MCSCF Calculations Research Articles

Symmetry-adapted-cluster configuration interaction study of the doublet states of HCl+: Potential energy curves, dipole moments, and transition dipole moments

The electronic structure of the HCl(+) molecular ion has been calculated using the general-R symmetry-adapted-cluster configuration interaction (SAC-CI) method. The authors present the potential energy curves, dipole moments, and transition dipole moments for a series of doublet states. The data are compared with the previous CASSCF and MCSCF calculations. The SAC-CI results reproduce quite well the data available in literature and extend the knowledge on the HCl(+) electronic structure for several higher states. The calculated R-dependent behavior of both dipole moments and transition dipole moments for a series of bound and unbound states reveals an intricate dissociation process at intermediate distances (R>R(e)). The pronounced maxima in transition dipole moment (TDM) describing transitions into high electronic states (X (2)Pi-->3 (2)Pi, X (2)Pi-->3 (2)Sigma, 2 (2)Pi-->3 (2)Pi, 3 (2)Pi-->4 (2)Pi) occur at different interatomic separations. Such TDM features are promising for selection of excitation pathways and, consequently, for an optimal control of the dissociation products.

An ab initio study of the electronic structure of BCl2+3 and its decomposition pathways

Ab initio methods have been used to characterise the lowest energy potential energy surfaces of 1BCl3(2+) and 3BCl3(2+). The methods used are MP2, CCSD, CCSD(T) and MCSCF with 6-311G(d), cc-pVTZ and aug-cc-pVTZ basis sets. While the singlet surface is relatively straight-forward, the triplet surface is very complicated, with many stationary points in close energetic proximity. The singlet surface can fragment to the following products (1BCl + 1Cl+ + 1Cl+), (1Cl+ + 1B+ + 1Cl2), (2BCl+ + 2Cl), while the triplet surface can fragment to (1BCl2+ + 3Cl+) and (2BCl2(2+) + 2Cl). 2BCl2(2+) can further fragment to (1Cl+ + 2BCl+). These results are in good agreement with previous experimental data from coincidence mass spectroscopy. [symbol: see text]1 diagnostic values have been calculated for all of the stationary points of BCl3(2+), using the method of Lee and Taylor. These data, together with CCSD/CCSD(T) energy differences and MCSCF calculations, are used to conclude that most of the stationary points on the singlet surface are well represented using single reference methods. The stationary points of the triplet system have [symbol: see text]1 diagnostic values greater than those for the singlet system, as expected when using the closed-shell [symbol: see text]1 diagnostic method of Lee and Taylor. However, all of the structures have acceptable single reference wavefunctions if the open-shell upper limit of Rienstra-Kiracofe et al. (0.045) is used, a conclusion fully supported by CCSD/CCSD(T) energy differences. CCSD(T) energies determined for the fragmentation asymptotes have been compared with experimental data collated from the NIST Theoretical and Scientific Data website, and the generally very good agreement between theory and experiment reinforces the reliability of the CCSD(T) method.

Modelling of Octahedral Manganese II Complexes with Inorganic Ligands: A Problem with Spin-States

Quantum mechanical ab initio UHF, MP2, MC-SCF and DFT calculations with moderate Gaussian basis sets were performed for MnX6, X = H2O, F-, CN-, manganese octahedral complexes. The correct spin-state of the complexes was obtained only when the counter ions neutralizing the entire complexes were used in the modelling at the B3LYP level of theory.

Pseudo-Jahn−Teller Distortion from Planarity in Heterocyclic Seven- and Eight-Membered Ring Systems with Eight π Electrons

To elucidate the nature of a pseudo-Jahn−Teller (JT) distortion from planarity, ab initio MCSCF calculations with the 6-31G(d,p) basis sets were carried out in the ground states of seven- and eight-membered unsaturated heterocycles with eight π electrons. The monocyclic systems examined were found to show a variety of structural changes. Azepine and oxepin undergo the pseudo-JT distortions from a planar C2v to a boat Cs conformation. In 1,5-diazocine, the pseudo-JT distortion takes place in two stages, the initial step being from a symmetric planar D2h to a skew C2h structure and the subsequent step from the skew C2h to a tub C2 structure. The 1,3,5,7-tetrazocine molecule undergoes pseudo-JT distortions from a symmetric planar D4h to skew C4h and crown-like D2d structures through the respective in-plane and out-of-plane nuclear deformations. Moreover, the C4h and D2d structures are distorted into the same tub-shaped S4 conformation. An inspection of the energy components comprised in the total energy reveals that the stability of nonplanar structures arises from a lowering of the electron−nuclear attraction energy. The energy variation is accounted for in terms of an electrostatic interaction and the proximity among the nuclei and electron clouds owing to a folding of the molecular skeleton. It is shown that the theoretical structural characteristics for azepine, oxepin, 1,5-diazocine, and 1,3,5,7-tetrazocine are in good agreement with available experimental facts.

