Dynamic Electron Correlation Effects Research Articles

Double excitations and state-to-state transition dipoles inπ−π∗excited singlet states of linear polyenes: Time-dependent density-functional theory versus multiconfigurational methods

The effect of static and dynamic electron correlation on the nature of excited states and state-to-state transition dipole moments is studied with a multideterminant wave function approach on the example of all-trans linear polyenes C4H6 ,C 6H8, and C8H10. Symmetry-forbidden singlet nAg states were found to separate into three groups: purely single, mostly single, and mostly double excitations. The excited-state absorption spectrum is dominated by two bright transitions: 1Bu-2Ag and 1Bu-mAg, where mAg is the state, corresponding to two-electron excitation from the highest occupied to lowest unoccupied molecular orbital. The richness of the excited-state absorption spectra and strong mixing of the doubly excited determinants into lower-nAg states, reported previously at the complete active space self-consistent field level of theory, were found to be an artifact of the smaller active space, limited to orbitals. When dynamic - correlation is taken into account, single- and double-excited states become relatively well separated at least at the equilibrium geometry of the ground state. This electronic structure is closely reproduced within time-dependent densityfunctional theory TD DFT, where double excitations appear in a second-order coupled electronic oscillator formalism and do not mix with the single excitations obtained within the linear response. An extension of TD DFT is proposed, where the Tamm-Dancoff approximation TDA is invoked after the linear response equations are solved a posteriori TDA. The numerical performance of this extension is validated against multideterminant-wave-function and quadratic-response TD DFT results. It is recommended for use with a sum-over-states approach to predict the nonlinear optical properties of conjugated molecules.

Ab initio molecular orbital study of ground and low-lying electronic states of NiCN

The electronic ground state and some low-lying excited states of NiCN have been studied by ab initio multi-reference single and double excitation configuration interaction calculations (MR-SDCI) with Davidson’s correction Q and Cowan–Griffin’s relativistic corrections E rel. The electronic ground state of NiCN is 2Δ i and the equilibrium geometry is linear with bond lengths of r e(Ni–C) = 1.8141 Å and r e(C–N) = 1.1665 Å. According to multi-reference averaged quadratic coupled-cluster theory (MR-AQCC) with E rel, the first excited state is 2Σ +, separated from the ground state by 446 cm −1, the second and third excited states are 2Π i (at 1594 cm −1) and 4Δ i (at 8930 cm −1), respectively, and other quartet states follow. The relative stabilities and the molecular properties of the low- and high-spin states having the same electronic total angular momentum are shown to be determined by dynamical electron correlation effects. A spin–orbit interaction scheme for the lowest doublet manifold is proposed. The predicted term values (in cm −1) are 0 ( X ∼ 2 Δ 5 / 2 ) , 793 ( 2 Σ 1 / 2 + ) , 891 ( 2Δ 3/2), 2321 ( 2Π 3/2), and 2773 ( 2Π 1/2). Thus, an unassigned state reported by Kingston et al. [C.T. Kingston, A.J. Merer, T.D. Varberg, J. Mol. Spectrosc. 215 (2002) 106] at 755 cm −1 could be the 1 2 Σ 1 / 2 + state.

Comment on “The Water-Exchange Mechanism of the [UO2(OH2)5]2+ Ion Revisited: The Importance of a Proper Treatment of Electron Correlation” [F. P. RotzingerChem. Eur. J., 2007,13, 800

Fulfilled satisfactorily: As a reply to the statements of F. P. Rotzinger [Chem. Eur. J., 2007, 13, 800] we demonstrate that the MP2 method can be applied to uranyl(VI) complexes because dynamic electron correlation effects dominate and static electron correlation of the near-degeneracy type is absent.

