Multireference Configuration Interaction Wave Functions Research Articles

Theoretical studies of spin-forbidden radiationless decay in polyatomic systems. II. Radiationless decay of a-N2O2

The stability with respect to spin-forbidden radiationless decay of the previously reported [J. Chem. Phys. 88, 7248 (1988)] asymmetric dimer of NO, N–N–O–O (a-N2O2) is considered. The spin-allowed decay channel a-N2O2(1A′)→N2O(X 1Σ+)+O(1D) is endoergic. However, the spin-forbidden decay channel a-N2O2(1A′)→N2O(X 1Σ+)+O(3P) is exoergic. Large scale multireference configuration interaction wave functions, approximately 300 000–1 400 000 configuration state functions, based on double zeta polarization and triplet zeta polarization bases are used to study this process. The minimum energy crossing of the ground singlet 1A′ state and the lowest excited triplet 3A″ state was determined as was the interstate spin–orbit coupling. This electronic structure data was used in the context of a simple one-dimensional model to show that a-N2O2 is rapidly predissociated to N2O(X 1Σ+) and O(3P).

Theoretical study of the low-lying states of trans-1,3-butadiene

We present extensive ab initio calculations on the low-lying electronic states of trans-1,3-butadiene within the multireference configuration interaction (MRCI) framework by selecting the configurations with a perturbative criterion. The X 1Ag ground state and 1 3Bu, 1 3Ag, 2 1Ag, and 1 1Bu valence excited states have been calculated at a fixed geometry. The results obtained are in good agreement with previous experimental and calculated values, and could help to understand polyene spectroscopy, photochemistry, and photophysics. The advantages of a MRCI method where the most important contributions to the total MRCI wave function, perturbatively selected, are treated variationally, and the remaining terms are evaluated by means of a perturbational approach, are also discussed. Furthermore, a criterion in order to build a correlation-consistent configuration interaction space is stated and, therefore, a reliable approximation to achieve accurate energy differences is obtained. Several monoelectronic molecular-orbital basis functions are tried in order to select the most adequate to describe each state.

Theoretical and neon matrix electron spin resonance studies of the methanol cation: CH3OH+, CH3OD+, CH2DOH+, and 13CH3OH+

Four isotopes of the methanol cation radical (CH3OH+) have been generated by three independent methods and isolated in neon matrices at 4 K for a detailed electron spin resonance (ESR) investigation. The ion generation methods employed were X irradiation, photoionization, and electron ionization. The nuclear hyperfine (A tensors) measurements were compared with those obtained from ab initio extended basis set multireference configuration interaction (CI) wave functions. The relationships between geometry and electronic structures were fully explored. The trend in the large isotropic methyl hydrogen A values for the isoelectronic series CH3F+, CH3OH+, and CH3NH2+ was found to follow the trend in dissociation energies for these radical cations. The neon magnetic parameters for CH3OH+ are gx=2.0036(4) and gz=2.010(1); Aiso (methyl hydrogens)=229(1) MHz, ‖Ax‖=54(2) and ‖Az‖=80(3) MHz for the hydroxy hydrogen; ‖Ax‖=40(2) and ‖Az‖=29(4) MHz for 13C. The observed magnetic parameters for CH2DOH+ indicate an unusually large deuterium effect Aiso (CH2)=329 MHz with ‖Aiso‖=4.1(3) MHz for the methyl deuterium. These results show that averaging of the methyl hydrogen environments is occurring on the ESR time scale.

Multireference configuration interaction calculations of the low-lying electronic states of ClO2

Using extensive internally contracted multireference configuration interaction wave functions and large basis sets, near-equilibrium potential energy functions for the first four doublet electronic states (X 2B1, 2B2, 2A1, and A 2A2 ) of OClO and the X 2A″ electronic state of ClOO have been calculated. Electric dipole moment functions have also been computed for the ground states of both isomers. Spectroscopic constants derived for the X and A states of OClO, as well as for the X state of ClOO, are compared to the available experimental data, and predictions for the other states are made. In agreement with previous assumptions about the photodissociation of OClO, strong interactions between the first three excited electronic states in the Franck–Condon region of the A←X transition are indicated from cuts of the potential energy surfaces. In particular, the experimentally observed predissociation of the A 2A2 state is proposed from this work to proceed initially by an interaction with the close-lying 2A1 state. Additionally, the calculated asymmetric stretch potential for the A 2A2 state of OClO does not show evidence of a double minimum as has been previously proposed.

