MCSCF Method Research Articles

The Miracle of Vitamin B12 Biochemistry

For decades, the comparison of experimental data with theoretical results in studying the biochemistry of vitamin B12 has been very confusing. While the methylcobalamin cofactor-dependent Methionine Synthase process can undergo unlimited turnovers, and some of the adenosylcobalamin-dependent processes run with close-to-unity equilibrium constants (e.g., with close-to-zero energy barriers), the DFT and QM/MM based on density functional theory, the most used and appreciated methods for calculating the electronic structure of molecules, have been showing a much shorter than experimental-determined Co-N distances in the vitamin B12 cofactors of Co+2 and the inadequate large energetic barriers of their enzymology bioprocesses. The confusion was even larger since some in vitro experimental data showed large barriers to the vitamin B12 cofactor reactions (which in fact play a destructive role in the Methionine Synthase process and which barriers were caused mostly by the influence of the solvents in which the reaction took place). It reached the point where solid contributions to the study of the biochemical processes of vitamin B12 were almost officially questioning the correctness of the experimental determination of the Co-N chemical bond distances in the cobalt(II) cofactors of vitamin B12. Unexpectedly, all the theoretical biochemistry of the vitamin B12 cofactors began to agree with all in vivo experimental data only when they were treated with the MCSCF method, the method that considers the orbital mixing, or in other words, the Pseudo-Jahn–Teller Effect. MCSCF data establish unknown mechanistic details of the methyl radical and hydrogen transfers, the origin of the electronic transfers between bioreagents, and the nature and the relationship between the bioreactions. The Pseudo-Jahn–Teller Effect, e.g., orbital mixing, governs vitamin B12 chemistry in general and provides insight into particular details of vitamin B12-dependent reactions in the human body. It turns out that the DFT or QM/MM based on DFT method theoretical data are incongruent with the experimental data due to their limitations, e.g., the unaccounted-for effects of orbital mixing.

The Determination of the Vitamin B12 Bioprocesses Preliminary Step Mechanism by the Mcscf Method

The Determination of the Vitamin B12 Bioprocesses Preliminary Step Mechanism by the Mcscf Method

The complete electronic structure and mechanism of the methionine synthase process as determined by the MCSCF method

The methionine synthase process is regenerating the methionine from cysteine in the S-adenosylmethionine cycle running throughout several interactions and electron transfers between methylcobalamin cofactor and substrates. The methionine synthase process in connection with the methionine synthase reductase process can run, in principle, unlimited number of turnovers without side products or effects. This raises questions about the energy barriers of the methionine synthase process reactions. The CASSCF geometry optimization with 13 electrons and 13 orbitals in the active zone of the methylco(II)balamin cofactor species was used to calculate the full mechanism of the methionine synthase process. We have shown that the anticipated reaction of the methionine synthase process is the cleavage of the Co-N (dimethylbenzimidazole) axial bond under the influence of the homocysteine ion and the histidine substrates. Our results also show that the active species in the methylation of homocysteine is a base-on methylco(II)balamin cofactor with the dimethylbenzimidazole ligand substituted by the histidine trans ligand. This methylation process takes place during the methylco(II)balamin cofactor interaction with the homocysteine negative ion, proving that this reaction is of SN2. We have shown that the triggering factor of this process is the initial electron transfer from a homocysteine negative ion to a base-on methylco(II)balamin-histidine cofactor particle. Another step of the methionine synthase process is the N-C(CH3) bond cleavage in the protonated 5-methyltetrahydrofolate systems under the influence of the negative total (and the atomic charges of the central part) of the co(I)balamin cofactor. Simultaneously, the cleaved methyl (+1) positive particle is leaving an electron back to tetrahydrofolate. The no energy barrier and the minimum energy of the in-vivo reaction products have been proved for all the methionine synthase process reactions. Finally, the full mechanism of the methionine synthase process has been drawn.

