A simplified method for molecular correlation energy calculations by separation into internal and non-internal parts. Application to multiconfigurational zeroth-order wavefunctions

A simplified method of determining the molecular correlation energy by two separate calculations, one for the internal and one for the non-internal correlation energies, is extended to multiconfigurational zeroth-order wavefunctions. This extension offers the possibility of deriving correlated potential energy curves or surfaces for processes involving configurational changes. The internal correlation energy is shown to be correctly determined by an MC/CI procedure combining the use of minimal and extended basis sets. An original semi-empirical “atoms-in-molecules” method based on the L.C.A.O. expansion of the molecular wavefunction is proposed for the non-internal correlation energy calculations. This method is shown to be able to overcome some of the shortcomings of a previous populations analysis approach. Test calculations concern potential curve parameters (D _e ,T _e ,R _e ,W _e ) of the ground and some excited states of the NH, C₂, HCN and CN molecules. The results are found to be in good agreement with corresponding experimental and large CI results. Aspirant du Fonds National Belge de la Recherche Scientifique Boursier I.R.S.I.A.     

Symmetry adapted formulation of the generalized Brillouin theorem

The singly excited functions satisfying Brillouin theorem are expressed as linear combinations of configuration-state functions for any spin and spatial symmetries (atomic or molecular) and for any reference wave function. The generality of the formulation is ensured by the use of the irreducible tensor method that can be adapted to any symmetry point group of interest. The expansion coefficients are simply written as products of fractional parentage coefficients, spin- and orbit-recoupling coefficients, and phase factors. The formalism is illustrated for some atomic (K_h) and molecular (C_∞v, C_3v, and T_d) configurations. Group theoretical techniques are also used to correlate the Brillouin conditions within a chain of groups.     

Extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms. I. Methodological developments

An extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms is presented. In addition to the use of pseudo-potentials in the calculations, the consequences of this extension on the different components of the energy partition which is the basic idea of the method, is analysed. Particular emphasis is placed on the specific role played by the 3d orbitals in each of the energy components. First, at the zeroth order, the energy is found to be very sensitive to the optimization of the 3d polarization functions. Secondly, the internal correlation energy, calculated by CI, requires the optimization of distinct 3d correlation orbitals to describe adequately the strong near-degeneracy effects that occur within the valence space. Finally it is shown that the 3d orbitals contribute partially to the non-internal correlation energy and that, the atoms-in-molecule structures corresponding typically to all-external contributions are negligible. The concept of error energy is introduced in place of the non-internal correlation energy: it includes the relativistic contributions within the semi-empirical tables. Such tables are presented for second row atoms and for the chlorine atom. From these tables, predicted values for some atomic term energies, experimentally undetermined, are derived. The methodological tests are limited here to the chlorine atom which is chosen for further applications in the next paper of this series. The conclusions concerning the applicability of the method to third row atoms are however quite general.Boursier I.R.S.I.A     

Ab initio study of hydrazoic acid

SCF and CI calculations were carried out on the ground^1A state of HN₃. The equilibrium geometry and vibration frequencies were computed. The results point to a planar structure (groupC _s) but to a non-linear (170 °) N-N-N conformation. The calculated vibration frequencies are in fair agreement with experimental assignments.The dissociation path of the molecule to NH and N₂ products was investigated and compared to the isoelectronic reaction of diazomethane. The dissociation energy of hydrazoic acid is estimated to be about –8 kcal/mole, with a potential barrier to dissociation of about 30 kcal/mole.Boursier IRSIA     

A method for molecular correlation energy calculations. Application to the determination of dissociation energies of diatomic and polyatomic molecules

A simple and economical method for molecular correlation energy calculations is developed. In this method, the internal part of the correlation energy is calculated by means of a CI in a minimal basis set and the non-internal part (semi-internal and all-external) is evaluated using an original atoms-in-molecule method. It is successfully applied to the determination of dissociation energies of some diatomic (H₂, NH, C₂, CN, N₂, CO, NO, O₂, F₂) and polyatomic (H₂O, N₂O, CO₂, N₃H, CH₂N₂, CH₂CO, C₂N₂) molecules. The results are compared to those obtained using very elaborate variational methods.Aspirant du Fonds National Belge de la Recherche Scientifique.     

