Multiconfigurational Perturbation Theory Research Articles

Photoexcited O3(H2O)n cluster decay: Nonempirical simulation of model systems

AbstractThe ground and excited electronic states of an individual ozone molecule and its clusters with up to five water molecules are considered at the multiconfigurational quasidegenerate perturbation theory level with the geometrical optimization of structures carried out in the multiconfigurational self‐consistent field approximation in complete active space with 6‐31G basis set extended with diffuse and polarization functions on all nuclei. The vertical photoexcitation spectra of an ozone molecule and ozone–water clusters in the energy range up to 6.0 eV are compared. An interaction between singlet dissociation products of ozone and either a single water molecule or a small water cluster is considered, and the formation of radical species is predicted. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Ab Initio Study of Aromatic Side Chains of Amino Acids in Gas Phase and Solution

The vertical transition properties have been calculated for the valence electronic excited ππ* singlet states 1 L b , 1 L a , 1 B b , and 1 B a of the chromophores benzene, phenol, and indole in bulk solvent. The polarizablecontinuum model was employed in the framework of a complete active space self-consistent reaction field with use of an atomic natural orbital basis set. Dynamical electron correlation was accounted for through the use of second-order multiconfigurational perturbation theory. The predicted solvatochromic shifts are compared with previous experimental and computational results. We find general agreement, in particular for the 1 L b state of each species, where a red-shift is observed in bulk solvent. To our knowledge this is the first ab initio self-consistent reaction field study of the high-lying 1 B b and 1 B a states of benzene, phenol, and indole in bulk solvent. At the correlated level, the 1 B b and 1 B a states undergo red-shifts for benzene, shifts to the red and to the blue respectively for phenol, and shifts to the blue for indole.

The allyl radical revisited: a theoretical study of the electronic spectrum

In this Letter, we report the electronic spectrum of the allyl radical, obtained with multiconfigurational perturbation theory (MS-CASPT2). The assignment of the spectrum is in accordance with experiment to within 0.2 eV. We have computed the complete first Rydberg series and the beginning of the second Rydberg series. A new valence-excited 2B 1 state has been found which has hitherto been hidden by Rydberg transitions. A rationalisation of the electronic spectrum is provided in terms of resonance forms in ground and excited states. This model shows that while a multiconfigurational wavefunction is necessary to qualitatively model the system, the large ionic character of the valence electronic states makes an accurate treatment of the dynamical correlation necessary for a quantitative description of the spectrum.

Calculation of accurate binding energies for the transition-metal carbonyls Ni(CO) 4 , Fe(CO) 5 and Cr(CO) 6

Using new atomic natural orbital basis sets constructed to treat correlation of all M-shell electrons for the first transition row, we have calculated the energies of the reaction M(CO) n →M+nCO for M=Ni,Fe,Cr and n=4,5,6, respectively. Both coupled-cluster and multiconfigurational reference perturbation theory are used as correlation treatments, and although they give qualitatively similar results once basis set superposition error is accounted for, multireference perturbation theory gives binding energies that are larger than both coupled-cluster theory and experiment. The agreement between our best calculated results and experiment is excellent for Ni(CO)4 and Fe(CO)5, but very poor for Cr(CO)6. The experimental result for the latter is old and we suggest that revisiting this system experimentally would be valuable.

Ferrimagnetic coupling in oxamido-bridged Mn(II)Cu(II) compounds: a combined CASPT2 and DDCI study

Multiconfigurational perturbation theory (CASPT2) and difference dedicated configuration interaction (DDCI) are applied to study the ferrimagnetic coupling in an oxamido-bridged Mn(II)Cu(II) molecular species. CASPT2 reproduces the experimental coupling very well. From the partition of the CASPT2 energy, the most important contributions to the coupling are established. Spin populations are calculated with DDCI. The successive improvement of the N-electron wave function allows us to analyse the contributions to the spin delocalization.

