Potential energy curve for isomerization of N2H2 and C2H4 using the improved virtual orbital multireference Møller-Plesset perturbation theory

Multireference M?ller-Plesset (MRMP) perturbation theory [K. Hirao, Chem. Phys. Lett. 190, 374 (1992)] is modified to use improved virtual orbitals (IVOs) and is applied to study ground state potential energy curves for isomerization and dissociation of the N2H2 and C2H4 molecules. In contrast to traditional MRMP or multistate multiconfiguration quasidegenerate perturbation theory where the reference functions are obtained from (often difficult to converge) state averaged multiconfiguration self-consistent field methods, our reference functions are represented in terms of computationally efficient IVOs. For convenience in comparisons with other methods, a first order complete active space configuration interaction (CASCI) calculation with the IVOs is followed by the use of the IVOs in MRMP to incorporate residual electron correlation effects. The potential energy curves calculated from the IVO-MRMP method are compared with computations using state-of-the-art coupled cluster singles and doubles (CCSD) methods and variants thereof to assess the efficacy of the IVO-MRMP scheme. The present study clearly demonstrates that unlike the CCSD and its variants, the IVO-MRMP approach provides smooth and reliable ground state potential energy curves for isomerization of these systems. Although the rigorously size-extensive completely renormalized CC theory with noniterative triples corrections (CR-CC(2,3)) likewise provides relatively smooth curves, the CR-CC(2,3) calculations overestimate the cis-trans barrier height for N2H2. The ground state spectroscopic constants predicted by the IVO-CASCI method agree well with experiment and with other highly correlated ab initio methods.     

Ab initio potential energy surface and excited vibrational states for the electronic ground state of Li_2H

A 285-pomt multi-reference configuration-interaction involving single and double excitations ( MRS DCI) potential energy surface for the electronic ground state of L12H is determined by using 6-311G (2df,2pd)basis set.A Simons-Parr-Finlan polynomial expansion is used to fit the discrete surface with a x2 of 4.64×106 The equn librium geometry occurs at Rc=0.172 nm and,LiHL1=94.10°.The dissociation energy for reaction I2H(2A)→L12(1∑g)+H(2S) is 243.910 kJ/mol,and that for reaction L12H(2A')→HL1(1∑) + L1(2S) is 106.445 kl/mol The inversion barrier height is 50.388 kj/mol.The vibrational energy levels are calculated using the discrete variable representation (DVR) method.     

The properties of 4′-N,N-dimethylaminoflavonol in the ground and excited states

The mechanism of protonation of 4-N,N-dimethylaminoflavonol and the structure of its protolytic forms in the ground and excited states were studied by electron absorption and fluorescence (steady-state and time-resolved) spectroscopy and with the use of the RM1 quantum-chemical method. A comparison of equilibrium constants and the theoretical enthalpies of formation showed that excitation should be accompanied by the inversion of the basicity of the electron acceptor groups of this compound and, as a consequence, changes in the structure of its monocationic form. An analysis of the spectral parameters of the protolytic 4-N,N-dimethylaminoflavonol forms, however, showed that their structure and the sequence of protonation in the excited state were the same as in the ground state. Changes in the structure of the monocation in the excited state were not observed because of the fast radiationless deactivation of this form and the occurrence of excited state intramolecular proton transfer in aprotic solvents.     

Accuracy of the three-body fragment molecular orbital method applied to Møller-Plesset perturbation theory

The three‐body energy expansion in the fragment molecular orbital method (FMO) was applied to the 2nd order Møller–Plesset theory (MP2). The accuracy of both the two and three‐body expansions was determined for water clusters, alanine n‐mers (α‐helices and β‐strands) and one synthetic protein, using the 6‐31G* and 6‐311G* basis sets. At the best level of theory (three‐body, two molecules/residues per fragment), the absolute errors in energy relative to ab initio MP2 were at most 1.2 and 5.0 mhartree, for the 6‐31G* and 6‐311G* basis sets, respectively. The relative accuracy was at worst 99.996% and 99.96%, for 6‐31G* and 6‐311G*, respectively. A three‐body approximation was introduced and the optimum threshold value was determined. The protein calculation (6‐31G*) at the production level (FMO2/2) took 3 h on 36 3.2‐GHz Pentium 4 nodes and had the absolute error in the MP2 correlation energy of only 2 kcal/mol. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007     

A CAS SCF CI study of the 1Σ+g and 3IIu states of the C2 molecule and the 4Σ−g and 2IIu states of the C+2 ion

Ab initio calculations of the X ¹Σ⁺_g and a ³II_u states of C₂ and the X⁴Σ⁻_g and a²II_u states of the C⁻₂ molecular ion are performed to determine the corresponding potential curves around the potential minima and at the dissociation limits. A large Gaussian basis set augmented by three d-type polarization functions on each carbon center is used to approximate the molecular orbits. The calculations are done at the complete-active-space SCF and multi-reference configuration interactions level. Spectroscopic constants and rotation—vibration energies are derived from the ab initio calculated potentials. Good agreement between theory and experiment is obtained for the X¹Σ⁺_g and a ³II_u states of C₂. In the earlier tentative assignment of the observed electronic transition around 2490 Å to the ²Σ⁻_g ← ²II_u system in C⁺₂, the lower state is confirmed by the present calculations to be C⁺ ₂ (²II_u).     

