Theoretical studies of atmospheric molecules: SCF and correlated energy levels for the NO2, NO 2 + and NO 2 − systems

SCF and MC-SCF/CI calculations were carried out on the low-lying electronic states of NO₂, NO ₂ ⁺ and NO ₂ ^– , using a double-zeta quality basis set of contracted Gaussian functions. The calculations were performed primarily at the equilibrium geometry (R _NO = 2.25 a_o, _ONO=134 °) of theX ² A ₁ state of NO₂. SCF calculations on NO ₂ ⁺ in a linear conformation were also performed. Results are presented and compared with experiment and other calculations.Research supported in part by Air Force Delivery Orders F33615-72-M-5015 and MIPR889474-00117 and Air Force Office of Scientific Research and in part by the United States Energy Research and Development Administration.     

A CAS SCF study of reactive interactions between Be(3 P) and H2(1ε g + )

Summary TheC _2v symmetry section of the Be(³ P)+ H₂(¹ _g ⁺ ) adiabatic energy surface is investigated by using the CAS SCF method. The small active space CAS SCF calculations in the valence approximation are followed by a perturbation treatment of the dynamic, core, and core-valence contributions in the framework of the CASPT2 method. The possibility of the nonradiative chemical deactivation of the lowest triplet state of Be by the insertion mechanism is studied. The structure of the³ B ₂ reaction intermediate BeH₂ is established. The calculations show that the symmetric dissociation of this intermediate into Be(¹ S) and 2H(² S) does not involve any barrier beyond the endothermicity of the corresponding reaction. The hydrogen abstraction mechanism via a linear configuration is shown to possess the activation barrier of about 25 mH.     

Intensity distribution in the vibronic side bands of the Γ7(2 T 2g ) → Γ8(4 A 2g ) origin of ReX 6 2- doped K2PtCl6-type crystals

Intensities of vibronic transitions are calculated using an electronic vibrational coupling scheme of symmetrized and localized interactions. The model consists of an active central ion subject to a valence force field originating from nearest-neighbor displacements. The intensities of vibronic fundamentals are obtained from a generalized Lorentzian line shape function which is applied to the ₇(² T _2g ) ₈(⁴ A _2g ) transition of ReCl ₆ ^2- and ReBr ₆ ^2- in various cubic host crystals A₂MX₆ (A = Rb, Cs; M = Te, Sn, Pb; X = Cl, Br). Relative intensities of the odd vibronic side bands are calculated without knowing actual values for ligand field and spin-orbit coupling parameters, and considering only octahedral vibrational frequencies. The sidebands acquire intensity by a coupling which is cubic in the electron coordinates and linear in the nuclear normal coordinates. With some necessary approximations the present model is able to reproduce the experimental intensity distribution satisfactorily.Dedicated to Professor Dr. H. Hartmann on the occasion of his 65th birthday     

Intensity distribution in the vibronic Γ7(2 T 2g )→Γ8(4 A 2g ) transition of ReBr 6 2− in Hexahalogenostannate host crystals

The phosphorescence spectra of ReBr ₆ ^2– doped A₂SnX₆ (A = K, Rb, Cs; X = Cl, Br) have been measured at 10 K. The spectra consist of a weighted sum of progressions associated with the local modes of the ReBr ₆ ^2– center. By a fit to a generalized Lorentzian line shape function the totally symmetric distortion of the ₇(² T _2g ) excited state relative to the ₈(⁴ A _2g ) ground state has been determined.Dedicated to Professor Dr. H.-H. Schmidtke on the occasion of his 50th birthday.     

A theoretical study on the ionization of tetrafluoroethylene with analysis of vibrational structure of the photoelectron spectra

Ab initio calculations have been performed to study on the molecular structures and the vibrational levels of the low-lying ionic states (²B_2u,²A_g,²B_2g,²B_3u,²A_u,²B_1g,²B_1u, and²B_3g) of tetrafluoroethylene. The equilibrium molecular structures and vibrational modes of these states are presented. The theoretical ionization intensity curves including the vibrational structures of the low-lying eight ionic states are also presented and compared with the photoelectron spectrum. Some new assignments of the photoelectron spectra are proposed.     

Ab initio Calculations of the potential energy surface of the reaction of singlet methylene with the hydrogen molecule

The potential energy surface for the insertion of singlet methylene into H₂ has been computed on theab initio SCF level as well as with inclusion of electron correlation by means of the CEPA method. The results are compared with those of previous semiempirical,ab initio SCF and CI calculations. The system is a prototype of a reaction where an allowed and a symmetry-forbidden path can compete. The electron correlation energy was found to be very different for different regions of the surface, but did not have much influence on the optimum reaction path. From the computed heat of the reaction, the heat of formation of singlet methylene was estimated to be 101.5 kcal/mol. According to the calculations the reaction does not need any activation energy.     