The Electronic Structure and Mechanism of the Adenosylcobalamin-Dependent Bio-Processes as Determined by the MCSCF Method

The CASSCF geometry optimization of the adenosylcobalamin cofactor dependent processes common models with 12 orbitals and 12 electrons in the active space has been performed. The MCSCF geometry optimization shows a strong HOMO-LUMO coupling during the CASSCF orbitals mixing process. The HOMO-LUMO coupling causes an electronic density transfer from the HOMO, which at the beginning of the optimization process is constituted from the substrate atoms orbitals, to the LUMO, which is constituted from the adenosylco(III)balamin structure atomic orbitals. The Co-C bond cleavage reaction is starting from the beginning of the geometry optimization process due to the intermolecular transferred electronic density from the substrates to the adenosylco(III)balamin cofactor compound. Then, the HOMO and LUMO of the calculated models are converting into a bonding and an antibonding pair of orbitals with a central atom plus σ-axial ligands orbitals contribution and with a corrin ring plus axial ligands orbitals contribution, respectively. The HOMO-LUMO mixing process in the CASSCF procedure causes the intermolecular charge transfer process that converts into intramolecular charge transfer process, which is increasing up to about 1e- at the Co-C bond cleavage distance. The substrates of the adenosylcobalamin cofactor dependent bio-processes from one side and the 5'- deoxy-5’-adenosyl radical from another side are permanently growing their direct interactions along with the Co-C bond rupture process up to a strong direct interaction at the Co-C bond cleavage distance. Evidently, this is allowing for a hydrogen atom transfer between them. Altogether, the total energy barrier of the hydrogen transfer reaction from the substrate to the 5'- deoxy-5’-adenosyl radical reaction, the CASSCF HOMO and LUMO surface orbitals of the substrate and 5'-adenosyl radical interaction common model before and after the hydrogen transfer and a strong Pseudo-Jahn-Teller effect for only direct reaction demonstrate that the hydrogen transfer is an irreversible tunneling process, which certainly leads to the final products. All these results are pointing out to the Co-C bond cleavage and hydrogen transfer from substrate to 5'- deoxy-5’-adenosyl ligand concerted reactions in full agreement with the experimental data.

Insight into spin-orbital interaction using MCSCF method: A special analysis of the 1 Σg + electronic state in C2 and the linear polyacetylenic C4 and C6.

The symmetry-broken wave function can transform the 1 Σg + state of C2 from the classic double bonding to the quadruple bonding, where the transformed wave functions of ϕ L and ϕ R are singly occupied by two opposite-spinning electrons. In this article, the effective bond order (EBO) contribution of the fourth bond in C2 is assessed through the overlap integral between ϕ L and ϕ R , namely the value (0.60) is the EBO contribution of the fourth bond in the transformed scheme. Hence, the new EBO is 3.36, which is more equitable than the original EBO (2.15) in the traditional scheme. In addition, the singlet diradical character of the linear polyacetylenic C4 and C6 in the 1 Σg + state is addressed for the first time. No spin-polarized bonding exists in other linear C2n clusters, because the ionic interaction in the polyacetylenic 1 Σg + state of C4 is negligible. Moreover, the coupling energy between α and β single electrons in C4 is only 4.0 kcal mol-1 based on the electron spin-flip energy. © 2019 Wiley Periodicals, Inc.

PPP Hamiltonian for polar polycyclic aromatic hydrocarbons

Total energies of charged states and configurations of different spin multiplicity of two polar non-alternant polycyclic aromatic hdrocarbons (PAH), namely, pentaheptafulvalene and azulene, calculated by means of a Multi-Configurational (MCSCF) method which includes correlation only amongst π orbitals, have been fitted by exact solutions of the Pariser-Parr-Pople (PPP) and the Hubbard Hamiltonians for π electrons. As both molecules are planar, such an approach is in principle feasible. As found in our previous analysis of PAH, PPP fittings are significantly better than those attained with the Hubbard Hamiltonian. In addition, parameters for the Hubbard Hamiltonian are around twice those derived for the PPP model, indicating that parameters are not model independent. Fitted PPP parameters are close to those derived from a similar study of the PAH 2, 5, 8-trihydrogenated phenalene and those originally proposed by Pariser et al. providing further support to a wide applicability of the fitted parameters. Fittings obtained for a MCSCF method that MM298001also includes σσ and σπ correlations (MCSCF/MP2) are slightly less accurate giving an on-site repulsion 10–15% smaller. The accuracy of the fittings further diminishes when parameters are derived from energies obtained by means of a DFT method (B3LYP) with an additional decrease in U of 5–25%. In the latter two cases, parameters have to be considered as effective, accounting for effects of σ orbitals not explicitly included in the model Hamiltonians. Electron affinities, ionization energies and dipole moments, calculated by means of the model Hamiltonians, are compared to those derived from DFT and ab initio methods and, whenever available, to experimental data.