Ab initio study of the molecular vibrations and electronic structure of the X,B, D and F2Σ+ states of AlO

Molecular vibrations and electronic structure of the X²Σ⁺, B²Σ⁺, D²Σ⁺, and F²Σ⁺ states of AlO are studied by carrying out ab initio configuration interaction calculations and molecular vibration calculations using accurate potential energy functions. An avoided crossing between the D²Σ⁺ and F²Σ⁺ potential energy curves occurs in the neighborhood of 4.0 a₀ and results in irregular vibrational levels of the D and F²Σ⁺ states. The vibrational constants for the F²Σ⁺ state are predicted from the vibrational levels not involved in the irregularity. Configuration mixing is important in describing the B, D, and F²Σ⁺ states. The F²Σ⁺ state at and around its well minimum and the D and F²Σ⁺ states in the avoided crossing region are characterized in terms of their main configurations and dipole moment functions.     

Second-order Møller-Plesset calculations on the water molecule using Gaussian-type orbital and Gaussian-type geminal theory

The Gaussian-type orbital and Gaussian-type geminal (GGn) model is applied to the water molecule, at the level of second-order M?ller-Plesset (MP2) theory. In GGn theory, correlation factors are attached to all doubly-occupied orbital pairs (GG0), to all doubly-occupied and singly-excited pairs (GG1), or to all orbital pairs (GG2). Optimizing the GG2 model using a weak-orthogonality functional, we obtain the current best estimate of the all-electron MP2 correlation energy of water, -361.95 mE(h). In agreement with previous observations, the GG1 model performs almost as well as the GG2 model (-361.26 mE(h)), whereas the GG0 model is poorer (-351.36 mE(h)). For the barrier to linearity of water, we obtain an MP2 correlation contribution of -463 +/- 5 cm(-1).     

Adiabatic calculations of the 2Σ+g excited states of He+2

The first six ²Σ⁺_g adiabatic potential energy curves of He⁺₂ are calculated with the MRD CI method employing configuration selection (T = 10 μ hartree) and perturbative energy corrections and using two basis sets differing in the number of diffuse functions. The non-adiabatic matrix elements at the numerous avoided crossings are also calculated and approximate diabatic curves are constructed. Various aspects of the results are discussed.     

Flickering dipoles in the gas phase: structures, internal dynamics, and dipole moments of β-naphthol-H2O in its ground and excited electronic states

Described here are the rotationally resolved S(1)-S(0) electronic spectra of the acid-base complex cis-β-naphthol-H(2)O in the gas phase, both in the presence and absence of an applied electric field. The data show that the complex has a trans-linear O-H???O hydrogen bond configuration involving the -OH group of cis-β-naphthol and the oxygen lone pairs of the attached water molecule in both electronic states. The measured permanent electric dipole moments of the complex are 4.00 and 4.66 D in the S(0) and S(1) states, respectively. These reveal a small amount of photoinduced charge transfer between solute and solvent, as supported by density functional theory calculations and an energy decomposition analysis. The water molecule also was found to tunnel through a barrier to internal motion nearly equal in energy to kT at room temperature. The resulting large angular jumps in solvent orientation produce "flickering dipoles" that are recognized as being important to the dynamics of bulk water.     

The Curl–Divergence equations for the electronic non-adiabatic coupling terms: study of the C2H molecule and the H2+H system

This Letter is part of an effort to use the Curl equations to calculate non-adiabatic coupling terms, subject to ab initio boundary conditions. As examples we consider two-state, planar, systems characterized by two coordinates, θ and q and treat the corresponding non-adiabatic coupling terms, namely, τ_θ(q,θ) and τ_q(q,θ). The theory, which yields τ_q(q,θ) once τ_θ(q,θ) is given, is applied to three cases: an analytical model and two ab initio treatments – one for the C₂H molecule and one for the H+H₂ molecular system. In all three cases encouraging agreements were obtained between the theoretical τ_q(q,θ) values and the ab initio ones.     

Consistent generalization of the Møller-Plesset partitioning to open-shell and multiconfigurational SCF reference states in many-body perturbation theory

The Møller-Plesset partitioning of the many-electron Hamiltonian is generalized for arbitrary open-shell and multiconfigurational SCF reference states. The method has been initially implemented at the second and third orders for two-configuration generalized valence bond reference wavefunctions in which only two electrons are correlated. Potential curves for the hydrogen molecule, lithium hydride and the helium dication agree excellently with full CI results.     

