MRD-CI Calculations Research Articles

MRD-CI study on the isomers SiOH and HSiO

Large scale MRD-CI calculations have been carried out for various low-lying electronic states of SiOH and HSiO. The non-linear ground state equilibrium geometries were optimized at the CI level. The more stable isomer SiOH lies 61·9 ± 4·6 kJ mol-1 below HSiO (without zero point corrections). SiOH is a π-type radical, while HSiO shows σ-character, in agreement with recent E.S.R. measurements. The electronic spectra of the two isomers are quite different. The 1 2 A″ state of SiOH (T vert. = 0·37 eV) is found to be bent, in variance with Walsh's rules, while 2 2 A′ (T vert. = 2·87 eV) is a semidiffuse state. The Rydberg series starts at 4·0 eV. The low-lying X 2 A′ and 1 2 A″ states of HSiO can be derived from two different configurations depending on geometry. The transition X 2 A′ → 1 2 A″ (T vert. = 2·59 eV) is expected to have a complex spectrum since the excited state can relax either to a linear geometry or to a strongly bent structure. The semidiffuse 42 A′ state is placed at 5·00 eV vertically. The l...

The low-lying electronic states X3Σ-, a1Δ and b1Σ+of PO-, NS-and PS-according to MRD-CI calculations

Large-scale MRD-CI computations have been carried out on the pi 4 pi *2 states X 3 Sigma -, a 1 Delta and b 11 Sigma + of PO-, NS- and PS-, using extended AO basis sets. The a 1 Delta state of NS- is found to be stable upon electron attachment, as experimentally known for the similar state of PO-. For both NS- and PO-, the zero vibrational level of the b 1 Sigma + state is predicted to be slightly more stable than the ground state of the corresponding neutral molecule, while both singlet states of PS- are placed well below X 2 Pi of neutral PS. The electron affinity of PS is estimated to be 1.60+or-0.10 eV. Spectroscopic parameters and Franck-Condon factors for electron detachment are given for NS- and PS-. The dipole moments for the ground state of the neutral molecules and all negative-ion states, are reported.

Calculation of hyperfine coupling constants

The hyperfine coupling constant for the nitrogen atom is evaluated by large-scale MRD-CI calculations. A detailed analysis of the charge density at the nucleus and the spin polarization in the 1s and 2s shell as a function of various technical parameters is undertaken. Various (s, p) AO basis sets and the influence of correlation orbitals is investigated as well as selection threshold and other properties in CI calculations. The best value, obtained for the isotropic hyperfine coupling constant in an s, p, d basis, based on theoretical judgment of ‘best’ quantities, is 9·9 MHz compared to 10·4509 MHz.

Characterization of the excited electronic states of the SH radical byab initiomethods

Ab initio MRD-CI calculations have been performed for the SH radical in its low-lying valence states as well as vertically for the first Rydberg terms (2π24s, 2π24p and 2π23d). The lowest 1 4,2Σ-, 1 2Δ and 2 2Σ+ states are found to be of valence character in the vertical region, while a Rydberg structure was suggested by an earlier ab initio study. For the bound X 2Π i and A 2Σ+ various molecular constants such as spectroscopic parameters, dipole moments, Franck-Condon factors and spin-orbit constant are reported. The predissociation of A 2Σ+ in its low-vibrational levels observed by Ramsay is confirmed to be caused by the repulsive 1 4,2Σ- states. Furthermore, a complete reassignment of the electronic structure of the experimentally measured Rydberg levels is given: all these states are found to have a 2π24s (B 2Σ- and C 2Δ), 2π23d σ (E 2Σ-) and 2π2 nd σ, n = 3–6 (D, F, G, H 2Δ) electronic configuration respectively. The E 2Σ- and C 2Δ states are classified here for the first time, while the B 2Σ- has be...

Bond functions in molecular excited states: MRD CI calculations for the A 3Σ +u, B 3Π g and W 3Δ u states of N 2

Using double-zeta plus polarization (DZP) basis sets systematically augmented with a variety of bond functions, the term dissociation energies are calculated for the A 3Σ + u, B 3Π g and W 3Δ u states of N 2. It is found that the best agreement with literature values is generally with a basis set composition of DZP augmented by a set of s, p and d orbitals at the bond midpoint. The excited state potential energy curves and spectroscopic constants for the B 3Π g state are calculated from this basis and compared with experimental values. Good agreement was obtained, considering the small basis set size, with the spectroscopic constants ω e, ω eχ e, ω e y e, B e and α e and the dissociation energy D e (e.g., D e = 3.38 (3.681, exp.), 4.75 (4.897) and 4.77(4.873) eV for the A, B and W stages, respectively). Poorer agreement was obtained for the term energy T′ 0 (7.92 versus 7.35 eV, exp., for the B state). The error in term energy arises largely from an error in the calculated 4S → 2D splitting (2.705 versus 2.383 eV, exp.), and shifting the potential curve for the B state by a constant amount leads to much improved agreement relative to the ground state. The counterpoise correction applied to the potential curve of the B state causes a drastic deterioration of the results and shows qualitatively incorrect behaviour, and is therefore not recommended for calculations of this type.