The mechanism of the reaction CH(X 2Π) + N 2 (X 1Σ +g) → HCN (X 1Σ +) + N ( 4S). : II. The intermediate complex region

The spin-forbidden reaction CH(X 2Π) + N 2(X 1Σ + g) → HCN (X 1Σ +) + N( 4S) involves a doublet → quartet intersystem crossing. It has been postulated that although the probability for a single pass intersystem crossing is small the existence of a bound intermediate on the lowest doublet potential energy surface increases the overall transition probability by enabling multiple crossings of the doublet—quartet surface intersection. This work considers this proposition, using large scale ((3.2 − 3.8) × 10 6 term), multireference configuration interaction wavefunctions. Two local minima on the lowest doublet potential energy surface are reported, a datively bonded structure N 2 → CH, and a C 2v structure, with HC along the perpendicular bisector of the N 2 bond, which resembles the recently reported geometrical arrangement at the transition state for this reaction, the minimum energy point on doublet—quartet intersection surface. These results enable a clear conceptual picture for the mechanism of this reaction to be presented.

A b i n i t i o calculations on the four lowest electronic states of AlF+ and AlCl+

The potential energy curves of the two lowest 2Σ+ (X,B) and the two lowest 2Π (A,C) electronic states of the AlF+ and AlCl+ molecular ions have been calculated using highly correlated multireference configuration interaction (MR-CI) wave functions. It is found that both 2Σ+ states and the C 2Πr state are bound, whereas the A 2Πi state is repulsive. Electronic transition moment functions for all six pairs of states of both ions have also been calculated and used for evaluation of the radiative transition probabilities between bound vibrational states. The calculated charge distributions show that the X and C states are dominated by Coulombic attraction between a doubly charged positive aluminum and the singly charged negative halogen ion. The results provide a new assignment of the photoelectron spectra of the neutral AlF. They are also in good agreement with the recently observed optical B–X emission spectra of both molecular ions and C–X bands of AlCl+. The absence of C–X emission of AlF+ is most likely due to predissociation of the C 2Πr state by the repulsive A 2Πi state.

On the mechanism of the reaction CH(X 2Π)+N2(X 1Σ+g)→HCN(X 1Σ+) +N(4S ). I. A theoretical treatment of the electronic structure aspects of the intersystem crossing

The reaction CH(X 2Π)+N2(X 1Σ+g)→HCN(X 1Σ+) +N(4S) has been suggested as the initial step in the formation of ‘‘prompt’’ NO in flame fronts. Since the reaction is spin-forbidden an intersystem crossing must occur in the vicinity of the allowed crossing hypersurface of the lowest doublet and quartet potential energy surfaces. In this work the electronic structure aspects to this intersystem crossing are considered using multireference configuration interaction wave functions. The key to this treatment is a new implementation of a constrained analytic gradient search algorithm which is used to locate regions of the doublet–quartet crossing hypersurface. In those regions of nuclear coordinate space the spin–orbit coupling (matrix elements of HSO) is determined using the full microscopic Breit–Pauli spin–orbit interaction (that is both the spin–orbit and spin–other–orbit contributions are included). Included in this treatment are the largest configuration state function expansions, 700 000–900 000 terms, used to date to evaluate matrix elements HSO within the full Breit–Pauli approximation. Our conclusions are as follows. The lowest energy point on the doublet–quartet crossing hypersurface corresponds, approximately, to a C2v nuclear configuration in which the HC moiety has been inserted into a highly stretched N2 bond. The spin–orbit coupling in this region is approximately 12 cm−1. This region is estimated to be endoergic with respect to the reactant channel asymptote by approximately 7.5 kcal/mol. A second region of the crossing hypersurface corresponds to a perturbed nitrogen atom collinearly adjacent to the nitrogen side of the HCN moiety which is in its ground electronic state. The spin–orbit coupling in this region is considerably larger, approximately 44 cm−1. However, this region is estimated to be endoergic with respect to the reactant channel asymptote by over 50 kcal/mol. A qualitative Landau–Zener analysis of the electronic structure data provides the first computational evidence supporting the role of this reaction in the production of prompt NO in flame fronts.

