MCSCF/MCLR Studies of potential energy surfaces,spectra, and properties of the X1A1 and a3B2 states of ozone

Potential energy surfaces, properties, and spectra of singlet (X¹A₁) and triplet (a³B₂) ozone are investigated by means of MCSCF /MCLR analytical response theory calculations. MCSCF analytical gradients and Hessians are used to locate equilibrium and transition-state structures and to obtain associated vibrational and rotational constants, infrared intensities, and dipole moments. By means of MC linear response functions, electronic excitation energies, and oscillator strengths, static and dynamic polarizabilities as well as dispersion (C₆) coefficients are obtained. Good agreement is achieved, in some cases within experimental error margins, for properties where experimental data are known. A very low IR intensity for triplet ozone is predicted.     

Convergence of the Rayleigh—Ritz method in self-consistent-field and multiconfiguration self-consistent-field calculations

We investigate the analytical convergence of SCF and MCSCF calculations, when the dimension of the subspaces to which the orbitals are restricted tends to infinity. We show that the completeness only inL ²(R ³;C ²) of the orbital bases does not ensure the convergence of the Ritz-energy, neither in SCF nor in MCSCF calculations, but that this convergence — as well as the convergence of the Ritz-orbitals in SCF calculations — is on the contrary guaranteed if the orbital bases are complete in the Sobolev spaceW ^1,2(R ³;C ²). Some consequences on the choice of the orbital exponents of Slater and Gauss functions are also discussed.     

Spectroscopic and structural features of small thiocarbonyl molecules in low-lying excited states: Further applications of a variant of the orthogonal gradient method

Structural parameters of a set of five thiocarbonyl molecules in the lowest nπ* states are calculated by using a generalized orbital optimization algorithm (a variant of the orthogonal gradient method) in an INDO MCSCF framework. Transition energies, singlet-triplet splittings, planar inversion barriers, and dipole moments in nπ* states of different spin multiplicities are reported. Predicted structural features agree reasonably well with available experimental or theoretical data. Some interesting trends are noted in the computed inversion barrier heights, singlet-triplet splittings, and dipole moments in nπ* states.     

Electronic rearrangements during chemical reactions. II. Planar dissociation of ethylene

The direct dissociation of ethylene into two methylenes is studied along the least motion reaction path by means of an ab initio multiconfiguration self-consistent-field (MCSCF ) calculation. All eight configurations arising from those valence orbitals that form the CC bonds, seven of them singlet coupled and one triplet coupled, are taken into account. The HCH bond angle is optimized along the entire reaction path. Separate MCSCF optimizations are carried through for the lowest two states of ¹A_g symmetry. The (¹A_gσ²π²) ethylene ground state dissociates into two (³B₁σπ) ground-state methylenes. The (¹A_gσ²π*²) excited state of ethylene dissociates into two (¹A₁σ²) excited methylenes. It is established that both these dissociations proceed without any barrier in the energy curve. In the ground state, where orbital symmetry is conserved, the π-bond breaks before the σ-bond, and the calculated heat of reaction agrees within 6 kcal/mol with the experimental value. In the excited state, where orbital symmetry is not conserved, the nonbonded repulsion between methylene σ₂ lone pairs is found to blend into the antibonding character of the excited ethylene, yielding an energy curve that is everywhere repulsive. However, the variation of the HCH angle during the dissociation process is not simple, initially it expands and subsequently it contracts. Quantitative analytical approaches are developed which furnish conceptual interpretations of the orbital changes and configurational changes along the reaction path.     

Macroscopic solvation of molecules in excited states: An MCSCF model including solvent polarization effects-I

An MCSCF model including the effects of solvent polarization is developed. The model is applied within the limitations of INDO approximations to look into the dominant effects of solvent polarization on the electronic structure in the excited states of a model system (e.g.nπ ^* states of H₂CO). Important features of macroscopic solvation-induced reorganization of electron density and some consequence thereof are noted.     