Theoretical investigation of the character of the electronic states of H 2O along a linear dissociation path leading to OH + H

A series of MRD CI calculations is presented for the linear asymmetric dissociation of singlet states of the water molecule. The present calculations complement previous work on H 2O, providing further information on conical intersections in the higher excited states and on the nature and dissociation limits of the third 1A' state in C s symmetry, which is shown to correlate with the ion-pair limit (OH − +H +). At large distances the ion-pair state is no longer the third 1A' species as other states, corresponding to the OH(X 2Π) + H(2s,2p) dissociation limit, are then lower in energy.

Is there a stable B2Π state for the CNO molecule?

We report MRD-CI calculations on the ground state X 2Π and the excited states A 2Σ + and B 2Π of the CNO molecule in linear geometry. The surfaces for oxygen and carbon extraction are calculated using a limited CI expansion of 47 configuration state functions; in the vicinity of the minima obtained with this procedure large-scale CI calculations are carried out including deter-mination of the spin-orbit splitting of the 2Π states of the minima. We find that the B 2Π state will be difficult to detect spectroscopically due to an avoided crossing just at the equilibrium geometry of the ground state at R CN = 2.25 a.u., R NO = 2.30 a.u. Accordingly we find two shallow minima for B 2Π at R CN = 2.33 a.u., R NO = 2.91 a.u. and R CN = 2.78 a.u., R NO = 2.28 a.u., respectively.

Factors involved in the accurate calculation of oscillator strengths: the A 1B 1-X 1A 1 transition of H 2O

The oscillator strength for the A 1B 1-X 1A 1 transition of water is computed by means of ab initio MRD CI calculations employing a variety of AO basis sets. The advantages of carrying out a large CI computation are emphasized in this work, withy f L and f v values of 0.0500 and 0.0576 resulting from the most extensive treatment, as compared to experimental values for these quantities of 0.046 and 0.060 ±0.006.

Ab Intitio MRD-CI calculations on protonated cyclic ethers. I. Protonation pathways involve multipotential surfaces (protonation of oxetane). II. Differences from SCF in dominant configurations upon opening non-protonated oxirane rings (epoxides)

Ab Intitio MRD-CI calculations on protonated cyclic ethers. I. Protonation pathways involve multipotential surfaces (protonation of oxetane). II. Differences from SCF in dominant configurations upon opening non-protonated oxirane rings (epoxides)

Ab initioMRD-CI calculations for the propagation step of cationic polymerization of oxetanes based on localized orbitals

In the propagation step of the cationic polymerization, oxetane reacts with the protonated oxetane formed in the initiation step, with concomitant ring opening of the protonated oxetane. To describe properly bond making or bond breaking, it is necessary to use MC-SCF or CI calculations. We have carried out ab initio MODPOT/VRDDO MRD-CI calculations (by the multireference double excitation–configuration interaction technique of Buenker and Peyerimhoff into which we have also meshed a number of desirable computational options for ab initio calculations on large molecules). The CI calculations were carried out on strictly orthogonalized localized occupied and virtual orbitals in the reaction region, with the remainder of the occupied molecular orbitals being folded into an effective CI Hamiltonian. The calculated potential energy surfaces indicate that a preferred pathway for this reaction resembles an SN2 reaction with the oxygen of the oxetane attacking linearly along the C4O direction of the protonated oxetane and inversion of the hydrogens around the C4 atom.

Potential energy hypersurfaces of H 4 in the ground and the first two singlet excited electronic states

MRD-CI calculations on the first three singlet electronic states of H 4 are presented. These calculations show that the trigonal pyramidal geometry, which has been predicted for the energy minimum in the S 2 state on the basis of the recently proposed Maximum Ionicity of the Excited State (MIES) model, is lower in energy than the corresponding planar structures. The calculated total energies at the optimum trigonal pyramidal geometry are −2.04606, −2.04603 and −2.04601 Hartree for S 0, S 1, and S 2, respectively. The corresponding energies for the kite structure are −2.14608, −2.04523 and −1.98163 Hartree while for an optimum square geometry the total energies are −2.09866, −2.02452 and −2.01822 Hartree for S 0, S 1 and S 2, respectively.

