Theoretical study of the energetics of the O3(X̃ 1A1) → O2(X 3Σ−g) + O(3P) dissociation process

The dissociation energy (D_e) for the O₃(X̃ ¹A₁) → O₂(X ³Σ⁻_g) + O(³P) process is computed using MC SCF, CI, MBPT, and CCD methods. A full-valence MC SCF calculation utilizing a [9s5p3d1f/5s3p2d1f] basis set yields a D_e value of 0.43 eV, far below the experimental value of 1.13 eV, demonstrating the importance of correlation effects involving non-valence orbitals. A CI calculation in the same basis set allowing for all single and double excitations from three-reference configuration yields a D_e value of 0.72 eV. This value is increased to 1.06 eV when the Davidson correction is included. When the number of reference configurations is increased to eight, the resulting CI calculation gives a D_e value of 0.82 eV prior to the Davidson correction and 1.10 eV after this correction.     

An extended-valence MC SCF procedure: determination of the dissociation energies of C2, N2, O2, and F2

A series of MC SCF calculations have been carried out on C₂, N₂, O₂, and F₂ with the goal of obtaining compact wavefunctions which recover a significant fraction of the electron correlation effects important for bond dissociation. The active orbital space is varied in size, with the largest spaces including the molecular orbitals derived from 2s, 2p, 3s, 3p and 4p atomic orbitals. Several basis sets ranging in size from 5s3p to 5s4p2d1f are investigated to determine the flexibility in the basis set needed with various choices of the active orbital space. The best extended-valence MC SCF (EVMC) dissociation energies are 0.2–0.5 eV less than the experimental values, indicating that further enlargement of the active orbital space is necessary to achieve 0.1 eV accuracy in the computed dissociation energies. The EVMC calculations reveal that, for the calculation of the dissociation energies, inclusion of non-valence orbitals is much more important for O₂ and F₂ than for C₂ and N₂. The EVMC results are compared with the predictions of full fourth-order perturbation theory, coupled cluster theory, and with the best available CI calculations.     

The ground-state potential curve for F2

The ground-state potential curve for F₂ has been obtained using large-scale MC SCF and CI methods. MC SCF curves were obtained with the CAS SCF method using a variety of sets of active orbitals. The main conclusion from the CAS SCF calculations is that the 2π_u orbital is important. CI curves were obtained using the contracted CI method. The largest calculations contained 312000 configurations proper spin and space (d_2h) symmetry. The main conclusions from the CI calculations are that the configuration XXX are important, otherwise errors in D_e of 0.3 eV and in r_e of 0.02 Å are found. The remaining errors at the CI level are 0.08 eV for D_e, 0.005 Å for r_e and less than 10 cm^?1 for the lowest vibrational levels.     

SCF MO CI perturbation calculations of inner shell and valence shell vertical ionization potentials

A CI method for calculating inner and valence shell vertical ionization potentials is presented. It is based on ab initio SCF MO calculations for the neutral closedshell ground state followed by CI perturbation calculations for the ground and ion states including all spin and symmetry adapted singly and doubly excited configurations with respect to the main configurations of the state of interest. The state energy is computed by performing a CI calculation for a set of selected configurations, and then adding the contributions of the remaining configurations as estimated by second order Brillouin-Wigner perturbation theory. The use of the same set of MO's for all states together with the CI perturbation method makes the method rather rapid. The numerical results are, in spite of the limited Gaussian basis sets used, in good agreement with experiment.     

Mo2分子的ab initio研究

We have investigated the electronic structure and potential energy curve of molecule Mo_2 using ECP ab initio method at SCF and CI levels. Relativistic effective core potential have been used for molybdenum. It is found that the ground state of Mo_2 is ~1Σ_g~+: 1σ_g~2 1π_u~4 1δ_g~4 2σ_g~2. It is predicted that the bond length are 1.75 and 2.01 at SCF and SCF+CI, respectively, and dissociation energy are 10.3 eV and 5.2 eV. As bond length increase, the correlation energy increase rapidly, and got a reasonable dissociation procedure at SCF+Cl level.     

Valence-bond calculations with polarized atomic orbitals

A new method for computing polarized atomic orbitals (PAOs) is described: this method leads to very easy calculations. The space of the resulting PAOs is close to that of MC SCF MOs. Using these PAOs in the frame of a VB calculation has led to the same level of accuracy as the comparable MC SCF calculation for the dissociation energies and the lowest electronic transition energies of H₂, H₃ and N₂.     