Phenol-water1⩽n⩽3 revisited: An ab initio study on the photophysics of these clusters at the level of coupled cluster response theory

The S1(pi*<--pi) state surfaces of the phenol-water(1<or=n<or=3) clusters are reexplored at the level of coupled cluster response theory. The global minima for n=2 and n=3 so obtained are qualitatively different from those reported so far, which were obtained with methods such as configuration interaction singles or complete active space self-consistent field lacking dynamical electron correlation effects. Furthermore, the minimum-energy points on the conical intersection seams were located in this work. The results of these calculations offer a qualitative explanation for the anomalous photophysical behavior (broad congested absorption band structure, low quantum yield, short lifetime) of n=2 and the observed predissociation of n=3 at excess energies beyond approximately 100 cm(-1), resolving a disagreement between theory and experiment which persisted for almost a decade.

Are intramolecular dynamic electron correlation effects detectable in X-ray diffraction experiments on molecular crystals?

In order to assess whether the effects of intramolecular dynamic electron correlation on the electron density would be experimentally detectable, X-ray structure factors which include thermal averaging effects have been calculated from the electron densities of a range of small-molecule molecular crystals [C(2)H(6), C(2)H(4), C(2)H(2), BH(3)NH(3), NH(3), NH(2)CN, OCl(2), CO(NH(2))(2)] using the procrystal, Hartree-Fock, B3LYP and QCISD wavefunction models with the superposition-of-independent-molecules method to create the electron density in the crystal. A naive R-factor-like criterion of 1% has been used to assess detectability, as well as a more sophisticated method based on real X-ray data for estimating experimental errors. Correlation effects on the density are found to be only marginally above the 1% detectability threshold, and are about one to two orders of magnitude smaller than deviations from the procrystal model. Further, only 10% of the data up to 1.2 A(-1) are significant for detecting correlation effects; and of those 10%, many are at low intensity and therefore difficult to measure. Another method to estimate the experimental errors indicates that the intramolecular correlation effects would not be measurable. Although thermal averaging effects are important for the absolute value of the calculated structure factors, the use of different thermal averaging models does not change our overall conclusion of detectability. Likewise, calculations using the B3LYP method for some molecules do not show significant changes in the amount of, or distribution of, the changes that would be detectable by experiment.

Theoretical Models on the Cu2O2 Torture Track: Mechanistic Implications for Oxytyrosinase and Small-Molecule Analogues

Accurately describing the relative energetics of alternative bis(mu-oxo) and mu-eta2:eta2 peroxo isomers of Cu2O2 cores supported by 0, 2, 4, and 6 ammonia ligands is remarkably challenging for a wide variety of theoretical models, primarily owing to the difficulty of maintaining a balanced description of rapidly changing dynamical and nondynamical electron correlation effects and a varying degree of biradical character along the isomerization coordinate. The completely renormalized coupled-cluster level of theory including triple excitations and extremely efficient pure density functional levels of theory quantitatively agree with one another and also agree qualitatively with experimental results for Cu2O2 cores supported by analogous but larger ligands. Standard coupled-cluster methods, such as CCSD(T), are in most cases considerably less accurate and exhibit poor convergence in predicted relative energies. Hybrid density functionals significantly underestimate the stability of the bis(mu-oxo) form, with the magnitude of the error being directly proportional to the percentage Hartree-Fock exchange in the functional. Single-root CASPT2 multireference second-order perturbation theory, by contrast, significantly overestimates the stability of bis(mu-oxo) isomers. Implications of these results for modeling the mechanism of C-H bond activation by supported Cu2O2 cores, like that found in the active site of oxytyrosinase, are discussed.

Assessing the zero‐field splitting in magnetic molecules by wave function‐based methods

AbstractThe effect of spin‐orbit coupling is assessed through the spin‐orbit state interaction method. This method involves a two‐step procedure to include both dynamical electron correlation effects and spin‐orbit effects on the relative energies of the low‐lying electronic states. Accurate energies of the spin free states are obtained with the complete active space self‐consistent field/complete active space second‐order perturbation theory (CASSCF/CASPT2) procedure. Second, the spin‐orbit coupling is taken into account by interaction of the CASSCF states using the CASPT2 relative energies. The method is validated on the Co2+ ion in vacuum and in the ionic insulator CoO. Afterward the method is applied to CoCl2(PPh3)2 and the dinuclear complexes [TM2Cl6]2− (TM = Mn, Fe, Co). For the monomeric species, the results compare favorable with experimental data or fully relativistic benchmarks. We discuss the difficulties to interpret the dimer results in terms of the parameters that are usually derived from experiment. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Influence of Multi-atom Bridging Ligands on the Electronic Structure and Magnetic Properties of Homodinuclear Titanium Molecules