O + C<Subscript>2</Subscript>H<Subscript>4</Subscript> potential energy surface: excited states and biradicals at the multireference level

The focus of this study is to understand the multiconfigurational nature of the biradical species involved in the early reaction paths of the oxygen plus ethylene PES. In previous work (J Phys Chem A 113, 12663, 2009), the lowest-lying O(³P) + C₂H₄ PES was extensively explored at the MCSCF, MRMP2, and MR-AQCC levels of theory. In the current work, ground and excited, triplet- and singlet-state reaction paths for the initial addition of oxygen to ethylene were found at the MCSCF and MRMP2 levels along with five singlet pathways near the ^·CH₂CH₂O^· biradical at the MCSCF, MRMP2, and CR-CC(2,3) levels. One of these five paths can lead to the CH₂CO + H₂ products from CH₃CHO rather than from the ^·CH₂CH₂O^· biradical, and this pathway was investigated with a variety of CAS sizes. To provide further comparison between the MRMP2 and CR-CC(2,3) levels, MR-AQCC single-point energies and optimizations were performed for select geometries. After the initial exploration of this region of the surface, the lowest singlet–triplet surface crossings were explicitly determined at the MCSCF level. Additional MRMP2 calculations were performed to demonstrate the limitations of single-state perturbation theory in this biradical region of the PES, and SO-MCQDPT2 single-point energies using SA MCSCF were calculated on a grid of geometries around the primary surface crossing. In particular, these calculations were examined to determine a proper active space and a physically reasonable number of electronic states. The results of this examination show that at least four states must be considered to represent this very complex region of the PES.     

Full configuration interaction benchmark calculations for transition moments

Full configuration-interaction (FCI) calculations have been performed for the ã ¹A₁–b¹B₁and ã ¹A₁–(2)¹A₁transitions in CH₂ and for selected dipole and quadrupole transitions in BeO. The FCI transition moments are compared to those obtained from correlation treatments that truncate the n-particle expansion. The state-averaged MCSCF/SOCI and FCI results agree well, even for BeO, where the CASSCF level nonorthogonal transition moment differs from the state-averaged CASSCF transition moment.     

An efficient first-order CASSCF method based on the renormalized Fock-operator technique

Summary A new efficient first-order CASSCF method (multiconfiguration SCF (self consistent field) in a complete active space) is described. Its main characteristics are (i) use of the generalized Brillouin theorem (Fock-operator method), (ii) renormalization of single excitations, (iii) fast microiterations containing only two-index transformations, i.e. M ³N² steps. Convergence is generally reached in eight to twelve macroiterations. The method is applied to several examples (LiH, N₂, AlO) and compared to other MCSCF (multiconfiguration SCF) methods.     

Excitation energies,oscillator strengths,and frequency dependent polarizabilities of Be: Comparison of TDHF,EOM (second order), and MCTDHF

Low-lying excitation energies from the ground state of Be were calculated using a basis set of 61 Cartesian Gaussian functions. Three approximations were employed: the time-dependent Hartree–Fock (TDHF ), second-order equations-of-motion (EOM ), and multiconfigurational time-dependent Hartree–Fock (MCTDHF ). The TDHF excitation energies are 0.5–1.1 eV lower than experiment, and the EOM values are 0.3–1.2 eV lower than experiment, whereas the MCTDHF excitation energies deviate on the absolute average from experiment by only 0.03 eV. We found that in an MCTDHF calculation, any proper MCSCF stationary point is a good reference (i.e., initial) state, not just the ground state. Experimental values for oscillator strength are accurately known only for the 2s²X¹S → 2s2p¹P⁰ transition. The TDHF value and the MCTDHF value agree with experiment, but the EOM value does not. The agreement of the TDHF value with experiment seems to be coincidental, because for higher lying transitions the TDHF values differ by approximately a factor of two or more from the more accurate MCTDHF . Frequency independent polarizabilities, α(0), were also calculated with the TDHF , HRPA , and MCTDHF and frequency dependent polarizabilities, β(ω), were calculated with the MCTDHF . No experimental data for Be polarizabilities exist, but we expect the MCTDHF values to be among the most accurate calculations available.     

Adiabatic Potential Energy Surface of the 1,2,3-Trifluorobenzene Cation-Radical

Ab initio study of the adiabatic potential energy surface (PES) for 1,2,3-trifluorobenzene cation-radical was carried out by the ROHF, UHF, MCSCF, MP2, and DFT (B3LYP) methods with the 6-31G* basis set. The PES in question is a pseudorotation surface at all calculation levels. The pseudorotation barrier height does not exceed 3.2 kcal/mol, suggesting a possibility for its manifestations in experimental EPR spectra.     