Configuration selection in the MCSCF method. I. Application to the B1∑+ state of HF

Due to the relatively small number of configurations used in MC wavefunctions, proper selection of configurations is essential. Systematic selection methods, allowing for the anticipated changes in orbital characteristics, are developed for an excited state system, the B1∑+ state of HF. Configurations qualifying for inclusion into the MC wavefunction must have either a large coefficient in CI trial functions, or a large energy lowering relative to a few reference configurations. The MCSCF results for the B1∑+ state of HF compare well with CI results obtained here and obtained previously by other authors.

Direct restricted-step MCSCF calculations on the structure and spectrum of cyclobutadiene

The structure of cyclobutadiene in the ground 1A9 state and the lowest excited 3B1g, 1A1g, and 1B1g, states are investigated by means of a direct, step-restricted, second order MCSCF method. The barrier height for interconversion between the rectangular forms of the ground state minima is predicted to be 6.2kcal/mol and the singlet-triplet state separation at the ground state square confirmation is predicted to be 9.7 kcal/mol. All investigated excited states are fond to have square equilibrium geometry the and adiabatic transition energy to the 1A1g, state is predicted to be lower than that to the 1B1g, state.

An improved MCSCF method

An improved scheme for calculating multiconfiguration self-consistent field wavefunctions has been developed. This scheme is powerful in its algebraic formulation and quadratic in its convergence behavior. Shell and wavefunction replacement operators are introduced to make equation manipulation more transparent and less tedious. The configuration state function coefficients as well as the orbital expansion coefficients are improved in each iteration by exponential unitary transformations. The symmetry properties of the wavefunctions are fully exploited. The present scheme should be convergent for a wider range of applications than currently available schemes.

Spectroscopic properties of dipicolinic acid and its dianion

If robust spectroscopic techniques are to be developed for the detection and identification of pathogens, one must understand the relevant spectroscopic properties of the target molecules. In this paper, we employ density functional theory (DFT) to study the structural, electronic, vibrational, optical, and magnetic properties of dipicolinic acid (DPA) and its dianion DPA −2. Our full geometrical optimization and Mulliken charge analysis show that DFT does not lead to the significant discrepancies between charges on symmetric carbon, hydrogen, and oxygen atoms that are found in less accurate calculations based on the complete active space MCSCF method. Our calculated vibrational frequencies, Raman spectra, and infrared spectra for ground-state DPA and DPA −2 are in good agreement with experiment, and this is also true of the four calculated 13C NMR spectral lines (for α, β, γ, and carboxyl sites). Our time-dependent DFT study of the optical excitation and absorption of both DPA and DPA −2 provides the first interpretation of the observed near ultraviolet absorption and fluorescence spectra. Finally, we discuss for the first time the effect of a solvent on the spectral properties of DPA.

Isomerizations of Bicyclo[2.1.0]pent-2-ene and Tricyclo[2.1.0.02,5]pentane into Cyclopenta-1,3-diene: A Computational Study by DFT and High-Level ab Initio Methods

The thermal isomerizations of bicyclopentene (bcp) and tricyclopentane (tcp) into cyclopentadiene (cp) are investigated by a combination of DFT, CASSCF, CASSCF-MP2, and CR-CCSD(T) methods. Coupled-clusters and B3LYP methods predicted the reaction enthalpies excellently whereas the MCSCF method worked well only when dynamic correlation energy was taken into account. Both processes are concerted, and the reaction paths pass through transition states with high biradical character. Measures of biradical character in DFT and ab initio methods are discussed. The activation enthalpy in the rearrangement of bcp into cp was predicted by the CR-CCSD(T) method to be 25.5 kcal/mol, in good agreement with experiment. The UB3LYP functional also performed well in this case despite the high spin contamination that was present in the singlet biradicaloid transition state. The reaction enthalpy for the conversion of tcp into cp was predicted to be −63.7 kcal/mol. The transition state involved in the isomerization of tcp wa...

Combining two-body density functionals with multiconfigurational wavefunctions: diatomic molecules

