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.     

CAS SCF/CI calculations of potential energy surfaces of He3+ and He2+

Complete active space MC SCF (CAS SCF) calculations followed by second-order configuration interaction (SOCI) calculations are carried out on the potential energy surfaces (bending surface, linear surfaces) of the ²Σ_g⁺ ground state of He₃⁺. The potential minimum for the ²Σ_g⁺ state occurs at a linear geometry with HeHe bond length of 1.248 Å. The binding energy of He₃⁺ with respect to He + He⁺ + He was calculated to be 2.47 eV at the SOCI level. The energy required to dissociate He₃⁺ (²Σ_g⁺) into He₂⁺ (²Σ_u⁺) and He(¹S) is calculated to be 0.14 eV. The same level of SOCI calculations of He₂⁺ yield a D_e value of 2.36 eV.     

The effect of bond functions on dissociation energies

The procedure employing bond functions recently suggested by Wright and Buenker has been applied to the N₂ X ¹Σ_g⁺ potential curve within the CAS SCF+MRSD Ci treatment of electron correlation. The basis set used herein is identical to that employed by these authors in their SCF+CI calculations. The D_e and the shape of the resulting potential curve, as judged by the computed vibrational levels, is not so accurate as would be expected from the results reported by Wright and Buenker. Our results indicate that using the CI superposition errors associated with bond functions to cancel basis set incompleteness depends on the treatment of the electron correlation.     

Theoretical evidence for multiple 3d bondig in the V2 and Cr2 molecules

Calculated CAS SCF potential curves are reported for the ³Σ_g^? state of V₂ and the ¹Σ_g⁺ state of Cr₂. At the CAS SCF level the ³Σ_g^? state of V₂ is calculated to be bound (R_c = 1.77 Å ω_c = 593.6 cm^?1, D_e 0.33 eV) and to involve a triple 3d bond; while the Cr₂ potential curve is not bound but shows a shoulder near the experimental R_e and the wave function shows multiple 3d bonding in this region.     

Electron spectroscopy of hydrogen fluoride resonances

Transmission electron spectroscopy has been applied to determine the energies of resonances in HF. In addition to a sharp resonance at 10.05 eV, a resonance series exhibiting both vibrational and rotational structure is resolved in the energy range between 12 eV and 13 eV and the following molecular constants are obtained: B = 20.4 cm^?1, r_e, = 0.93 Å, ω_e 0.132 eV, ω_ex_e = 0.006 eV and D_e = 0.73 eV. The resonance spectrum is analysed with reference to an electron energy loss spectrum and approximate potential energy curves are deduced. Serious discrepancies are found between the present results and the data reported by Spence and Noguchi.     

Multireference CCI calculations on the bond distance and dissociation energies of methane

Large CAS SCF and multireference CCI calculations have been performed on CH₄ to determine the bond distance, the CH bond dissociation energy and the atomization energy. The best calculatid dissociation energies are in excellent agreement with experiments with relative errors of 2% and less, but the discrepancy between theory and experiment for r_e in methane remains. The same problem is found for r_e in CH₃.     

A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach

A density matrix formulation of the super-CI MCSCF method is presented. The MC expansion is assumed to be complete in an active subset of the orbital space, and the corresponding CI secular problem is solved by a direct scheme using the unitary group approach. With a density matrix formulation the orbital optimization step becomes independent of the size of the CI expansion. It is possible to formulate the super-CI in terms of density matrices defined only in the small active subspace; the doubly occupied orbitals (the inactive subspace) do not enter. Further, in the unitary group formalism it is straightforward and simple to obtain the necessary density matrices from the symbolic formula list. It then becomes possible to treat very long MC expansions, the largest so far comprising 726 configurations. The method is demonstrated in a calculation of the potential curves for the three lowest states (¹Σ⁺_g, ³Σ⁺_u and ³Π_g) of the N₂ molecule, using a medium-sized gaussian basis set. Seven active orbitals were used yielding the following results: D_e: 8.76 (9.90), 2.43 (3.68) and 3.39 (4.90) eV; r_e: 1.108 (1.098), 1.309 (1.287) and 1.230 (1.213) Å; ω_e: 2333 (2359), 1385 (1461) and 1680 (1733) cm^?1, for the three states (experimental values within parentheses). The results of these calculations indicate that it is important to consider not only the dissociation limit but also the united atom limit in partitioning the occupied orbital space into an active and an inactive part.     