Rotational barrier in phosphatriafulvene: An MCSCF study

As probed by ab initio calculations at SCF and MCSCF levels, the rotational barrier of the PC double bond in the title compound is similar in magnitude to the corresponding one in methylenephosphane. The transition state for rotation is dipolaric in nature. On this basis, a combination of electron releasing and electron accepting substituents reduces the magnitude of the rotational barrier in phosphatriafulvene. It is supported by experimental investigations. © 1993 John Wiley & Sons, Inc.     

On the lowest electronic states of the C2F radical

The adiabatic energy surfaces of the lowest three electronic states [²(²A′ and ²A′)] and ²Σ⁺[²A′] of the C₂F radical were investigated by the Hartree-Fock multiconfiguration self-consistent field (HF—MCSCF) ab initio method using a large set of atomic natural orbitals (ANO) and an extended configuration space, and the results were shown to be in agreement with the predictions of valence theory for this radical. The electronic ground state was found to have a bent equilibrium structure, hence contradicting the Walsh rule which predicts for the isoelectronic molecules a ² linear state. The three states were found to be nearly degenerate and the potential energy surfaces of the two lowest electronic states exhibit an avoided crossing at an energy ∼2000 cm⁻¹ above the ground-state minimum, lower than the highest vibrational fundamental. The strong adiabatic interaction which is responsible for the ordering of the electronic states and their equilibrium geometry involves not only the bending coordinate as normally found for Renner-Teller pairs of states, but also the C—C stretching coordinate, due to the near degeneracy of the ²Σ⁺ and the ² lowest electronic states at linear geometries. © 1996 John Wiley & Sons, Inc.     

Electric dipole polarity of diatomic molecules

The restricted SCF (single-configuration SCF) and MCSCF (multiconfiguration SCF) calculations are performed to compute the ground-state electric dipole moments of four pairs of diatomic molecules—(1) CO and BF; (2) SiO and AlF; (3) CS and BCl; and (4) SiS and AlCl—at a number of internuclear distances on both sides of the equilibrium position. Near Hartree–Fock accuracy is obtained in the SCF calculations. All eight molecules have a range of internuclear distance in which electric dipole moments are of the polarity of A^?B⁺. The shapes of computed electric dipole moment functions are discussed in the language of the molecular orbital method and in relationship to electronegativities of atoms. The present study gives us deeper understanding of electron transfer inside molecules and consequently of the apparent contradiction between electronegativity and the dipole polarity of some molecules. © John Wiley & Sons, Inc.     

Second- and higher-order convergence in linear and nonlinear multiconfigurational Hartree–Fock theory

We discuss how the local convergence of Newton–Raphson and fixed Hessian MCSCF iterative models may be rationalized in terms of a total order of convergence in an error vector and a corresponding error term. We demonstrate that a sequence of N Newton–Raphson iterations has a total order of convergence of 2^N and that a sequence of N fixed Hessian iterations has a total order of convergence of N + 1. We derive the error terms of a Newton–Raphson and a fixed Hessian sequence of iterations. We discuss the implementation of the fixed Hessian and the Newton–Raphson approaches both when linear and nonlinear transformations of the variables are carried out. Sample calculations show that insight into the structure of the local convergence of Newton–Raphson and fixed Hessian models can be based on an order of convergence and an error term analysis.     

Transition-state structures for the reaction between styrene and tbutyl cyanoketene: Theoretical evidence for antarafacial characteristics in a π2 + π2 thermal cycloaddition

Semiempirical AM 1 SCF ? MO models for the cycloaddition between monosubstituted alkenes (RCH = CH₂, R = Me, Ph, CF₃) and ^tbutyl cyanoketene predict the lowest-energy transition state to be relatively polar and asynchronous in character and to have a cis relationship between the R and the ^tbutyl groups, in agreement with the experimentally determined product for R = Ph. We interpret this stereochemistry as resulting from the presence of a significant antarafacial component in the transition state, which enables these two bulky groups to adopt pseudoequatorial positions in which steric interactions are minimized. The alternative higher energy trans geometry forces the R and the cyano groups to adopt more sterically hindered pseudoaxial positions. Alternative biradical-like transition states inferred by others from ab initio MCSCF calculations on the reaction between ketene and ethene do not retain any significant antarafacial component on the ketene and, therefore, form less satisfactory models for this specific reaction. © 1992 John Wiley & Sons, Inc.     