G Tensor and Spin Density of the Modified Tyrosyl Radical in Galactose Oxidase: A Density Functional Study

The influence of ortho sulfur substitution in the modified tyrosyl radical in apo-galactose oxidase on the g tensor and the spin-density distribution has been studied by calculations on various model systems using an accurate DFT approach. Computed g tensors agree well with experimental observation, and they are intermediate between the extremely large substituent effect found in a previous DFT study and the very small changes found in MCSCF calculations. The origin of the substituent effects has been studied by fragment analyses of the spin−orbit/orbital-Zeeman g-tensor contributions, and it is discussed in relation to the spin-density distributions. The influence of hydrogen bonding on g tensors is studied by appropriate model complexes with water. Further calculations on radicals including heavier chalcogen substituents XH (X = O, S, Se, Te) predict very large gx and gy components with selenium- and tellurium-substituted systems due to large, direct substituent spin−orbit contributions. In view of an unexpectedly large gauge dependence of the g-tensor orientation in several cases, a recently developed implementation of gauge-including atomic orbitals (GIAO) has been applied.

Analytic MRCI gradient for excited states: formalism and application to the n-π* valence- and n-(3s,3p) Rydberg states of formaldehyde

The previously developed formalism for the calculation of the analytic multireference (MR) CI energy gradient with respect to nuclear coordinates based on a single-state MCSCF calculation was extended to the case of state-averaged MCSCF. This extension is of particular importance for calculations of electronically excited states and enables automatic high-level geometry optimizations and saddle point searches on excited-state energy surfaces. Beyond MR-CI, the present analytic gradient method is also available for the MR-ACPF/AQCC methods including size-extensivity corrections for the multireference case. Full geometry optimizations for six electronic states of formaldehyde (valence and Rydberg states) are reported.

Conformation and dynamics of normal and damaged DNA.

The genetic information that determines the structure and function of living organisms is encoded in the nucleotide sequence of double-stranded DNA molecules. Despite an apparent structural homogeneity displayed by DNA, subtle local variations in structure and dynamics are functionally significant. Short sequences exhibit specificity for regulatory and catalytic proteins, which mediate fundamental processes necessary to the survival of the cell. However, the molecular basis for specific recognition is still incompletely understood. The "indirect readout" mechanism suggests that the relative propensity of DNA to undergo structural deformations induced by the protein contributes to specific protein-DNA recognition. Although the hypothesis was originally formulated to explain recognition of specific nucleic acid sequences by DNA-binding proteins, it may have particular application to the recognition of DNA damage, because damaged sites in DNA have different equilibrium structure and dynamics from undamaged DNA. In this work, we review the approaches that we took to investigate the questions of sequence- and damage-dependent structure and dynamics of DNA. We describe a statistical thermodynamic model that relates DNA configurational flexibility to sequence-specific protein-DNA binding. The model provides a theoretical basis for interpreting experimental measurements of DNA dynamics. We describe results from MCSCF calculations of the excited states of 2-aminopurine (2AP), which provide the theoretical basis for the intramolecular mechanism of quenching as well as the effect of environment on this process. We then describe our investigations of the effect of stacking, base pairing, and base dynamics on the fluorescence of 2-AP in model systems, which allow us to develop the relationships between steady-state and time-resolved fluorescence parameters on the one hand and local structural and dynamic properties of DNA on the other hand. Finally, we describe the application of the experimental approach to study the conformational heterogeneity of DNA abasic sites, a commonly occurring type of DNA damage. We demonstrate the power of the experimental algorithm to characterize the physical differences between undamaged and damaged DNA, as well as the effects of nucleic acid sequence in both of these contexts. Thus, the work described herein comprises a combination of theoretical and experimental approaches to the problem of sequence- and damage-dependent DNA deformation.