The electronic structure and magnetic properties of homodinuclear titanium(III) molecules with bridging ligands from groups 14, 15, and 16 are examined. Single- and multireference methods with triple-zeta plus polarization basis sets are employed. Dynamic electron correlation effects are included via second-order multireference perturbation theory. Isotropic interaction parameters are calculated, and two of the complexes studied are predicted to be ferromagnetic based on multireference second-order perturbation (MRMP2) theory, using the TZVP(fg) basis set. Zero-field splitting parameters are determined using spin-orbit coupling obtained from complete active space (CAS) self-consistent field (SCF) and multiconfigurational quasi-degenerate perturbation theory (MCQDPT) wave functions. Three Breit-Pauli-based spin coupling methods were employed: full Breit-Pauli (HSO2), the partial two-electron method (P2E), and the semiempirical one-electron method (HSO1).

Theoretical Study on Electronic and Spin Structures of [Fe2S2]2+,+ Cluster: Reference Interaction Site Model Self-Consistent Field (RISM-SCF) and Multireference Second-Order Møller−Plesset Perturbation Theory (MRMP) Approach

Electronic structures of [Fe(2)S(2)(SCH(3))(4)](2-,3-) in DMSO solution are calculated using reference interaction site model complete active space self-consistent field (RISM-CASSCF)/multireference second-order Møller-Plesset perturbation theory (MRMP) method. For the reduced state, we obtain both the low-spin Fe(3+)Fe(2+) localized and high-spin Fe(2.5+)Fe(2.5+) delocalized forms, which are very close in energy. The spin interaction constants obtained from the energies of states with various spin multiplicities are in good agreement with the available experimental estimates both for the oxidized and for the reduced states. The dynamic electron correlation effect is found to be important in estimating the spin interaction between the Fe ions. The redox potentials are calculated to be 2.87 and 2.78 eV for the localized and delocalized reduced states, respectively, which are close to the experimental values. We devise a simple model for calculating the free energy curves of the reduction process based on the RISM-SCF theory. The activation barrier height is calculated to be 7.4 kcal/mol at the equilibrium geometry of oxidized state, indicating that the reduction reaction will occur efficiently in DMSO solvent. The effect of solvent fluctuation on the free energy profiles is discussed on the basis of the present calculations.

Prediction of pressure-induced redshift of f1→d(t2g)1 excitations in Cs2NaYCl6:Ce3+ and its connection with bond-length shortening

Quantum chemical calculations including embedding, scalar relativistic, and dynamic electron correlation effects on Cs(2)NaYCl(6):(CeCl(6))(3-) embedded clusters predict (i) redshifts of the f(1)-->d(t(2g))(1) transition with pressure and (ii) bond-length shortening upon f-->d(t(2g)) excitation. Both effects are found to be connected which suggests that new high-pressure spectroscopic experiments could reveal the sign of the bond-length change.

Intramolecular Charge-Transfer State Formation of 4-(N,N-Dimethylamino)benzonitrile in Acetonitrile Solution: RISM-SCF Study