The MCSCF method provides a correct zero-order wavefunction for all regions of molecular potential energy surfaces. To obtain quantitative accuracy a proper treatment of the dynamic correlation problem must be implemented. Traditionally this has been achieved through multireference variants of perturbation theory, configuration interaction and coupled cluster theory. The computational cost of such techniques makes them prohibitive for all but the smallest molecular problems. Reported here is an investigation into the efficacy of two-body density functionals in providing the dynamic correlation energy for MCSCF reference states. Tests were made on the two-body density functionals of Colle and Salvetti (CS), Moscardó and San-Fabán (MSF), and Moscardó and Pérez-Jiménez (MPJS) in predicting the equilibrium bond lengths, harmonic frequencies and dissociation eneries of fifteen diatomic molecules (3B2, 3BN, 2BS, 1C2, 2CN, 1CO, 1F2, 1FC1, 1N2, 3NCl, 3O2, 1PN, 3Si2, 1SiO, 3SO) using full valence-shell CASSCF reference wavefunctions. Also studied were modifications of these functionals recently suggested by Miehlich, Stoll and Savin (MSS) and Gráfenstein and Cremer (GC). The results obtained show accuracy comparable with and typically superior to the popular Kohn-Sham BLW and B3LW methods. However, the latter methods are not applicable in all regions of a potential energy surface, and even predict incorrect ground states for some systems. The use of two-body density functionals with MCSCF reference states does not share this shortcoming.

The spin–spin coupling constants in the ammonia dimer

The indirect spin–spin coupling constants have been calculated by means of the linear response MCSCF method for the three stationary points of the (NH 3) 2 dimer. The obtained intermolecular coupling constants and the dimerization-induced changes of the intramolecular coupling constants are compared with the results for the (HF) 2 and (H 2O) 2 complexes and discussed as parameters of the hydrogen bond. The best correlation with the strength of the X–H⋯Y hydrogen bond is exhibited by the dimerization-induced change in the reduced intramolecular 1K (XH) coupling. The reduced hydrogen-bond-transmitted 1 h K (YH) coupling constant also correlates to some extent with the interaction energy. No correlation with the interaction energy has been found for the reduced 2 h K( XY) coupling constant. The intermolecular coupling constants in (NH 3) 2 seem to be determined primarily by the internuclear distances.

MCSCF linear response study of the three-body dissociative recombination CH 2++e→C+2H

A number of excited states of the CH 2 molecule and of its ion are optimized by MCSCF method. Potential energy curves (PEC) along the linear and bent reaction coordinates for 36 excited states obtained by linear response calculation are presented. Account of these data permit us to simulate the linear and bent model for the three-body dissociative recombination (DR) CH 2 ++ e −→ C( 3 P, 1 D, 1 S)+2 H . From a simple linear reaction coordinate a principal possibility of the direct mechanism for the three-body DR by the electron capture to the 1 3Σ u − state is qualitatively understood. It is stressed that the DR is governed by exchange interaction. For the more realistic bent structure the analysis is more complicated. The bending potentials for the upper excited states (in the close energetic proximity with the ion 1 2 A 1 state) are not very sensitive to the angle variation in the region 180°–130°. Nevertheless the bent structure of the ion facilitates the three-body dissociation: the valence excited 3 3 A 2 state fits the energy of the ion and dissociates without barrier to the carbon atom and triplet spin pairing of the hydrogen radical pair C( 3 P)+2 H( 3Σ u +) . The hydrogen radical pair spin pattern is important for preventing the H 2 molecule production. The role of spin functions and exchange coupling are crucial for the DR process.

Ab Initio MCSCF Study on Eight π-Electron Heterocyclic Conjugated Systems: Energy Component Analysis of the Pseudo-Jahn−Teller Distortion from Planarity

To clarify the origin of nonplanarity in eight π-electron heterocyclic conjugated systems, an energy component analysis was carried out for the ground states by using ab initio MCSCF method with 6-31++G(d,p) basis set. Inspection of the energy components comprised in the total energy reveals that the type of pseudo-JT stabilization is classified into two groups, one in which the stability of nonplanar structure arises from a lowering of the interelectronic and internuclear repulsion energies and the other in which the stability results from a lowering of the electron−nuclear attraction energy. This sharp distinction in energy changes is accounted for in terms of an expansion or contraction of the molecular skeleton and a proximity among the nuclei and the electron clouds owing to a folding of the six-membered ring. Besides, it is shown that the theoretical structural characteristics for 1,2-dihydro- and 1,4-dihydro-1,2,4,5-tetrazines are in good agreement with available experimental facts.