Electronic Spectra, Excited-State Geometries, and Molecular Electrostatic Potentials of Hypoxanthine: A Theoretical Investigation

The ground-state geometry of hypoxanthine was optimized at the MP2, B3LYP, and HF levels by employing the 6-311++G(d,p) basis set. The vertical singlet transition energies were calculated at the CASSCF/ 6-31+G(d), TD-B3LYP/6-311++G(d,p), and CIS/6-311++G(d,p) levels by using the MP2-, B3LYP-, and Hartree−Fock-optimized geometries, respectively. In the case of the CASSCF calculations, the active space consisted of the 2σ, 6π, and 4π* orbitals. The σ orbitals were used to compute the nπ* transitions. The effects of dynamic correlation on the CASSCF energies were considered at the second-order multiconfigurational quasi-degenerate perturbation (MCQDPT2) theory. The effect of hydration was considered by including three water molecules in the first solvation shell of hypoxanthine. The geometry of the molecule was also optimized in the lowest singlet ππ* and nπ* excited states at the CIS/6-311++G(d,p) level. The characteristics of the ground and excited-state potential energy surfaces were ascertained from a ha...

Magnetic coupling in oxalato-bridged hetero-bimetallic compounds: an ab initio study

Multiconfigurational perturbation theory (CASPT2) and difference dedicated configuration interaction are applied to study the ferromagnetic coupling in oxalato-bridged Cr(III)Cu(II) molecular species, where the external ligands of the Cr(salen)C2O4Cu(acpy) complex, with salen=N,N′-ethylenebis(salicylideneaminate) and acpy=N-acetylacetonylidene-N-(2-pyridylethyl)aminate, are modeled by simple H2O or NH3 groups. The results show little dependence on the external ligand modeling. The experimental coupling is very well reproduced at both calculation levels when the model nearly reproduces the experimental geometrical structure. CASPT2 calculations on an oxalato-bridged Cr(III)Ni(II) model of Cr(salen)C2O4Ni(taea)BPh4, where taea=tris(2-aminoethyl)amine, are also in good agreement with experiment.

Ground and excited state CASPT2 geometry optimizations of small organic molecules.

A method for computing second-order multiconfigurational perturbation theory (CASPT2) energy gradients numerically has been implemented and applied to a range of elementary organic chromophores, including 1,3 butadiene, acrolein, and two protonated Schiff bases. Geometries of ground and excited states-as well as conical intersections-are compared with the corresponding CASSCF structures, illustrating the effect of including the correction for dynamical electron correlation. It is shown that the differences between the two methods are not readily categorized, but that, while individual changes in bond lengths can be quite large ( approximately 0.01-0.02 A), the natures and CASPT2 energetics of the structures remain similar. Exceptions to this tend to be systems that have a strong ionic character and that are not well described at the CASSCF level. Basis set effects (double- vs. triple-zeta) were examined for a limited number of examples, and found to be quite dramatic at both levels of theory.

Identification of Cu(ii) coordination structures in Cu-ZSM-5, based on a DFT/ab initio assignment of the EPR spectra

The coordination structures of Cu(II) exchanged into ZSM-5 were obtained by B3LYP-DFT geometry optimizations on cluster models, representing the cation sites. The EPR g-factors of the resulting cluster models were calculated by means of the CASPT2 method (multi-configurational perturbation theory), with the inclusion of spin–orbit coupling. In order to facilitate the confrontation of theoretical and experimental results, the EPR spectra of a selection of dehydrated Cu(II)-ZSM-5 samples are presented as well. The axially symmetric signal with g∥ = 2.30–2.33, which is present over the whole range of copper loadings, is assigned to a five-fold or distorted three-fold Cu(II) coordination in site α, a six-ring with bridging T-site, containing 2 lattice Al's. The axially symmetric species with g∥ = 2.26–2.28, present at medium copper loadings, is assigned to a square-planar Cu(II) coordination in six-rings and a square-pyramidal Cu(II) coordination in five-rings, with both rings containing only one Al and no extra-lattice oxygen (ELO). The near absence of the g∥ = 2.26–2.28 signal at the highest Cu/Al ratio's is explained by the coordination of ELO to Cu(II) in these sites with one Al, yielding an EPR silent species.