Predissociation lifetime of the 1σ g 2 2σ g diabatic state of He 2 + : a one-channel approach

Summary This work is concerned with the application of a one-channel model to obtaining predissociation lifetimes and transition rates in a system of crossing diabatic states. The calculation focuses on the first shape resonance of the 1 _g ² 2 _g diabatic state of He ₂ ⁺ , which is relatively stable with respect to tunneling. This resonance predissociates as a result of the 1 _g ² 2 _g state being crossed by the 1 _g 1 _u ² dissociative diabatic state near the resonance level. We have estimated its predissociation lifetime to be of the order of 10^–11 s.     

Theoretical study of the H 5 + system

Ab initio calculations have been carried out for the ground state of H ₅ ⁺ in order to predict its equilibrium geometry, binding energy, enthalpy of formation, and the features of the H₂ · H ₃ ⁺ interaction at large and intermediate intermolecular distances. The extended basis set of Gaussian functions was carefully optimized to describe the various kinds of intermolecular interactions. Electron correlation was accounted for by means of CI calculations. Different from previous studies we find a D _2d equilibrium geometry with D _e = 7.4 kcal/mol and H ₃₀₀ ⁰ –8.7 kcal/mol. The potential surface turns out to be extremely shallow in the vicinity of the D _2d structure which results in a great mobility of the central nucleus at room temperature.     

Diatomic interactions in momentum space. The 1sσg and 2pσ u states of H 2 + system

The method of momentum electron density for interatomic interactions has been applied to the two lowest σ states of the H ₂ ⁺ system. For attractive (1sσ_g) and repulsive (2pσ _u ) interactions, the behaviour of momentum density and its effect on the stabilization energy of the system are examined quantitatively. The concept of contraction and expansion of the momentum density is shown to form an important guiding principle in this approach. The origin of covalent bonding is discussed based on the energy partitioning proposed previously.     

Adiabatic corrections for thei 3Π g state of the hydrogen molecule

Summary The adiabatic corrections of thei ³_g state of H₂ are calculated for a wide range of internuclear distances using an explicitly correlated wavefunction. The vibrational structure of this state is calculated in the adiabatic approximation. It is shown that forN=1 levels of the – substate, for which the nonadiabatic corrections are negligible, the agreement between theory and experiment is excellent; the small mass independent discrepancy of the order of 0.5–3 cm^–1 is due to the convergence error in the Born-Oppenheimer calculations. For higherN the discrepancy is much larger. However, it is mass andN-dependent and it is almost entirely due to the nonadiabatic effects caused by³_g-³_g interactions. The still larger discrepancy for the + substate of thei state is evidently caused by additional interactions of thei state with close-lying states of³ _g ⁺ symmetry.Dedicated to Prof. Klaus Ruedenberg on the occasion of his 70th birthday     

The C2H 3 + cation and its interaction with HF

The structure and stability of classical and bridged C₂H ₃ ⁺ is reinvestigated. The SCF and CEPA-PNO computations performed with flexibles andp basis sets including twod-sets on carbon confirm our previous results. We find the protonated acetylene structure to be more stable than the vinyl cation by 3.5–4 kcal/mol. The energy barrier for the interconversion of these two structures is at most a few tenths of a kcal/mol. The equilibrium SCF geometries of Weberet al. [15] are affected insignificantly by further optimization at the CEPA-PNO level. Several structures for the interaction of C₂H ₃ ⁺ with HF have been investigated at the SCF level. With our largest basis set which includes a complete set of polarization functions we find a remarkable levelling of the stabilities of most of the structures. In these cases the stabilization energy ΔE ranges from −10 to −13 kcal/mol.     

Diatomic interactions in momentum space. The 2pπ u and 3dπ g states of H 2 + system

The recently proposed method of momentum electron density for interatomic interactions is applied to the two states of the H ₂ ⁺ system. The processes of the attractive 2P _u and repulsive 3d _g interactions are analysed based on the behaviour of the momentum density and Compton profile. The results are compared with the previous ones for the 1 _{S g} and 2p _u states. The guiding principle of contraction and expansion for the energy-density relation in momentum space is shown to be common to both the and states.     

An ab initio potential energy surface and spectroscopic constants for the XΣg state of NO2

A three-dimensional potential energy function has been calculated for the X¹Σ⁺_g state of NO⁺₂ from ab initio MRD-CI data. With this PE function, converged vibrational calculations have also been performed for ten vibrational states, with the aid of a computer program developed in the present work for this purpose. The calculated harmonic frequencies, vibrational term values and rotational constants are in good agreement with experimental data.     