Theoretical study of the reaction of OH with HNO

A complete-active-space (CAS) multiconfiguration self-consistent field (MCSCF) wavefunction with a polarized correlation-consistent basis set was used to determine the stationary points on the OH + HNO potential energy surface. The single-point energies were determined with a multireference configuration interaction (MRCI) wavefunction consisting of single and double excitations from selected configurations chosen from the reference wavefunction. Saddle points were confirmed at the five-electron, five-active-orbital CASSCF level by calculating analytical second derivatives. Segments of the minimum-energy paths (MEPs) for the hydrogen abstraction reaction and for the radical addition to nitrogen were calculated. It was found that the zero-point energy contribution for the abstraction pathway increases as one moves away from the MCSCF saddle point toward the reactants. An evaluation of the MRCI energy and the MCSCF zero-point energy contribution on the MEP at a few points towards the reactants suggests that the true transition state is earlier than the computed MCSCF saddle point, and that abstraction occurs with little or no activation barrier. At the MRCI level, the maximum in the vibrationally adiabatic potential along the MEP for the addition of OH to the nitrogen of HNO occurs at 5.6 kcal mol −1 above the reactants and, like the abstraction, this structure is earlier than the MCSCF saddle point. The resulting product of the OH addition, HN(O)OH, is not expected to decompose to H + HONO because the barrier to H elimination (31.4 kcal mol −1) is significantly higher than the barrier for the reaction back to OH + HNO (20.3 kcal mol −1). Statistical rate calculations have been performed for the abstraction and addition reactions, and the results are fitted to standard three-parameter temperature-dependent rate expressions.

Theoretical investigation of collision induced rotational alignment in N+2–He

Collision induced rotational alignment of N+2 ions drifting in a helium buffer gas is studied by quantum closed coupled calculations using an ab initio interaction potential obtained from multireference configuration interaction wave functions. New formulas are derived for the tensor cross sections. For a given velocity distribution of the collisional partners a set of kinetic equations is solved under steady-state conditions. The resulting alignment parameters are found to be smaller than the experimental values for the velocity distribution assumed so far in drift tube experiments. However, by modification of the anisotropy of this distribution, good agreement between the theoretical quadrupole moments of the rotational angular momentum distributions and the corresponding experimental data can be obtained. It is shown that the attractive part of the potential has a significant influence on the collision dynamics of the N+2–He system. The closed coupled m-resolved cross sections indicate that collision induced transitions between magnetic sublevels of a single rotational state contribute more to the alignment effect than transitions between different rotational states.

Configuration interaction study of the electronic spectrum of methinophosphide, HCP

Ab initio configuration interaction (CI) studies were performed on low-lying linear and nonlinear states of methinophosphide (HCP), using large basis sets with polarization and s, p Rydberg functions, and extensive multireference CI wave functions. Potential curves for linear states of HCP as functions of RCP and RCH and for nonlinear states as functions of αHCP were obtained, from which spectroscopic constants Te, Re, and ωe were evaluated. For the X1Σ+ ground state, the energy of dissociation into H + CP and the dipole moment were also calculated. The assignment of states based on the observed spectrum had to be revised in several instances. The ã state remained 13Σ+ (or 13A′), but the [Formula: see text] state became 13A″, the [Formula: see text] state, 13Δ, the à and [Formula: see text] states remained 11A″ and 21A′, respectively, [Formula: see text] was not seen as a seperate state, and [Formula: see text] became 13Σ−. In the energy range from 0 to 8 eV, 22 linear and 11 nonlinear stable states were found. Nonlinear states were stabilized for excitations from π(9a′, 2a″) into the in-plane component of π*, 10a′. Several doubly excited states of the type π2 → π*2 were bound, lying at relatively small excitation energies.