Numerical MC SCF and CI calculations of the ground-state potential energy curve of N2

The numerical procedure of McCullough is used in calculations of Hartree-Fock and MC SCF wavefunctions for ground state of N₂. The latter are derived using the complete set of 18 spin and symmetry adapted configurations in the space of MOs that arise from 2p atomic orbitals. An increase in dissociation energy of 0.17 eV is observed when compared to MC SCF calculations in a large basis of Slater-type functions and the same set of configurations. Integrals involving the numerical MC SCF MOs are used in CI calculations in which substitutions involving the 1s and 2s electrons are included. The increase in dissociation energy due to numerical versus basis set valence CI is 0.08 eV. Spectroscopic constants and molecular quadrupole moments are reported.     

The impact of higher polarization basis sets on molecular ab initio results.: III. The ground state of Cl2 in comparison with other diatomics

The ground state potential curve of Cl₂ has been computed near R_c by means of the SCF, MC SCF, CI(SD), and the recently proposed CPF methods. The convergence of the total energy, of D_c and R_c is studied with the aid of computations for various basis sets which include up to three d, two f and one g set. Higher polarization functions have a larger effect than for F₂ for all methods, the g set still affects D_c by 0.15 eV and R_c by 0.02 a₀ on the CPF level. The most elaborate calculation, on the CPF [7,4,3,2,1] level, yields D_c and R_c with an accuracy of 0.08 eV and 0.02 a₀. The same accuracy is obtained for the MC-178 CAS SCF treatment employing a 2d1f polarization basis set. The present results allow us to order the polarization functions according to their relative importance as: d⁽¹⁾ > f⁽¹⁾ > d⁽²⁾ > f⁽²⁾ = d⁽³⁾ > g⁽¹⁾ for the SCF and d⁽¹⁾ > f⁽¹⁾ > d⁽²⁾ > g⁽¹⁾ > f⁽²⁾ = d⁽³⁾ for methods including external correlation. CI(SD) or CPF. A comparison of the results for N₂, F₂, P₂, and Cl₂ shows the higher polarization functions d⁽³⁾, f⁽²⁾, g⁽¹⁾ to contribute 0.1 (F₂) to 0.3 eV (F₂, Cl₂) to D_c and affect R_c by 0.005 a₀ (N₂) to 0.01 7 a₀ (P₂).We have focused our attention mainly on the impact of the atomic basis set incompleteness on the accuracy of results obtained from various methods of computation. Cl₂ turns out to be more demanding than the first-row counterpart F₂ on all levels of theory, which is mainly due to the slower angular convergence rate for E, D_c and R_c (for Cl₂), tables 2 and 3. The more pronounced influence of higher polarization functions is already noticed on the SCF and MC SCF level: f⁽¹⁾ increases D_c by 0.18 eV and reduces R_c by 0.052 a₀ on the MC-178 level for Cl₂, table 6, typical corresponding results for F₂ are only 0.04 eV and 0.013 a₀ [1]. CAS SCF calculations furthermore appear to require larger active spaces for Cl₂, as discussed in section 3.3.On the CI(SD) or CPF level — which aim to account for the entire external correlation — one even finds a pronounced influence of the first g set which contributes ≈ 0.15 eV to D_c and reduces R_c by ≈ 0.02 a₀ (on the CPF level, table 3), the corresponding effects for F₂ were only ≈ 0.04 eV and 0.01 a₀ [1]. The 2d1f polarization basis, which will remain the “standard” large basis for treatments of tri- and tetraatomic molecules, appears to underestimate D_c by still 0.5 eV and to overestimate R_c by ≈ 0.02 a₀ for P₂ and Cl₂, table 7, and probably all molecules in-between. This conclusion emerges from the cumulative effect of adding d⁽³⁾, f⁽²⁾ and g⁽¹⁾ which amounts already to 0.3 eV and 0.015 a₀, table 7.     