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.     

Vertical proton affinities of CH2O and CH2OH+ in their ground singlet,excited triplet and ionized doublet states

Vertical proton affinities were calculated with closed and open shell direct SCF-MO methods for the ground, excited triplet and ionized doublet states of CH₂O and CH₂OH⁺.The computed gas phase basicity of CH₂O follows the order: CH₂O(¹ A ₁) > CH₂O*(³ A ₁ or ³ A ₂) > CH₂O⁺(² B ₂ or ² B ₁).     

Natural spin orbital analysis of diatomic molecular wave functions in terms of generalized diatomic orbitals

Starting from the demi-H ₂ ⁺ -model for Rydberg states, ab initio calculations of the energy and the wave function for some excited states of H₂ have been carried out with the help of diatomic orbitals. The potential curves and wave functions for the following states: 2¹ _g< ^/+ , 3¹ _g< ^/+ , 1³ _g< ^/+ , 2³ _g< ^/+ , 1¹ _u< ^/+ , 2¹ _u< ^/+ , 1³ _u< ^/+ , 2³ _u< ^/+ , 3³ _u< ^/+ , 1¹ _g , 1³ _g , 1¹ _u , and 1³ _u , have been calculated by a complete CI (configuration interaction) calculation in the sense that all configurations of the state symmetry have been used which can be formed from a given basis set. From the wave functions thus obtained the natural spin orbitals are calculated subsequently to the variational calculations. The dependence of the occupation numbers of the natural spin orbitals on internuclear distance is interpreted according to the model and is used for the explanation of the special features like double minima and maxima which occur in the potential curves of H₂. For the curves of the occupation numbers a non-crossing rule in analogy to that for potential curves is valid. The potential curves for the states 1³ _g and 1³ _u have been improved by the use of linear combinations of diatomic orbitals with different nuclear charges, which allow a flexible transition to linear combinations of atomic orbitals.Dedicated to Professor Iwan N. Stranski on the occasion of his 80th birthday.     

Ab initio calculations on NO2 and NO 2 − : Optimization of diffuse Gaussian exponents

Ab initio calculations of NO₂ and NO ₂ ⁻ , using a Dunning [4s3p] basis augmented by 1 component diffuses andp functions were carried out. The SCF energies of NO₂ and NO_2/− (ground states) as a function of O _s , O _p , N _s , and N _p diffuse function exponents are given and discussed. The curves show some unexpected features which make the optimization of the diffuse function exponents problematic. The SCF vertical electron detachment energy for NO ₂ ⁻ as a function of the diffuse O _s , O _p , N _s , and N _p exponents is then discussed. Except for the case of O _p , the detachment energy is essentially independent of the O _s , N _s , and N _p exponents. Finally, results of SCF and MCSCF/CI calculations of the electron affinity of NO₂ are given and compared with experiment. Work performed under the auspices of the Division of Basic Energy Sciences of the U.S. Department of Energy. By acceptance of this article, the publisher and/or recipient acknowledges the U.S. Government's right to retain a nonexclusive, royalty-free license in and to any copyright covering this paper.     

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.     

The group-theoretical structure of the atomic g shell: connection with the alternating group <Emphasis Type="Italic">A</Emphasis><Subscript>6</Subscript> as <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>(9)

The special projective linear groups PSL(2ℓ + 1) or L ₂(2ℓ + 1) of order 2ℓ(2ℓ + 1)(ℓ + 1) can be used to study atomic shells of electrons with angular momentum quantum number ℓ corresponding to the atomic p, d, f, and g shells for ℓ = 1, 2, 3, 4, respectively. For the atomic g shell the group L ₂(9) is isomorphic with the alternating group A ₆ on six objects of order 360 or the symmetry group of the 5-dimensional simplex, a 5-dimensional analogue of the tetrahedron with 6 vertices and 15 edges. This leads to the subgroup chain SO(9) ⊃ SO(5) ⊃ L ₂(9) for the atomic g shell analogous to the subgroup chain SO(7) ⊃ G ₂ ⊃ L ₂(7) ≈⁷ O for the atomic f shell. In the L ₂(9) group only the representations of spherical harmonics or sums thereof, Γ(Y_ℓ), with dimensions dim Γ(Y_ℓ) or dim Γ(Y_ℓ) ± 1 divisible by 9 are found to be individually reducible to irreducible representations (irreps) or sums of irreps of L ₂(9). This leads to term groupings such as S, PD, G, PF, DH, L, PK, DI, FH, M, FI, PO, DN, HK, R, etc., of increasing total dimension for the irreps of SO(9) for various g ⁿ configurations in the atomic g shell.