Hyperfine coupling tensors for multi-configurational quasi-degenerate perturbation theory

Analytic calculation of the hyperfine coupling tensors for multi-configurational quasi-degenerate perturbation theory is developed based on the Lagrange multiplier formalism. Calculation of Lagrange multipliers is not required if the corresponding constraining conditions do not depend explicitly on the magnetic moments of the nuclei. Except for the explicit form of the one-electron perturbation operator, the derivation presented in this work is also applicable to other molecular properties for which the basis functions do not depend on the differentiation variable, and for which the dependence of the Hamiltonian is through a one-electron operator only.

Ab Initio CASSCF and DFT Investigations of (H2O)2+and (H2S)2+: Hemi-Bonded vs Proton-Transferred Structure

High level ab initio calculations using a complete active space self-consistent field (CASSCF) and multiconfigurational quasi-degenerate perturbation theory (MCQDPT2) methods as well as density functional theory (DFT)-based calculations with different exchange−correlation energy density functionals have been performed for predicting the relative stability of the proton-transferred vs hemi-bonded isomers of (H2O)2+ and (H2S)2+ species. For (H2O)2+, DFT calculation using conventional exchange−correlation functionals predicts the hemi-bonded structure to be the ground state while use of full or half Hartree−Fock exchange and local correlation predicts a higher stability of the proton-transferred structure in agreement with ab initio results. For the (H2S)2+ system, all of the methods lead to the prediction of lower energy for the hemi-bonded isomer. No regular trend of the exchange−correlation energy component with the total energy difference is however observed. Dynamical electron correlation effect incorporated through MCQDPT2 is found to be much stronger in (H2O)2+ as compared to (H2S)2+. An analysis of the nature of interactions involved in the (H2O)2+ and (H2S)2+ systems within the framework of Bader's topological theory of atoms in molecules is also presented through the plots of the Laplacian ∇2ρ of the electron density ρ(r) and also other related quantities at the bond critical points with the objective of rationalizing the relative stability of the two isomers in both (H2O)2+ and (H2S)2+.

A theoretical study of the low-lying states of the AuSi molecule: An assignment of the excited A and D states

The lowest 42 electronic states of diatomic gas phase gold silicide are calculated by complete active space self-consistent field and second-order multiconfigurational perturbation theory. The scalar relativistic effect is considered by the third-order Douglas-Kroll method and the spin–orbit coupling is treated perturbatively after the spin-free calculations. The ground state of AuSi is confirmed to be the Π21/2 state, and the spin–orbit splitting of Π21/2 to Π23/2 is estimated as 1527 cm−1. From the careful analysis of the potential energy curves and the spectroscopic constants, the experimentally observed A and D excited states are assigned to Ω=1/2(II) or Ω=1/2(III) and Ω=1/2(V) or Ω=1/2(VI), respectively.

Hardness and Polarizability Profiles for Intramolecular Proton Transfer in Water Dimer Radical Cation

In view of the recently reported discrepancies in the prediction of minimum energy structure (proton-transferred vs hemibonded) for the water dimer on ionization, we have performed complete active-space self-consistent field calculations followed by total energy evaluation using multiconfigurational quasi-degenerate perturbation theory to obtain very accurate relative energies of different structures and predicted the proton-transferred structure to be the most stable ones. The variations of hardness, polarizability, chemical potential, and energy for the proton-transfer process in this weakly interacting system (ionized water dimer species) are investigated through calculations using Hartree−Fock theory. It is observed that the transition state corresponding to the proton-transfer process is associated with maximum polarizability at different O−O distances for the water dimer cation, although the hardness minimum does not exactly correspond to the transition state. However, the hardness profiles scaled suitably with chemical potential are found to have minima at the transition states.