Intramolecular charge-transfer (ICT) state formation of 4-(N,N-dimethylamino)benzonitrile in acetonitrile solution is studied by the reference interaction site model self-consistent field (RISM-SCF) method. Geometry optimizations are performed for each electronic state in solution with the complete-active-space SCF wave functions. Dynamic electron correlation effects are taken into account by using the multiconfigurational quasidegenerate perturbation theory. Two-dimensional free energy surfaces are constructed as the function of the twisting and wagging angles of the dimethylamino group for the ground and locally excited (LE) states. The calculated absorption and fluorescence energies are in good agreement with experiments. The validity of the twisted ICT (TICT) model is confirmed in explaining the dual fluorescence, and the possibility of the planar ICT model is ruled out. To examine the mechanism of the TICT state formation, a "crossing" seam between the LE and charge-transfer (CT) state surfaces is determined. The inversion of two electronic states occurs at a relatively small twisting angle. The effect of solvent reorganization is also examined. It is concluded that the intramolecular twisting coordinate is more important than the solvent fluctuation for the TICT state formation, because the energy difference between the two states is minimally dependent on the solvent configuration.

Electron correlation studies by means of local-scaling transformations and electron-pair density functions

Electron correlation is one long standing problem of computational electronic structure theory. Even more, with the advent of the density functional theory and, in particular, with its Kohn–Sham implementation, the separation of the non-dynamical and dynamical components of the electron correlation has became an unavoidable requirement towards construction of reliable exchange-correlation functionals. In this paper, we address the analysis of the separation of the non-dynamical and dynamical electron correlation effects from two complementary viewpoints, namely, analysis of the correlation energy components and the analysis of the electron-pair density. The former approach will make use of the local-scaling transformations and the latter will be based on the study of intracule and extracule densities.

Local-MP2 electron correlation method for nonconducting crystals

Rigorous methods for the post-HF (HF-Hartree-Fock) determination of correlation corrections for crystalline solids are currently being developed following different strategies. The CRYSTAL program developed in Torino and Daresbury provides accurate HF solutions for periodic systems in a basis set of Gaussian type functions; for insulators, the occupied HF manifold can be represented as an antisymmetrized product of well localized Wannier functions. This makes possible the extension to nonconducting crystals of local correlation linear scaling On techniques as successfully and efficiently implemented in Stuttgart's MOLPRO program. These methods exploit the fact that dynamic electron correlation effects between remote parts of a molecule (manifesting as dispersive interactions in intermolecular perturbation theory) decay as an inverse sixth power of the distance R between these fragments, that is, much more quickly than the Coulomb interactions that are treated already at the HF level. Translational symmetry then permits the crystalline problem to be reduced to one concerning a cluster around the reference zero cell. A periodic local correlation program (CRYSCOR) has been prepared along these lines, limited for the moment to the solution of second-order Moller-Plesset equations. Exploitation of point group symmetry is shown to be more important and useful than in the molecular case. The computational strategy adopted and preliminary results concerning five semiconductors with tetrahedral structure (C, Si, SiC, BN, and BeS) are presented and discussed.

Ab Initio Investigation of the Structures and Properties of Polyaminoborane

We have investigated the structures and the properties of polyaminoborane oligomers by using ab initio computational tools including dynamic electron correlation effects. It turned out that the PBE0/6-31G(2d) method provides a good agreement between experimental and theoretical structures. The key data include geometries, rotational profiles, infrared spectra, vertical excitation energies, atomic charges, and dipole moments. The variations of these properties upon conformation changes are studied. Our results are compared to available experimental measurements.

First Hyperpolarizability of Polyaminoborane and Polyiminoborane Oligomers

The nonlinear optical properties of polyaminoborane, −(NH2−BH2)N−, and polyiminoborane, −(NH−BH)N−, oligomers are studied by using ab initio schemes, taking explicitly into account the dynamic electron correlation effects. We report the evolution with chain length of the geometries, charges, dipole moments, polarizabilities, and first hyperpolarizabilities of both systems. The first hyperpolarizabilities are rationalized in terms of the delocalization/asymmetry interplay.