MRD CI calculations of excited states of the SiH3 radical,including potential curves for the inversion mode and the dissociation SiH3 → SiH2 + H

Using the MRD CI method and large basis sets the vertical spectrum of silyl radical (SiH₃) has been calculated. The lowest excited state is the 4s Rydberg state, 41000 cm⁻¹ (5.2 eV) above the ground state. Only one excited valence state (2²E) was encountered, all other states are of Rydberg type. From potential curves for the inversion mode (symmetric bending motion) it was inferred that all Rydberg states are planar, whereas the valence excited state is highly pyramidalized. The investigation of the dissociation reaction SiH₃ → SiH₂ + H leads to the conclusion that the first excited state is dissociative.     

Ab initio second-order Møller-Plesset calculation of the vibrational spectra of C4 clusters

Second-order Møller-Plesset calculations on the C₄ potential surface yielded three isomers, a linear triplet and rhombic and tetrahedral singlets. A large discrepancy between observed and calculated frequencies of the Σ_u⁺ vibration of linear ¹²C₄ is outside the expected range of error. It is tentatively suggested that an observed absorption at 1544 cm⁻¹ previously assigned to C₅ might belong instead to C₄.     

The acid—base equilibria of dimethylphenols in the ground and the first excited singlet states

Measurements of the acidity constants in the ground (pK_a(S₀)) and the lowest excited singlet (pK_a(S₁)) states for 2,3-, 2,4-, 2,5-, 2,6-, 3,4- and 3,5-dimethylphenols in aqueous solution have been carried out spectrophotometrically at 25°C. The pK_a values in S₀ have been derived from the absorption spectra and the pK_a values in S₁ were estimated by means of the Forster cycle. It is found that the hydroxy group is more acidic in the first excited singlet than in the ground state.     

Theoretical study of the excited states and the redox potentials of unusually distorted ��-trifluoromethylporphycene

Quantum chemical calculations were performed to analyze the excited states and the redox potentials of a recently synthesised fluorine-containing porphycene, 2,7,12,17-tetraethyl-3,6,13,16-tetrakis(trifluoromethyl) porphycene. The reduction and oxidation potentials of the porphycenes measured by cyclic voltammetry were semiquantitatively reproduced using density-functional theory (DFT) and polarizable continuum model calculations, in which solvent effect and basis-sets extension effect were indispensable. Symmetry-adapted cluster configuration interaction and time-dependent (TD) DFT calculations were performed to analyze the visible region of the absorption spectra, and the results were in good agreement with the experimental data. The results of the calculations showed that both structural distortion and electronic effects cause specifically large stabilization of the LUMO level and become the origin of the particularly large positive-side shift of the reduction potential and the red-shift in the Q band absorption.     

Resolution of the identity atomic orbital Laplace transformed second order Møller-Plesset theory for nonconducting periodic systems

An improvement in performance of the atomic orbital Laplace transformed second-order M?ller-Plesset (AO-LT-MP2) method for periodic systems is reported using the resolution of identity (RI) technique. Transformation of the two-electron integrals constitutes the main computational bottleneck of the AO-LT-MP2 method. A substitution of regular four-center integrals by their three center counterparts in the RI approximation naturally reduces the computational cost of the integral transformation step. The RI divergence problem in the presence of periodic boundary conditions is solved in our implementation by restricting the fitting domain. Accuracy and computational efficiency of the RI-AO-LT-MP2 approach are assessed on a set of one-dimensional test systems: trans-polyacetylene and anti-transoid polymethineimine.     

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 M?ller-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.     

Comparison of the Hartree-Fock,Møller-Plesset,and Hartree-Fock-Slater method with respect to electrostatic properties of small molecules

Summary The results of various quantum chemical calculations, the Hartree-Fock (HF) method, the Møller-Plesset perturbation theory (MP2), and the Hartree-Fock-Slater (HFS) method are compared. Atomic charges, dipole moments, topological properties of the electron density distribution and polarizabilities, and first hyperpolarizabilities are calculated. Atomic charges obtained with the HFS method are found to be very close to those calculated with the MP2 method, from which we conclude that the HFS method describes to some extent electron correlation effects. Performing an MP2 calculation after an HF calculation improves the molecular dipole moments considerably, yielding values close to the experimental ones. HFS calculations are computationally less demanding than MP2 and yield comparable results for the electron density distributions, dipole moments and polarizabilities.     

Vibronic coupling in the A2Π and B2Σ+ electronic states of the NCS radical

The spin-rovibronic energy levels of the A(2)Π and B(2)Σ(+) electronic states of thiocyanate radical have been calculated variationally, using high-level ab initio coupled diabatic potential energy surfaces. Computations up to J = 7∕2 have been performed, obtaining all levels with K ≤ 3 (Σ(1/2),Π(1/2,3/2),Δ(3/2,5/2),Φ(5/2,7/2)), for energies up to 2000 cm(-1) above the A(000)(2)Π(3∕2) level. The available experimental data have been critically reviewed in the light of the theoretical findings.