Application and development of multiconfigurational localized perturbation theory

Generalization of localized perturbation theory, which results with a method able to span the spin space correctly, is presented. This generalization is achieved by using a multiconfigurational (MC) wave function as the reference. This is the most comprehensive expansion used within MC–LMP2 approach to date, with, however, low computational cost [computational scaling with system size (N) of the new method is O(N3)]. Recently, we have reported the successful Jaguar2 (J2) model for calculating atomization energies. Within the MC–LMP2 framework, the J2 model for calculating heats of formation is based on the generalized valence bond–perfect pairing (GVB–PP) wave function. The J2 model was applied only to closed shell cases because of the perfect pairing (PP) restriction in the reference function. In order to describe other systems, the PP restriction needs to be lifted. This work describes efforts in that direction. The PP restriction can be lifted by a restricted configuration interaction (RCI) procedure applied to the GVB–PP wave function. In this paper, the equations describing the application of LMP2 theory to self-consistent RCI wave function are derived and explained. The RCI wave function is a “true” MC expansion as opposed to the GVB–PP, which uses only a single spin eigenfunction (SEF). We also present the self-consistent (SC) optimization of the RCI wave function. The SC–RCI–LMP2 is the first MC–LMP2 method where the spin space is spanned in the reference. This is important for describing the nondynamical correlation (near degeneracy) effects associated, for example, with bond breaking processes. The SC–RCI–LMP2 is an efficient method applicable to large systems; it is shown to reproduce the potential energy surfaces calculated by the complete active space–second order perturbation (CAS–SCF–PT2) method. This is demonstrated, for the first time, on some widely used test cases.

Multiconfigurational Perturbation Theory: An Efficient Tool to Predict Magnetic Coupling Parameters in Biradicals, Molecular Complexes, and Ionic Insulators

The performance of the complete active space second-order perturbation theory (CASPT2) to accurately predict magnetic coupling in a wide series of molecules and solid state compounds has been established. It is shown that CASPT2, based on a reference wave function that only includes the effects described by the Anderson or Hay−Thibeault−Hoffmann model, correctly reproduces all experimental trends. For a complete quantitative agreement with experiment (or with accurate results arising from the difference dedicated configuration interaction method), it is necessary to include effects that go beyond the Anderson model in the reference wave function. The CASPT2 method is computationally less demanding than CI based methods and, hence, allows us to extend the study of magnetic coupling parameters to larger molecules or systems with elevated spin moments. Moreover, CASPT2 provides a reliable and accurate alternative to density functional based methods that require the use of a broken symmetry approach.

Dipole moments of [formula omitted] and [formula omitted] states of CN radical at different internuclear distances via Fock space multi-reference coupled cluster linear response approach

Dipole moments of 2Σ and 2Π states of CN radical at different internuclear distances are reported using the multi-reference coupled cluster (MRCC) linear response approach. We also report as a by product the potential energy surface, equilibrium geometry and harmonic frequency of CN radical states that agree well with those calculated using multi-configuration quasi-degenerate perturbation theory (MCQDPT). The dipole moment of the ground state of the radical is in excellent agreement with the experimental value. Dipole moments are also calculated using MRCI using bigger complete active space and state specific orbitals and results of both methods agree well.

Optical properties of peroxy radicals in silica: Multiconfigurational perturbation theory calculations

The low-lying electronic transitions in a peroxy radical, ≡Si–O–O•, a fundamental radiation induced point defect in silicon dioxide, have been investigated by means of ab initio multiconfiguration perturbation theory calculations, CASPT2, and cluster models. The accuracy of the computed transition energies and intensities as predicted by the CASPT2 approach has been checked by studying the exited state properties of two molecular analogues, the HOO• and CH3OO• radicals, and of a well-characterized paramagnetic defect in silica, the nonbridging oxygen center, ≡Si–O•, for which unambiguous assignments exist. We found that the peroxy radical gives rise to two optical absorption bands, a very weak one at 0.7 eV and an intense one at 5.49 eV, in agreement with the experimental assignments of Radzig [V. A. Radzig, Chem. Phys. Reports 14, 1206 (1995)].