The Shielding Constants and Scalar Couplings in N−H···OC and N−H···NC Hydrogen Bonded Systems: An ab Initio MO Study

The scalar spin−spin coupling constants, both intra- and intermolecular, were evaluated for the models of biological systems: formamide−formamide (Fa−Fa) and formamide−formamidine (Fa−Fi) dimers using the MCSCF method. Additionally, the shielding constants were calculated at the MCSCF and MP2 levels. 1J(NH) and 2J(NH) couplings are the most significantly affected by the hydrogen bond formation. The hydrogen-bond transmitted coupling constants 1hJ(NH) and 2hJ(NN) calculated for the Fa−Fi dimer are in agreement with recent experimental results for nucleic acids. The short-distance hydrogen-bond-transmitted couplings (e.g., 1hJ(NH) and 2hJ(NN)) decrease fast with increase in the hydrogen bond length, in contrast to the long-distance proton−proton intermolecular couplings. The changes in the shieldings of the protons engaged in the hydrogen bond formation and proton acceptors are found to decrease fast with increase in the hydrogen bond length, in accordance with the previous results.

Excited singlet state time-resolved Raman spectra of 4,4′-bipyridine and quantum chemical analysis of resonance Raman intensities

The low-energy S1→ Sn electronic transitions of 4,4′-bipyridine (44BPY) and the related resonance Raman intensities were analysed by ab initio calculation using the MCSCF method. This calculation is based on the previously optimized S1 state geometry of 44BPY at the CIS level. The results are discussed in the light of experimental picosecond time-resolved Raman measurements probed in resonance with two different S1→ Sn transitions and lead to a better insight in the electronic and structural properties of the 44BPY S1 state. Although the calculated spectra are only in partial agreement with the measured intensities, the most characteristic resonance enhancement effects are correctly predicted. The asymmetric characteristic of the S1 structure proposed previously is confirmed on this basis. A comparison of these resonance Raman effects with those characterizing two photoreduced transient radical species of 44BPY is also discussed. Copyright © 2000 John Wiley & Sons, Ltd.

Ab Initio Molecular Orbital Studies on the Chemiluminescence of 1,2-Dioxetanes

The mechanism of chemiluminescence of 1,2-dioxetane (DO) and 3,3,4,4-tetramethyl-1,2-dioxetane (TMDO) are investigated by the ab initio molecular orbital calculation. The rate-determining step of the chemiluminescent reaction is the O−O bond breaking to form the biradicals. The potential energies along the reaction path are calculated by uB3LYP and uB3P86 methods with 6-31+G(d); the calculated potential barriers are in reasonable agreement with experimental activation energies. An overview of the potential surfaces for overall reaction is obtained. The intersystem crossing mechanism from the singlet biradical to the triplet state is investigated, and the reaction path is followed to the 3(nπ*) excited states of the carbonyl group of respective fragment molecules. The mechanism of promotion to the 1(nπ*) excited state of formaldehyde is investigated by the MCSCF method on DO. The reaction rates and the yield of chemiluminescence are discussed by the RRKM theory of unimolecular reaction.

Is GVB-CI superior to CASSCF?

Presently the most reliable approach for the study of reaction pathways where chemical bonds are broken and formed is to carry out CASSCF calculations followed by corresponding multireference perturbation or CI treatments. The latter step generally relaxes the “antibonding character” of the CASSCF results. In this study we demonstrate that similar results can be well approximated by using a less optimized MCSCF method and not performing the multireference perturbation or CI step at all. This is accomplished by performing a complete CI calculation within the active orbital space of the generalized valence bond perfect pairing (GVB-PP) model. The local bond/antibond character of the orbital space of the GVB-PP method also allows development of a fast, but robust, Bethe–Goldstone algorithm, which reconstructs the CI energy to an accuracy of a few tenths of a millihartree for most types of bond breaking cases found in chemical reactions. This algorithm executes at a speed proportional to N where Np is the number of localized electron pairs in the active space. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 999–1008, 1999

Ab Initio MCSCF Study on Electronically Excited Singlet States of Fulvalene Systems: Energy Component Analysis of the Pseudo-Jahn−Teller Effect

Geometry optimizations of the lowest (second) excited singlet states of the fulvalene systems were carried out by using the ab initio MCSCF method with the 6-31G(d) basis set. The electronically excited molecules are found to undergo a pseudo-Jahn−Teller (JT) distortion from D2h to C2v. On the basis of the results obtained, an energy component analysis of the total energy has been carried out to elucidate the physical picture of the pseudo-JT effect. Inspection of the energy components comprised in the total energy reveals that the stability of a less symmetric structure (C2v) is attributable commonly to the energy lowerings of the internuclear repulsion term and the interelectronic repulsive and kinetic terms due to σ electrons. These observations are consistent with an expansion of the carbon skeleton brought about by the pseudo-JT bond distortion. It is further found that in triafulvalene and heptafulvalene the nuclear−electron attractive and interelectronic repulsive terms due to π electrons contribut...