Left-right correlation energy

We first attempt to determine a local exchange functional Ex[p] which accurately reproduces the Hartree-Fock (HF) energies of the 18 first and second row atoms. Ex[p is determined from p and |δp|, and we find that we can improve significantly upon Becke's original generalized gradient approximation functional (commonly called B88X) by allowing the coefficient of the Dirac exchange term to be optimized (it is argued that molecules do not behave like the uniform electron gas). We call this new two parameter exchange functional OPTX. We find that neither δ p or t = Σ δ i |2 improve the fit to these atomic energies. These exchange functionals include not only exchange, but also left-right correlation. It is therefore proposed that this functional provides a definition for exchange energy plus left-right correlation energy when used in Kohn-Sham (KS) calculations. We call this energy the Kohn-Sham exchange (or KSX) energy. It is shown that for nearly all molecules studied these KSX energies are lower than the corresponding HF energies, thus giving values for the non-dynamic correlation energy. At stretched geometries, the KSX energies are always lower than the HF energies, and often substantially so. Furthermore all bond lengths from the KSX calculations are longer than HF bond lengths and experimental bond lengths, which again demonstrates the inclusion of left-right correlation effects in the functional. For these reasons we prefer to split the correlation energy into two parts: left-right correlation energy and dynamic correlation energy, arguing that the usage of the words ‘non-dynamic’ or ‘static’ or ‘near-degeneracy’ is less meaningful. We recognize that this definition of KSX is not precise, because the definition of a local Ex[p] can never be precise. We also recognize that these ideas are not new, but we think that their importance has been insufficiently recognized in functional determination. When we include third row atoms in our analysis, we are unable to find a local exchange functional which is a substantial improvement over B88X for the reproduction of HF energies. This must arise from the effects of the core orbitals, and therefore we do not consider that this detracts from the improved accuracy of OPTX. We report some MCSCF calculations constructed from bonding-antibonding configurations, from which we attempt to calculate ab initio left-right correlation. There is only moderate agreement between the two approaches. Finally we combine the OPTX functional with established correlation functionals (LYP, P86, P91) to form OLYP, OP86 and OP91; OLYP is a great improvement on BLYP for both energy and structure, and OP86, OP91 are an improvement over BP86, BP91 for structure. The importance of the exchange functional for molecular structure is therefore underlined.

MCSCF and DFT calculations of EPR parameters of sulfur centered radicals

The EPR parameters of sulfur centered radicals are different depending on the radical structure, charge and solvent. That is, the g- and A-tensor components provide significant patterns which may distinguish sulfur radical structures from each other. In the present work, these EPR parameters were calculated for monosulfide radicals (RS ), disulfide radicals (RSS ), radical cations (RS SR +) and anions (RS SR −), with R=CH 3, using the MCSCF linear response and DFT/B3LYP methods. Results were in agreement with experimental data for the cases when well-resolved EPR spectra are available. Especially, the assignment of the disulfide anion in ribonucleotide reductase was confirmed. The results indicate that investigations with the present computational methods on refined structures and solvent modeling may provide interpretations of experimental data on unassigned radical species.

Ab Initio MCSCF Study on the Pseudo-Jahn−Teller Distortion from Planarity in Cycloheptatriene, Heptalene, and Heptafulvalene

To elucidate the nature of a pseudo-Jahn−Teller (JT) distortion from planarity, ab initio MCSCF calculations with 6-31G(d) basis sets are carried out on the ground state of the titled molecules. Cycloheptatriene undergoes the pseudo-JT distortion from a planar C2v to a boat Cs conformation. In heptalene, the pseudo-JT distortion takes place in two stages, the initial step being from a symmetric planar D2h to a skew planar C2h structure and the subsequent step from the skew C2h to a twisted C2 one. In heptafulvalene, the symmetric planar D2h structure exhibits a third-order saddle point and, hence, the pseudo-JT distortions take place from the D2h to D2, C2v , and C2h ones through the respective out-of-plane nuclear deformations. Besides, the twisted D2 structure exhibits a second-order saddle point with respect to the syn- and anti-folding motions of the seven-membered rings and the structural changes take place from the D2 to the C2v and C2h structures. A comparison of the total energy reveals that the g...

