996)]. As a result the bond distance of (112)H+ (1.52 Å) is predicted to be smaller compared to those of the hydrides of the lighter congeners HgH+ (1.59 Å), CdH+ (1.60 Å) and similar to that of ZnH+ (1.52 Å). We predict that (112)H+ is the most stable hydride in the Group 12 series due to relativistic effects. As in the case of (111)H the relativistic increase of the stretching force constant is quite large, from 1.5 to 4.3 mdyn/Å at the coupled cluster level. The trend in the dipole polarizabilities of the Group 12 elements is discussed. Relativistic and electron correlation effects are nonadditive and due to the relativistic ns contraction (n=7 for 112), correlation effects out of the (n−1)d core are more important at the relativistic than the nonrelativistic level. We also show evidence that element 112 behaves like a typical transition element, and as a consequence the high oxida-tion state +4 in element 112 might be accessible.

Theoretical study of the di-imide (N2H2) molecule in ground and n→π* excited states

A number of ab initio approaches have been used to determine the equilibrium structures, energies, and vibrational frequencies of N2H2 in the ground state and in the excited singlet and triplet n→π* states. The methods included restricted Hartree–Fock (RHF) and unrestricted Hartree–Fock (UHF), multiconfiguration self-consistent field (MCSCF), single-reference configuration interaction (SRCI) and multireference configuration interaction (MRCI) including all single and double excitations from the reference configurations, and second-order Mo/ller–Plesset perturbation theory (MP2) using RHF and UHF orbitals for ground and excited states, respectively. Unlike the singlet excited state, for which broken-symmetry solutions were found at the RHF level, no symmetry breaking was encountered for the triplet state. The ground-state MCSCF and MP2 structures of N2H2, which have C2h (trans-planar) symmetry, are in good agreement with the experimental structure. The excited states are predicted to have nonplanar C2 structures with dihedral angles ranging from 96° to 106° for the triplet state and from 105° to 121° for the singlet state. Except for the SRCI singlet adiabatic excitation energy, the effect of configuration interaction is to increase the vertical and adiabatic excitation energies of both excited states relative to the RHF values in single-reference calculations, and to decrease these excitation energies relative to MCSCF values in multireference calculations, bringing the single-reference and multireference CI values into better agreement with each other. The MRCI vertical excitation energies are 2.6 eV for the triplet and 3.6 eV for the singlet, while the corresponding 0–0 transition energies are 1.9 and 2.9 eV, respectively.

Structures and energies for C4

Optimized geometries and relative energies for three states of the C4 molecule have been obtained from single-reference configuration interaction (SRCI) calculations. The 1Σ+g state, which is formed without activation from the dimerization of ground state C2 molecules, is calculated to lie approximately 25 kcal above the 3Σ−g state. At the SRCI level, a rhombic form is calculated to lie 1.2 kcal below the triplet form; consideration of the Davidson correction reduces this difference to 0.4 kcal, inclusion of a second set of diffuse d functions increased the difference only by about 0.2 kcal. Consideration of these effects, the difference in zero-point energy and previous results for methylene leads to a final estimated separation of 4.9 kcal, favoring the rhombus. Electron density distribution analysis for the rhomb is consistent with the existence of a bond between inverted sp2 carbon atoms. To aid the detection of this unusual molecule, preliminary estimates of the lowest optical transitions were obtained from SRCI calculations and vibrational frequencies were obtained from SCF calculations. Comparison of the calculated results with experimentally obtained spectra suggest the possibility that both the linear triplet and the rhombus may have already been observed.