Photodissociation dynamics of propynal (HCCCHO) and butynal (H3CCCCHO). Ab initio and RRKM calculations

The photodissociation dynamics of the lowest reaction channel on the electronic ground state potential surface of propynal (HCCCHO) and butynal (H₃CCCCHO), RCCCHO → RCCH+CO, with a dissociation rate constant k_diss(E), has been examined. Based on previous calculations, the geometry and the force constants of propynal's transition state were calculated at the CI(DZ+P) level and the energy profile along the reaction path determined. The barrier height of propynal is predicted to be 69.9 kcal/mol thus lying significantly below the S₁ zero-point level at 74.8 kcal/mol. With these data and the RRKM method, the unimolecular dissociation rate constant k_diss(E) was obtained. For butynal the same parameters were calculated using the less extensive SCF method. Furthermore, MC SCF CI calculations with a DZ+P basis set were used to examine the radical dissociation reaction HCCCHO →

on the T₁ potential surface. The barrier height is predicted to be 37.0 kcal/mol (without zero-point correction). These findings are discussed in the light of recent experimental results of propynal and butynal obtained in the bulk phase and in the supersonic free jet.     

Reliability of atomic natural orbital basis sets in calculations involving pseudopotentials

The performance of Atomic Natural Orbital (ANO) basis sets for calculations involving nonempirical core pseudopotentials has been studied by comparing the results for atomic and molecular nitrogen obtained using contracted ANO basis sets with those obtained using both the primitive set and a segmented one. The primitive set has been optimized at the SCF level for atomic N treated as a five-electron pseudo-atom, and consists of 7s and 7p primitive GTOs supplemented by 2d and 1f GTOs optimized at the CI level. From this primitive set three contracted [3s 3p 2d 1f] sets have been obtained. The first one has been derived from the ANOs of the neutral atom, the second has been obtained from an averaged density matrix and the third one is a segmented set. For the atom, the segmented set gives a zero contraction error at the SCF level as it must be in valence-only calculations. The ANO basis sets show some small contraction error at the SCF level but perform better in CI calculations. However, for the diatomic N₂ molecule the ANO basis sets exhibit a rather large contraction error in the calculated SCF energy. A detailed analysis of the origin of this error is reported, which shows that the conventional strategy used to derive ANO basis sets does not work very well when pseudopotentials are involved.     

An efficient second-order MC SCF method for long configuration expansions

A new second-order optimisation procedure for general MC SCF wavefunctions is described. The method shows greatly improved convergence as compared to previous methods. Using a determinant-based direct CI procedure which avoids the construction of a formula tape, very long complete active space (CAS SCF) wavefunctions can be handled. Energy averages of several states can also be optimised. Sample calculations for CH₂, FeO, and the vinoxy radical CH₂CHO with up to 178916 configurations are presented.     

Contracted Gaussian-type basis functions revisited. III. Atoms K through Kr

Six minimal basis sets of contracted Gaussian-type functions (GTFs) are developed for the third-row atoms K through Kr. The smallest and largest sets for transition metal atoms are (3333/33/3) and (8433/84/8), respectively, where a slash distinguishes the s, p, and d symmetries and single-digit figures in the parentheses denote the numbers of primitive GTFs. The two largest sets, (7433/74/7) and (8433/84/8), surpass the (62111111/33111/311) set of Schaefer et al. in the associated total energies. Our (8433/84/8) set is also superior to their (842111/631/411) set. The quality of the present basis sets is tested by self-consistent field (SCF) and configuration interaction (CI) calculations on the Cu₂ molecule. As the accuracy of the basis set increases, SCF calculations show a decrease in the dissociation energy and an increase in the equilibrium internuclear distance. The same tendencies are found in the results of CI calculations with and without a Davidson correction. All the present basis sets are freely available at the internet address: http://202.35.198.41/∼htatewak/. Received: 17 June 1998 / Accepted: 4 August 1998 / Published online: 23 November 1998     

AB initio SCF study of the electronic structure and spectrum of CuF2

MC SCF and contracted CI calculations have been performed for the three ligand-field states of CuF₂ and also for two charge-transfer states. With the most extensive basis set the calculated d-d transition energies, including a Davidson correctior for cluster effects, are 4150 cm^?1 (²11g) and 10560 cm^?1 (²Δg). These calculations were made with 98 basis functions, including of orbitals on Cu and d orbitals on F. To check the charge distribution in the molecule, calculations of the ESR g factors were also made at the SCF and CI levels of approximation. Resulting CI values are g_| = 1.93 (1.91) and g₁ = 2.76 (2.60). with corresponding experimental numbers in parentheses.     

A comparative basis-set study of NeH+ using coupled-cluster techniques

Unrestricted Hartree-Fock, coupled-cluster calculations are reported for the ground state of NeH⁺ using atomic basis sets of increasing size and accuracy for both Ne and H. The goal is to determine the basis set and coupled-cluster level of calculation needed to obtain a NeH⁺ potential energy curve of known accuracy. Here, it is shown that calculations using a quintuple zeta basis at the coupled-cluster singles and doubles level with noniterative triples, CCSD(T) , predict a Ne—H bond dissociation energy that is within about 0.01 eV of the exact Born–Oppenheimer molecular electronic structure result. Spectroscopic constants determined using the Simons–Parr–Finlan procedure are found to be in very good agreement with the experimental results. Calculations at the augmented quadruple zeta level for the two lowest triplet excited states of the NeH⁺ species are presented. Both of these states separate into ground-state Ne⁺ and H(1s). The resulting potential curves predict stable minima at the SCF, CCSD, and CCSD(T) levels with dissociation energies of about 0.07 eV. Spectroscopic constants from the potential curves and dissociation constants are reported. © 1994 John Wiley & Sons, Inc.     