CASSCF Investigation of Electronic Excited States of 2-Aminopurine

2-Aminopurine is a highly fluorescent analogue of adenine that can be incorporated synthetically into DNA with little perturbation of the native double-helical structure. The sensitive dependence of the quantum yield of this fluorophore on nucleic acid conformation has made it an invaluable probe of DNA structure, dynamics, and interactions. To assist in the development of models for the molecular interpretation of fluorescence measurements, the electronic structure of 2-amino-9-methylpurine has been calculated in the ground state and the lowest singlet ππ* and nπ* excited states. These computations employed the complete active space multiconfigurational self-consistent field method (CASSCF), supplemented by multiconfigurational quasi-degenerate perturbation theory (MCQDPT). The predicted energies for ππ* excitation and emission and nπ* excitation are in good agreement with previous experimental values. The permanent molecular dipoles of the ground and ππ* excited states are similar in magnitude and direction, consistent with experimental observations of weak solvatochromic shifts in ππ* absorption and emission spectra. However, the permanent dipole of the nπ* state is rotated approximately 60° relative to that of the ground state, implying that the nπ* excitation energy will increase in more polar solvents due to the relative destabilization of this state by unfavorably oriented solvent dipoles. This result demonstrates that the “blue-shift” of the nπ* state in polar solvents, which is commonly attributed to the effect of hydrogen bonding, can arise entirely from a general solvent effect. The energy of a radiationless vibronic transition from the ππ* state to the nπ* state will increase in more polar solvents, provided that the solvent does not rearrange during the transition. Consequently, the efficiency of fluorescence quenching by vibronic coupling between the ππ* and nπ* states is predicted to decrease significantly in such solvents. The geometry of the fluorescent emitting state, obtained by CASSCF optimization of the ππ* state, is moderately buckled due to the occupation of an antibonding orbital localized to C6. This buckling implies an out-of-plane vibration during the relaxation of the ππ* state, which is required for vibronic coupling between this state and the nπ* state. Such a solvent-sensitive intramolecular quenching mechanism may account for the observed dependence of the fluorescence lifetime of 2-aminopurine on the local environment both in pure solvents and in DNA.

Study of the coordination of Cu 2+ in zeolite Y: Interaction with water and ammonia

The ligand field spectrum of Cu(II) exchanged zeolite Y, obtained after saturation with H 2O and NH 3 and during the gradual desorption of these ligands, was measured by diffuse reflectance spectroscopy (DRS). DFT and ab-initio calculations on several model clusters were performed to interpret the spectra. The structure of the model clusters was optimized by means of density functional theory (DFT), using the B3LYP functional. The electronic spectra of the models were calculated using multiconfigurational perturbation theory based on a CASSCF wavefunction (CASPT2) and compared with the DRS spectra. Firstly, several [Cu(NH 3) y (H 2O) x ] 2+ complexes were studied. It was shown that in fully hydrated Cu(II)Y, a [Cu(H 2O) 6] 2+ complex can be present in the cages of the zeolite. In Cu(II)Y, saturated with NH 3, the [Cu(NH 3) 4] 2+ complex is present, but the Cu 2+ center in this complex must still be coordinated to one or two lattice oxygens in the zeolite. Secondly, calculations were performed on large cluster models, representing the adsorption complexes of one H 2O or one NH 3 ligand on Cu 2+ in the six-ring sites in zeolite Y. The ligand field spectrum of partially dehydrated and deammoniated Cu(II)Y shows d–d transitions at a lower energy than the spectrum of fully dehydrated Cu(II)Y, which is confirmed by the CASPT2 results of the six-ring clusters.

On the dissociation of N 6 into 3 N 2 molecules

The dissociation of the hypothetical system N 6 into three N 2 molecules has been studied using multiconfigurational second order perturbation theory (CASSCF/CASPT2) aided by a preliminary study using the density functional (DFT) approach. A concerted transition state with C 2 symmetry has been found between the most stable linear diazide form of N 6 and three N 2 molecules. The computed barrier is 28.7 kcal/mol (CASPT2) and 17.4 kcal/mol (DFT), respectively.