When is H3 stable to asymmetric distortion?

The theory of the second-order Jahn-Teller effect is used to show that for sufficiently short bond lengths H₃ should be stable to asymmetric distortion. This prediction has been confirmed by ab initio MCSCF calculations.     

Fe(CO)4 flexible as a two‐level system avoided conical intersection

This article reports new square‐planar Fe(CO)₄ D_4h structures that are optimized, using the Hartree–Fock (HF) approach, and multiconfiguration self‐consistent field (MCSCF) theory in active space [2b_2g2e_ga_1ga_2u]⁸, and which energy increased in sequence: ³B_2g TS < ¹A_1g TS < ¹A_1g GS. A triple ζ valence basis set supplemented with 4f for Fe and 3d for C and O polarization shells [TZV (DF)] was used. At the HF/TZV (DF) level, ¹A_1g TS and ³B_2g TS (³B_2g TS energetically more favorable), there are transition states of tetrahedral inversion (defining stereochemical flexibility of Fe(CO)₄) between known equivalent ¹A₁ and ³B₂ Jahn–Teller distorted tetrahedron C_2v structures with activation energy at ～0.96 kcal/mol according to the experimental data. ¹A_1g TS differs from ¹A_1g GS in electronic configuration by occupation of a_1g and a_2u MOs. At the MCSCF/ TZV (DF) level, ¹A_1g TS and ¹A_1g GS are optimized as near‐pure states in different potential energy surfaces (PES) avoided conical intersection with near‐equal interatomic distances, and define electronic flexibility of Fe(CO)₄. Estimation of the energy separation in a two‐level system that avoids a conical intersection from vibrational spectrum is based on the effective Hamiltonian of the perturbation theory. The energy gap between two square‐planar Fe(CO)₄ D_4h ¹A_1g TS < ¹A_1g GS is 0.27 kcal/mol. The energy gap between ¹A_1g GS and ¹A₁ is 1.28 kcal/mol. It is possible to observe ³B₂, ¹A₁ and ¹A_1g GS separately in the course of the experiment. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Electronic structure and vertical excitation spectrum of methylene amidogen CH2N

Ab initio electronic structure calculations are reported for five electronic states of the methylene amidogen radical. Structure parameters for the ground electronic state are predicted by RHF and D -MBPT (4) calculations. Vertical excitation energies were determined using four different theoretical chemical models: complete active space (CAS ) MCSCF , CAS /MCSCF plus singles and doubles Cl, fourth-order many-body perturbation theory SDQ -MBPT (4), and coupled-cluster theory.     

On the SCF calculation of excited states: Singlet states in the two-electron problem

The problem of determining SCF wave functions for excited electronic states is examined for singlet states of two-electron systems using a Lowdin natural orbital transformation of the full CI wave function. This analysis facilitates the comparison of various SCF methods with one another. The distribution of the full CI states among the natural orbital MCSCF states is obtained for the S states of helium using a modest Gaussian basis set. For SCF methods that are not equivalent to the full CI wave functions, it is shown that the Hartree-Fock plus all single excitation wave functions are equivalent to that of Hartree-Fock plus one single excitation. It is further shown that these wave functions are equivalent to the perfect pair or TCSCF wave functions in which the CI expansion coefficients are restricted to have opposite signs. The case of the natural orbital MCSCF wave function for two orbitals is examined in greater detail. It is shown that the first excited state must always be found on the lower natural orbital MCSCF CI root, thus precluding the use of the Hylleras-Undeim-MacDonald (HUM) theorem in locating this state. It is finally demonstrated that the solution obtained by applying the HUM theorem (minimizing the upper MCSCF CI root with respect to orbital mixing parameters) is an artifact of the MCSCF method and does not correspond to any of the full CI states.