On the geometrical structure and UV spectrum of the truncated icosahedral C60, molecule

The PPP CI molecular-orbital theory for three-dimensional systems has been applied to study the UV spectrum of the truncated icosahedral C₆₀ molecule. We have found that only the one-electron transitions to T_1u symmetry (4.2270,4.7498 and 6.5182 eV) have oscillator strengths different from zero. Using a bond-order-bond-length relation in SCF iteration connected to the PPP method, we have obtained two kinds of bond lengths r₁ = 1.439 Å and r₂ = 1.398 Å, which correspond to the edges of the regular pentagon and the edge of a hexagon not lying on a pentagon.     

CEPA calculations on open-shell molecules

Ab initio calculations at SCF and CEPA levels using large Gaussian basis sets have been performed for the two lowest electronic states,X ² Σ⁺ andA ² Π, of HeAr⁺. Spin-orbit coupling (SOC) effects have been added using a semiempirical treatment. The resulting potential curves for the three statesX,A ₁, andA ₂ have been used to evaluate molecular constants such as vibrational intervals ΔG(v + 1/2) and rotational constantsB _v as well as — by means of a Dunham expansion — equilibrium constants such asR _e , ω _e ,B _e etc. Comparison with the experimental data from UV emission spectroscopy shows that the calculated potential curves are slightly too shallow and have too large equilibrium distances:D _e = 242 cm^?1 andR _e = 2.66 Å compared to the experimental values of 262 cm^?1 and 2.585 Å, respectively, for theX ²Σ⁺ ground state. However, the ab initio calculations yield more bound vibrational levels than observed experimentally and allow for a more complete Dunham analysis, in particular for theA ₂ state. The experimental value of 154 cm^?1 for the dissociation energyD _e of this state is certainly too low; our best estimate is 180±5 cm^?1. For theA ₁ state our calculations are predictions since this state has not yet been observed experimentally.     

Electronic structure and bonding in the ground state of Cu2

Extended basis set calculations have been performed for the ground state of Cu₂ using CI(SD) and the coupled pair functional (CPF) method, a size-consistent modification of CI(SD). Special emphasis is given to the discussion of (i) basis saturation effects (up to g functions were included), (ii) effects of cluster corrections to achieve size consistency, (iii) relativistic effects, which were included in first order from the Cowan-Griffin operator. The final results are R_e = 4.23 au = 2.238 A, D_e = 1.84 eV, in close agreement with experimental values of 4.20 au = 2.22 A and 2.05 eV, respectively.     

The effect of bond functions on molecular dissociation energies

Multi-reference Cl calculations are reported for the ground states of HCl and N₂ at their equilibrium distances, and for their separated atoms. Basis sets of double-zeta and double-zeta plus polarization quality are systematically augmented by additional sets of functions located at the bond centers. It is shown that use of bond functions can lead to either an underestimate or an overestimate of the the bond energy. Optimum basis sets for each molecule were obtained, giving D_e values of 4.59 eV for HCl (expt. 4.62 eV) and 9.96 eV for N₂ (expt. 9.905 eV) at the estimated full Cl level. The quality of the potential curves obtained with these basis sets is discussed.     

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.     