MRD-CI-study of the positive molecular ions ArHe+and ArHe2+

The first five 2Σ+ and four 2Π states of ArHe+ are studied by MRD-CI calculations. It is found that various avoided crossings between Rydberg-like and strictly repulsive states occur. The interaction between the B 2Σ+[Ar(1 S) + He+(2 S)] with the higher states predicts the appearance of Ar+ ions in their 3s3p 6, 3s 23p 44s and 3s 23p 43d states at 7·28 eV, 9·38 eV and 11·96 eV respectively; this finding is consistent with appearance potentials for Ar ions at 7·35 eV, 9·3 eV and 10·9 eV derived from observed cross sections in He+-Ar scattering experiments [1]. It is pointed out that calculated data based on single-configuration-type procedures are not satisfactory for a theoretical treatment of charge-exchange reactions. The calculated potential curves for ArHe++ include the first two 3,1Π, three 1Σ+ and one 1Δ, 3Σ+ and 3Σ- states with the dissociation limits Ar+(2 P) + He+(2 S) and Ar++(3 P, 1 D, 1 S) + He(1 S). The interactions between the repulsive Ar+ + He+ and the more bonding Ar++ + He states explain qualitatively the charge transfer reactions between Ar++ and He atoms.

Electronic structure of the radicals NF and NCl. III. The radiative lifetimes of the b 1Σ + and a 1Δ states

The radiative lifetimes of the b 1Σ + and a 1Δ states have been evaluated by perturbation expansions including X 3Σ −, a 1Δ, b 1Σ +, 1 3,1Π, 2 3,1Π, 2 3Σ − and 2 1Σ + states. All wavefunctions result from large MRD CI calculations. The b—X transition is dominated by the parallel transition moment; it is found to be much stronger than the a—X transition. The calculated radiative lifetimes of τ( 1Σ +)=18 ms, τ( 1Δ)=2.2 s for NF and τ( 1Σ +)=2.5–3.5 ms for NCl are in good accord with corresponding experimentally deduced values. The lifetime for the a 1Δ state in NCl is found to be τ( 1Δ)=1.1 s, ie. much longer than derived from a recent experiment. Its magnitude is consistent with the τ(b 1Σ +)/τ(a 1Δ) ratio of similar systems and with the decrease in lifetime from NF to NCl and is thus believed to be quite reliable. A detailed analysis of all contributions of the perturber states to the transition mechanism is made and comparison with the related data in SO, O 2 and S 2 is undertaken. The b-a transition probability dominated by the quadrupole transition is fairly constant in all the systems in the order of A = 0.013 (NF) - 0.0013 (S 2) s −1.

Ab initioMRD-CI study of the Renner-Teller effect and spin-orbit coupling in theX2π ground state of NCO

A series of MRD-CI calculations on the bending potential curve of the X 2π ground state of the NCO molecule is reported, whereby the internuclear distances have been kept at their calculated equilibrium values corresponding to r(NC) = 2·36 a.u. (1·25 A) and r(CO) = 2·23 a.u. (1·18 A). The value of the spin-orbit splitting has been calculated to first order in perturbation theory and subsequently employed in a calculation of the vibronic energy levels. The theoretical treatment employs a basis set of 40 bending functions for l 1 = K - 1 and l 2 = K + 1 respectively. Reasonably good quantitative agreement with available experimental data is noted, especially for the low-energy portion of the spectrum. The sign of the spin-orbit splitting for the individual vibronic states exhibits an abrupt change at positions where the levels of the upper Renner-Teller component 1 2 A″ lie above those of the 1 2 A′ state, an effect which is also observed for the NH2 molecule.

MRD-CI calculations for the ground state potential energy surface of Ar 3 +

Configuration interaction calculations are carried out to study the potential energy surface for the system Ar-Ar 2 + . An all-electron as well as a pseudopotential treatment is employed. It is found that in the perpendicular Ar approach the Ar 2 + partner remains essentially unchanged and the potential can be characterized by an electrostatic ion-induced dipole interaction. In the collinear mode of Ar approach the Ar 2 + bond separation increases considerably, the charge is redistributed and the interaction can be characterized as chemical bonding. The minimum on the surface is found to be the linear symmetric molecule with bond lengths of 2.62 A. The optimum structure in the perpendicular approach lies 0.13 eV above the minimum and is the T-shaped molecule in which the Ar is 3.65 A away from the midpoint of the Ar 2 + (r=2.46 A) system; the best equilateral triangle structure has a bond length of 2.99 A but is found to lie 0.64 eV above the Ar 3 + minimum. The dissociation energy into Ar 2 + + Ar is calculated to be 0.16 eV in reasonable agreement with experimental values of 0.21 eV. The potential curves for the four lowest states of Ar 2 + are also treated.