Multiconfigurational Self-Consistent Field Study of the Excited State Properties of 4-Thiouracil in the Gas Phase

A comprehensive theoretical study of the vertical singlet and triplet electronic transitions of 4-thiouracil was performed at the multiconfigurational self-consistent field (MCSCF) level of theory. The ground state geometry of the molecule was optimized at the MP2/6-311++G(d,p) level. The MCSCF calculations were performed using the 6-311+G(d) basis set. The active space for the MCSCF calculations consisted of 12 orbitals in which 6 orbitals were the occupied π type while the remaining 6 orbitals were the virtual π* type. To compute the nπ* transitions, the two occupied orbitals were replaced with two σ orbitals localized at the thiocarbonyl and carbonyl groups, respectively. Further, MCSCF calculations were also performed with a slightly smaller active space where 10 electrons were distributed in 11 orbitals. The effects of dynamic electron correlation on the MCSCF energies were considered at the second-order multiconfigurational quasi-degenerate perturbation (MCQDPT2) theory. The computed transition energies after the MCQDPT2 correlation were found to be in agreement with the experimental data. The ground and excited state molecular electrostatic potentials and the Mulliken charge distributions in different states were also investigated.

On the bond-stretch isomerism in the benzo[1,2:4,5]dicyclobutadiene system--an ab initio MR-AQCC study.

Bond-stretch isomerism in benzo[1,2:4,5]dicyclobutadienle (BDCB) has been investigated using the MR-AQCC/6-31G(d) method, a high-level multireference ab initio approach including size-extensivity corrections. The applied theoretical approach includes both nondynamical and dynamical electron correlation effects. Full MR-AQCC geometry optimizations of localized (1) and delocalized (3) isomers as well as the transition structure (TS) have been determined using D2h, symmetry restriction. The calculations show that both isomers are approximately of equal stability separated by a barrier with a height of about 5 kcal mol(-1). Thus, the present results strongly indicate that benzof[1,3:4,5]dicyclobutadiene is a very good candidate for an organic compound exhibiting bond-stretch isomerism, since isomers 1 and 3 correspond to true minima on the double-well potential energy surface, which are separated by a sufficiently high barrier. It is particularly important to emphasize that isomer 3 represents a realization of the highly elusive quasi-[10]annulene.

Effects of Chain Substitution on the Structures and Properties of Polyphosphinoborane

The impact of side-group substitution on the three-dimensional structure and on the properties of the homologuous series of polyphosphinoborane oligomers has been investigated by using ab initio computational tools, taking into account dynamic electron correlation effects. This includes the evaluation of the following: geometries, conformations, rotational profiles, infrared spectra, vertical excitations energies, atomic charges, and dipole moments.

Theoretical study of the longitudinal first hyperpolarizability of polysilaacetylene.

With the help of ab initio tools taking into account dynamic electron correlation effects, we study the longitudinal electronic first hyperpolarizability of carbon-silicon analogues to polyacetylene. It turns out that the MP2/6-31G(d)//HF/6-31G(d) scheme is suitable to obtain a semiquantitative accuracy for the first hyperpolarizability of long polysilaacetylene oligomers. The conformation of the chain has a crucial impact on its second-order nonlinear optical properties. We also show that, for some chain lengths, the frequency dispersion effects may have a huge impact, even when far away from resonance. These phenomena are rationalized in terms of delocalization and asymmetry.

An Investigation of the BCP Potential Energy Surface

The singlet and triplet potential energy surfaces (PESs) of boron−carbon−phosphorus (BCP) isomers were investigated, using various theoretical methods. Geometries of the minima and transition states on the PES were optimized at the B3LYP/6-311+G(2df) and CASSCF(12,12)/6-311+G(2df) levels, and single-point calculations were made at the CASPT2/ANO-L level, to consider dynamic electron correlation effects. The most-stable isomer was linear singlet BCP (1Σ+); its calculated heat of formation (ΔfH°, 0 K) is 150.5 ± 2 kcal/mol. Study of the fragmentation processes in BCP revealed that the bond enthalpies of the B−C and C−P bonds in BCP (1Σ+) at 0 K are 111.7 and 128.9 kcal/mol, respectively, at the CASPT2/ANO-L level. A possible crossing mechanism between two electronic states (3A‘ and 3A‘ ‘) is discussed, and Renner−Teller species with 3Π state symmetry are investigated.