Theoretical studies on CuF+, CuF,CuF−, CuF2, and CuF2 −

Ab initio SCF studies were performed with Cu and F basis sets of near-Hartree-Fock (HF) limit quality to obtain accurate SCF results for the molecular ground state properties of CuF⁺, CuF, CuF^–, CuF₂, and CuF₂ ^–, as well as for the first two low-lying excited states of CuF₂. A study on the effects of electron correlation was carried out by Møller-Plesset (MP) and configuration interaction (Cl) calculations. The effect of relativity on the⁶³Cu nuclear quadrupole coupling in CuF was determined by use of a coupled HF procedure for a first-order spin-orbital-averaged Pauli operator. At the HF level the⁶³Cu coupling constant was found to be 35.8 MHz (in e²qQ h^–1), while allowing for relativity the value was reduced to 29.1 MHz, which is in better agreement with the experimental value of 22.0 MHz. The calculated molecular properties for CuF [r _e = 1.737 Å,D _e=4.38 eV, _e = 562 cm^–1 (MP4);r _e= 1.796 Å,D _e = 3.91 eV, _e=585 cm^–1 (CISD)] were in good agreement with experiment (r _e = 1.745 Å,D _e = 4.43 eV, _e=623 cm^–1). The adiabatic ground-state potential curve of CuF⁺ avoids crossing near the equilibrium distance between the two ionic potential curves Cu⁺-F and Cu²⁺-F^–. At the crossing point the Cu and F electric field gradients show a sharp discontinuity.     

Configuration interaction calculation of the potential curves for the C3 molecule in its ground and lowest-lying Πu states

Ab initio SCF and Cl calculations are reported for the C₃ molecule using a basis set of double-zeta plus polarization quality. Potential curves are obtained for the symmetric stretch and bending and antisymmetric stretch vibrational coordinates for the ground and 3σ_u → l π_g^3,1Π_u excited states of this system in order to calculate the intensity distributions for the associated electronic transitions. The calculated T₀ value for the ¹Π_u ← X?¹ ∑⁺_g transition of 3.03 eV is in quite good agreement with the location of the origin of the 4050 Å (3.06 eV) band system in C₃, confirming its previous assignment to this electronic transition; the lifetime of the ¹H_u upper state is also obtained in the CI treatment. A value of 2.04 eV is calculated for the corresponding ³Π_u ← X?¹ ∑⁺_g origin, which result in turn suggests that the weak feature starting at 2.10 eV (5900 Å) should be assigned thereto.     

Negative ion photoelectron spectroscopy of teo−

We have recorded the photoelectron spectrum of Te0⁻ using a hot-cathode discharge ion source and a negative ion photoelectron spectrometer. The adiabatic electron affinity of TeO is determined to be 1.697±0.022 eV. The negative ion parameters determined in this work are: (w_e″(TeO⁻) = 690 ± 80 cm⁻¹, r_e″(TeO⁻) = 1.884 ± 0.028 Å. and D_o     

Theoretical Determination of the X1Σ+g potential of Cs2 using relativistic effective core potentials

Theoretical potential energy curves are computed for the X¹Σ⁺_g state of Cs₂ using relativistic effective core potential and a large valence gaussian basis set. Eighteen electrons are correlated by a four-reference MC SCF Cl(SD) procedure. Our best calculation (with experimental values in parenthesis) gave R_e = 9.05 (8.78) bohr and D_e = 3141 (3648 ± 8) cm?1.     

Potential energy curves for ground and excited states of NaLi from ab initio calculations with effective core polarization potentials

Sixteen low-lying electronic states of NaLi are investigated by SCF/valence Cl calculations including core polarization effects by means of an effective potential. Spectroscopic constants are obtained with estimated uncertainties of ΔR_e ? 0.01 Å, Δω_e ? 0.6 cm^?1 and ΔD_e ? 80 cm^?1. From a comparison of experimental and theoretical G(υ) values, we suggest a ground-state dissociation energy of 7093 ± 5 cm^?1. Using our rovibrational energies and recently measured excitation lines, we are able to improve the T_e values and dissociation energies of five excited states to an accuracv of ±8 cm^?1.