Phosphorane−Iminato Complexes of Transition Metals with Heterocubane Structure: A Computational Study

The electronic structure of phosphorane-iminato complexes of transition metals is studied by means of ab initio/DFT methods. Accordingly, the transition metal nitrogen bond is best described as an ionic interaction between a transition metal complex fragment and the strongly polarized NPH3- ligand. By elaborate MCSCF calculations a weak antiferromagnetic coupling of the four transition metal centers in the cubane core is predicted. This coupling can be represented by a simple Heisenberg Hamiltonian.

Self-consistent treatment of the frequency-independent Breit interaction in Dirac-Fock and MCSCF calculations of atomic structures: I. Theoretical considerations

The self-consistent treatment of the Breit interaction in fully numerical atomic structure calculations is cumbersome due to the computationally demanding evaluation of two-electron integrals as they occur in the original formulation (Grant I P and Pyper N C 1976 J. Phys. B: At. Mol. Phys. 9 761). We present a reformulation of the frequency-independent Breit interaction operator in spherical coordinates and derive the corresponding matrix elements over spinors. With this formulation it becomes possible to compute the matrix elements of the Breit interaction efficiently and analogously to those of the Coulomb interaction: i.e., by determining the corresponding interaction potential functions using Poisson equations. The derived formulae will equally simplify computations using either basis sets or a numerical representation of the orbitals such that the Breit interaction can be included effectively in CI and SCF calculations for atoms and molecules. Of course, the computation of the Breit contribution to the total electronic energy as a first-order perturbation correction is also simplified. Furthermore, the frequency-dependent Breit interaction could be treated analogously.

A direct procedure for the evaluation of solvent effects in MC-SCF calculations

We extended the polarizable continuum solvation model to multi-configurational complete active space as implemented in the Gaussian program. The present formulation allows energy and gradient computations in a unified approach for closed and open shell systems: in this work we present the formal derivation and check the results with energy calculations and geometry optimizations in solution, for ground and excited electronic states.

The ethylene 1 1B1u V state revisited

We describe a general procedure to resolve the problem of artifical valence/Rydberg mixing encountered in ab initio CI calculations on the V (1 1B1u) state of ethylene. Davidson and McMurchie realized that the key to this problem are orbitals which adequately represent the V state. A two-step procedure is proposed, in which the first step focuses on generating appropriate molecular orbitals and the second step aims to describe the electron correlation quantitatively. A series of the currently most extensive MCSCF, MR-CISD, and MR-AQCC calculations for basis sets up to quadruple zeta quality and up to 80 million configurations are presented. Size extensivity corrections turn out to be crucial for highly accurate excitation energies. Our best estimate for the N–V state excitation energy of 7.7 eV lies between the experimental absorption maximum of 7.66 eV and a vibrationally corrected value of 7.8 eV. Hence, we do not find it necessary to refer to nonadiabatic effects in order to achieve agreement with the experimental data. The V state is characterized by its spatial extent, measured through the expectation value 〈x2〉, where x is the out-of-plane direction. With 16.5–17.0a02 it has a strong valence character, as compared to ≈90a02 for the 2 1B1u Rydberg state and 11.7a02 for the ground state.

Multiple Ionisation and Fragmentation of Molecules

The multiple ionisation and dissociation of molecules, e.g. H2, N2, H2O, CH4 and C60, by fast ions was studied using a position- and time-sensitive multi-particle detector. The data obtained allow a clear separation of various reaction channels. Of special interest are the ‘Coulomb explosion’ processes like N2 → Nq+ +Nn+ or H2O → H+ + H+ +On+. For these reactions the coincident measurement of the momenta of correlated fragment ion yields a kinematically complete image of the molecular break-up process, and the fragmentation energy as well as angular correlations can be derived for each individual event. In the case of H2 as target molecule the CE model describes the fragmentation energy rather well, whereas in the case of more complex molecules, e.g. N2, CO and CH4, the simple CE model is insufficient to explain the measured energy and angular spectra. Better agreement was achieved with ab initio MCSCF calculations which take into account several molecular states of the fragmenting highly charged molecular ion.