Theoretical study of the electronic structure of diazomethane

The least-energy dissociation path of the ground state of CH₂N₂ was determined fromab initio calculations using in a complementary way basis sets of minimal size (STO-3G) and double-zeta (DZ) quality. The results indicate that the least-energy point of attack of the N₂ molecule on CH₂ (¹ A ₁) is roughly perpendicular to the molecular plane (93 °), the C and N atoms being almost co-linear (angle C-N-N203 ° with outermost N atom pointing away from CH₂). The potential barrier of 1.2 eV found previously on theC _2v dissociation path, disappears completely along the least-energy dissociation path (point groupC _s (out-of-plane)). These findings corroborate the Woodward-Hoffman rules for this process since the outermost orbitals of the two intersecting states found in point groupC _2v (...2b ₁ and ...8a ₁) both correlate to the same irreducible representation (10á) in point groupC _s (out-of-plane).Larger basis set calculations (DZ + polarization functions on all centers, 3d _c and 3d _N developed here), were also carried out on CH₂N₂ (¹ A ₁,³ A ₂ and¹ A ₂) at the¹ A ₁ equilibrium geometry and on CH₂ (³ B ₁) and N₂ (¹ _g ⁺ ) at their respective equilibrium geometries. These calculations, together with consideration of correlation energy differences, yieldD ₀ ⁰ (CH₂N₂,¹ A ₁) = 19 kcal/mole and vertical excitation energies of 67 and 73 kcal/mole for the³ A ₂ and¹ A ₂ states respectively. The latter value is in good agreement with the measured experimental value: 72.4 kcal/mole corresponding to the maximum of intensity in the¹ A ₂¹ A ₁ absorption band.     

Extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms II. Application to HCl,HCl+, ClO and NCl molecules

A simplified method for molecular correlation energy calculations developed in I is applied to the determination of the potential curves of some diatomic chlorinated molecules HCl(¹⁺), HCl⁺(²II), ClO(²II) and NCl(X ^3–, a ¹, b ¹⁺). Dissociation energies, vibrational frequencies and equilibrium internuclear distances are derived from these curves. The ionisation potential (I _p) of HCl, the proton affinity (PA) of Cl, and the term energies of the excited states of the NCl radical are also calculated. It is shown that the results are very sensitive to correlation effects and that the correlated results converge to the corresponding experimental values within 10% for PA, D _e , T _e and _e, 2% for R _e and 0.3% for I _p. This agreement allows us to predict the following lower limits for the dissociation energies of the NCl radical: 2.14, 3.28 and 2.47 eV respectively for the X^3–, a ¹ and b ¹⁺ states. Results on HF and HF⁺ are also discussed and compared with those obtained for HCl and HCl⁺.Boursier IRSIA     

Comparative theoretical study of the dissociation process of the isoelectronic molecules BH3CO,CH2CO,HNCO, CO2 and BH3N2, CH2N2, HN3, N2O

Anab initio study of the electronic structure of several 22-electrons molecules is presented. The equilibrium geometries of their ground state are calculated at the SCF level using the 6–31G basis set and are found to be in good agreement with the experimental geometries. The dissociation process of these molecules leading to the isoelectronic products CO or N₂ on the one hand and BH₃, CH₂, NH and O on the other hand is studied. The least-energy dissociation paths of the ground states determined at the SCF level are compared on the basis of electron density interactions. The dissociation energies corresponding to the two lowest dissociation channels are calculated. In these calculations, the correlation energy is taken into account using a non-variational method developed previously. The calculated values of dissociation energies are in good agreement with the existing experimental values. The results permit to predict values for HNCO, BH₃CO and CH₂N₂ and to confirm the instability of BH₃N₂.Aspirant du Fonds National Belge de la Recherche Scientifique.     

ChemInform Abstract: Equilibrium Structure and Torsional Barrier of BH3NH3.

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