Valence type vacant orbitals for configuration interaction calculations

A method is proposed to determine the valence type vacant orbitals, which are suitable for CI calculations and for the initial guess orbitals in MC SCF calculations. The method was applied to calculate the ionization energies of series of molecules and to draw the potential energy curves of various states of N₂ and N⁺₂.     

Broken orbital-symmetry and the description of hole states in the tetrahedral [CrO4]− anion. I. Introductory considerations and calculations on oxygen 1s hole states

The localization of holes in systems containing spatially equivalent sites is discussed in terms of a simple one-particle model in which quantum mechanical delocalization effects compete with essentially classical polarization or dielectric relaxation effects. The predictions of the model for a tetrahedral system like CrO^?₄ compare favourably with the results of symmetry unrestricted SCF calculations on O_1s hole states. The connection with a Cl treatment using symmetry-restricted MOs is discussed. The calculated ionization energies are finally compared with XPS measurements on Na₂CrO₄. To this end the crystal surrounding of the CrO^?₄ anion has been represented by a point charge model and the ensuing Modelung field was included in the SCF calculations. In contrast to the Td restricted result of 551.4 eV, the completely localized C_3v results of 532.6 eV is in satisfactory agreement with the experimental data which are found around 530.0 eV.     

An analysis of the through-bond interaction using the localized molecular orbitals with ab initio calculations—II : Lone-pair orbital energies in bicyclo compounds: 7-azabicyclo[2.2.1]heptane and 2-azabicyclo[2.2.2]octane,and their n-methyl derivatives

Ab intio SCF MO calculations using STO-3G basis set were performed on 7-azabicyclo[2.2.1]heptane, N-methyl-7-azabicyclo[2.2.1]heptane, 2-azabicyclo[2.2.2)octane, N-methyl-2-azabicyclo[2.2.2)octane, and their model molecules. The orbital energies obtained by these calculations were compared with the experimental ionization potentials The canonical MOs obtained for the model molecules were then transformed into the localized Mos. With the use of the localized MOs thus obtained, the lone-pair orbital energies were pursued in the light of the through-space and/or the through-bond interactions between thw specified localized MOs. As a result of this analysis, it was found that the effects of the inner shell orbitals, 1s electrons of the N atom, and of the neighbouring N-C bonds of the skeleton (through-bond interaction) play a dominant role in the interaction with the lone-pair orbitals. It was also found that the effect of the N-Me group on the lone-pair orbital energy is considerably important.     

An ab initio study of the hydrated positron

Ab initio calculations are presented for the hydration energy of the positron. Tetrahedral molecular-dipole-oriented clusters e⁺(H₂O)₄ are considered. In performing these calculations, the Hartree—Fock MO LCAO SCF approximation with the 4-31G split-valence basis set is used. The method was modified to treat the positron problem. It is shown that e⁺ in liquid water, like an electron, can be strongly solvated, with the hydration energy 0.2–0.3 eV greater than that of e⁺.     

The externally contracted CI method applied to N2

An approximate multireference CI method is presented. By grouping together configurations with the same internal parts and freezing their relative weights by the use of perturbation theory, the number of variational parameters is drastically reduced. The loss of correlation energy is shown to be usually less than 2%, and the timing is less than one ordinary CI iteration. Examples from calculations on some states of the nitrogen atom and nitrogen molecule are given. The basis set convergence for the lowest excitation energy in the atom is very slow. Less than 50% of the correlation effect is obtained at the s, p, d limit. After the inclusion of ? functions this value is improved to 83%. The dissociation energies of the molecule also show slow basis set convergence with errors of 0.5 eV even after addition of ? functions. The bond distances are, howeever, accurately reproduced with errors of less than 0.005 Å for all the states. A qualitative discussion of predissociation in the a ¹Π_g and B ³Π_gstates caused by spin–orbit interaction with the ⁵Σ_g⁺ state, is finally presented. Rapidly oscillating lifetimes between the different vibrational states are predicted.     

Theoretical study of the vertical electron affinity and ionization potentials of C3

The electron affinity and first three ionization potentials of C₃ are calculated using the multiconfigurational SCF and configuration interaction methods and by Möller-Plesset perturbation theory. Whereas Koopmans' theorem and SCF calculations indicate that the first cation state is ²Π_u, upon inclusion of correlation effects both the ²Σ_u and ²Σ_g cation states are found to lie lower in energy. CI calculations indicate that the ground state (²Π_g) anion is stable by 1.74 eV. Allowing for the error in the calculated electron affinity of the carbon atom, C₃^? is estimated to be stable by 2.0 eV, in excellent agreement with the 2.05 eV value determined from recent photodetachment measurements. No excited anion states are found to be bound at the equilibrium geometry of the neutral molecule.