Parallel mechanisms for the cycloaromatization of enyne allenes †

The Myers–Saito cycloaromatization of enyne allenes is proposed to consist of two parallel mechanisms, one involving a biradical and the other with dipolar character. MCSCF calculations suggest that a nonplanar cyclic allene could be fairly close in enthalpy to the biradical, while the planar zwitterion originally proposed as a possible second intermediate is in fact a transition state for the interconversion of the two enantiomeric cyclic allenes. Competitive trapping experiments rule out the presence of a single intermediate and are consistent with the participation of parallel pathways. The reaction of (Z)-hepta-1,2,4-trien-6-yne in cyclopentadiene gave an inseparable mixture of two tetracyclic products whose structures were elucidated with 2-D NMR.

Reduction of Monophosphaallenes: An EPR Study and ab Initio Investigations of (HPCCH2)-• and (HPCHCH2)• Radicals

Cyclic voltammetry shows that monophosphaallene ArPCC(C6H5)2 (where Ar = C6H2tBu3-2,4,6), 1a, undergoes irreversible reduction at 2266 mV in THF. The EPR spectra of the reduction products are obtained in liquid and frozen solutions after specific 13C enrichment of the allenic carbon atoms. The resulting hyperfine tensors are compared with those obtained from ab initio MP2, MCSCF, CI, and DFT calculations for the radical anion (HPCCH2)-• and for the monophosphaallylic radical (HP•−CHCH2) ↔ (HPCH−•CH2). The most elaborate treatments of the hyperfine structure (CI and DFT) indicate that the species observed by EPR is the monophosphaallylic radical.

Ab initio quantum chemistry on the Cray T3E massively parallel supercomputer: II

Gaussian-94 is the series of electronic structure programs. It is an integrated system to model a broad range of molecular systems under a variety of conditions, performing its calculations from the basic laws of quantum chemistry. This new version includes methods and algorithms for scalable massively parallel systems such as the Cray T3E supercomputer. In this study, we discuss the performance of Gaussian using large number of processors. In particular, we analyze the scalability of methods such as Hartree–Fock and density functional theory (DFT), including first and second derivatives. In addition, we explore scalability for CIS, MP2, and MCSCF calculations. Scalability and speedups were investigated for most of the examples with up to 64 process elements. A single-point energy calculation (B3-LYP/6-311++G3df,3p) was tested with up to 512 process elements. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1053–1063, 1998

Ab Initio Study of the 1,3-butadienyl Radical Isomers

Ab initio calculations at the B3LYP, QCISD, and MCSCF levels of theory and using the 6-311G(d,p) basis set were carried out on the ground state of the 1,3-butadiene derived radicals. The 1,3-butadien-1-yl and 1,3-butadien-2-yl radicals are obtained from 1,3-butadiene by abstraction of a hydrogen atom from a primary and secondary carbon, respectively. The 1,2-butadien-4-yl radical was also studied to examine the possibility of the relocalization of the unpaired electron from 1,3-butadien-2-yl. 1,2-Butadien-4-yl was consistently found to be the most stable isomer. The MCSCF relative energies are 29 kJ mol-1 for 1,3-butadien-2-yl and 35 kJ mol-1 for the most stable of the 1,3-butadien-1-yl configurational isomers. The 1,3-butadien-2-yl structure is found to be a local minimum in MCSCF calculations, but with an isomerization barrier of less than 1 kJ mol-1, and deforms to the 1,2-butadien-4-yl isomer at all other levels of theory used. The energy of the most stable 1,3-butadien-1-yl isomer relative to 1,3-butadien-2-yl ranges from 6 to 18 kJ mol-1 across all levels of theory used, substantially lower than previous predictions by ab initio and semiempirical means. Optimized geometries, relative energies, permanent dipole moments, Fermi contact terms and harmonic vibrational frequencies are reported.

Coupled cluster response calculations of two-photon transition probability rate constants for helium, neon and argon

The implementation of two-photon transition moments is described for the hierachy of coupled cluster models CCS, CC2 and CCSD and applications are reported for the two-photon transition probability rate constants for transitions from the ground state to the first excited Se1 state in helium and to the lowest De1 and Se1 states in neon and argon. At the CCSD level the rate constant for the Se1 transition in argon is in good agreement with the experimental rate constant and also with a recent MCSCF calculation.