Electronic structure of the radicals NF and NCI. II. Potential energy curves for NCI

Large-scale MRD CI calculations are employed to determine the potential energy curves for the three lowest X 3Σ −, a 1Δ and b 1Σ + states of NCl with π *2 configuration, for the higher states arising from σ → π *, π → σ * and π → π* excitation and for the 2Π ion. Numerous avoided crossings are found to occur between curves in the region of internuclear separations treated. A comparison with the corresponding curves for the radicals NF, O 2 and SO is undertaken and the basic similarities and distinctions are discussed. The curves in NF and NCl are quite similar, with generally lower energy gaps in the second-row radical; they can to a large extent be constructed from the homonuclear counterpart by mixing of g and u symmetry and by taking into account the different multiplicities in the dissociation products N + Cl or F and O + O or S.

MRD CI calculations of excited states of the SiH 3 radical, including potential curves for the inversion mode and the dissociation SiH 3 → SiH 2 + H

Using the MRD CI method and large basis sets the vertical spectrum of silyl radical (SiH 3) has been calculated. The lowest excited state is the 4s Rydberg state, 41000 cm −1 (5.2 eV) above the ground state. Only one excited valence state (2 2E) was encountered, all other states are of Rydberg type. From potential curves for the inversion mode (symmetric bending motion) it was inferred that all Rydberg states are planar, whereas the valence excited state is highly pyramidalized. The investigation of the dissociation reaction SiH 3 → SiH 2 + H leads to the conclusion that the first excited state is dissociative.

AB initio MRD CI potential curves, dipole moments and zero-field splittings for the X 2Π ground states of the CF and CCl molecules

A series of ab initio MRD CI calculations at various levels of theoretical treatment is carried out for the X 2Π ground states of the CF and CCl molecules. The resulting potential energy curves lead to quite good agreement with known spectroscopic constants for these systems and also allow for the accurate computation of the corresponding vibrational wavefunctions. Particular attention is given to the dependence of the electric dipole moments and spin-orbit splittings on the choice of the one-electron basis in the CI calculations. Best agreement with experimental values for these quantities is obtained by employing the natural orbitals of X 2Π states, in which case errors of only 0.1–0.2 D and 2.0–4.0 cm −1 respectively in the computed dipole moments and zero-field splittings result.

Configuration interaction study of the oscillator strenghts for the 1A11A1 and 1A11A1 transitions of the water molecule

Abstract Oscillator strengths for transitions between the X 1 A 1 ground state of water and its B 1 A 1 and D 1 A 1 excited states are computed employing two different theoretical approaches. In one series of calculations a common orthonormal one-electron basis is employed for all of the above states, while in the other type of treatment two different, mutually non-orthogonal, sets are used; the multireference single- and double-excitation (MRD CI) method is employed in each case, with configuration selection, to generate the various electronic wavefunctions. It is found that the use of ground-state SCF MOs leads to poor convergence in the wavefunctions of the (Rydberg-type) B 1 A 1 and D 1 A 1 excited states and consequently also for the corresponding B  X and D  X f -values; this behavior is seen to be closely related to the near degeneracy of the two excited states, each of which is a mixture of the 3a 1 → 3sa 1 and 1b 1 → 3pb 1 configurations. Analogous computations with the A 1 B 1 1 b 1 → 3sa 1 MOs show much better convergence properties, and the resulting f -values compare well with what is obtained when state-specific orbital sets are employed separately for ground and excited states and non-orthonormal techniques are applied to compute the desired transition moments. These results tend to confirm previous findings which indicate conceptual and computational advantages for the calculation of excited-state wavefunctions and properties within the context of a state-specific theory. They also show that although the goal of eliminating the dependence of MRD CI calculations on the choice of MO basis is very nearly approached for energy quantities, it is less satisfactorily achieved for other properties, especially when the existence of nearly degenerate electronic states is a critical factor.

Spin-orbit splitting of the A2Π and D2Π states of BeF by ab initio MRD CI calculations

Abstract The electronic structure and energetics of the X 2 Σ + ground state and several excited states of beryllium-monofluoride have been investigated by means of the MRD CI method using a GTO DZP AO basis set. The potential curves are characterized by avoided crossings between bound ionic and repulsive covalent configurations leading to double minimum potentials in case of the second and fourth excited states, B 2 Σ + and D 2 Π. Concerning the first-order spin-orbit splitting of the A 2 Π state, the choice of one-particle functions is found to be essential for a proper description of the highly ionic charge distribution. Using parent natural orbitals the calculated spin-orbit splitting A 0 21.2 cm −1 is in excellent agreement with experiment results.