Theoretical investigations of the structures and binding energies of Ben and Mgn(n=3–5) clusters

We have determined the equilibrium geometries and binding energies of Be and Mg trimers, tetramers and pentamers using single and double excitation coupled cluster (CCSD) and complete active space self-consistent-field (CASSCF) multireference configuration interaction (MRCI) wave functions in conjunction with extended atomic basis sets. Our best estimates of the cluster binding energies are 24, 83, and 110 kcal/mol for Be3, Be4, and Be5; and 9, 31, and 41 kcal/mol for Mg3, Mg4, Mg5, respectively. A comparison of the MRCI and CCSD results shows that even the best single-reference approach (limited to single and double excitations) is not capable of quantitative accuracy in determining the binding energies of Be and Mg clusters.

Theoretical spectroscopy of the NO radical. II. Λ doubling in the ground X 2Π state and spin–orbit effects in the excited Π states

Spin–orbit splittings of the a 4 Π and the 2Π states X, C, B, and L of the NO radical were calculated as a function of internuclear separation R using multireference configuration interaction wave functions and the potential curves presented in part I of this work. The resulting values averaged over vibrational levels, agree within a few wave numbers with the experimental data whenever available. Subsequently the R-dependent Λ splitting of the X2Π ground state is determined in a perturbation matrix procedure which is independent of Hund’s coupling cases taking into account 2Σ+, 2Σ−, 4Σ−, 4Σ+, 4Π and 2Δ states as possible perturbers. The resulting splitting (0.011 81 cm−1) of the first vibrational level of the 2Π1/2 component compares well with the experimental value of 0.011 88 cm−1. The analysis of the contributions of the various perturbers to the Λ splitting shows that the 2Σ+ states and the G2 Σ− state are dominant and determine the magnitude of the splitting. A possible change of the parity with R is indicated which also affects the magnitude of the splitting.

A general procedure for the theoretical study of the Λ-doubling

A perturbation matrix procedure for the theoretical study of Λ-doubling is suggested based on van Vlecks formalism. It is independent of Hund's coupling cases and yields directly the energy levels and wavefunctions in terms of perturber states. The procedure is applied to the X 2Π states of OH and SH whereby the perturbation matrix was constructed in the basis of large-scale multi-reference configuration interaction wavefunctions, which are computed for the X 2Π, A 2Σ+, B 2Σ+, 12Σ-, 2Δ and 4Σ- and 4Π states as a function of internuclear separation. In OH a splitting of 0·1591 cm-1 for the 2Π1/2(j = ½) state and 0·0521 cm-1 for the 2Π3/2(j = 3/2) state is calculated compared to the corresponding measured splittings of 0·1577 cm-1 and 0·0551 cm-1. For SH the corresponding splittings are 0·3062 cm-1 compared to the experimental value of 0·2814 cm-1 for the 2Π1/2 component and 0·0041 cm-1 compared to the measured value of 0·0035 cm-1 for the 2Π3/2 component. It is found that for large internuclear separations...

A multiconfiguration self-consistent-field (MCSCF) study of the bent and linear conformations of HCCN

An MCSCF procedure of the complete active space (CAS) genre has been used to predict the structures and energetics of the HCCN molecule. Full configuration interaction (CI) within the π-electron space (1πx, 1πy, 2πx, 2πy, 3πx, 3πy orbitals, six electrons) was used in these MCSCF studies. With double zeta plus polarization (DZP) and triple zeta plus double polarization (TZ2P) basis sets, the bent structure lies 6.2 and 5.7 kcal, respectively, below the linear conformation. Multireference CI wave functions reduce this energy difference significantly.