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.     

Quantum-mechanical treatment of molecules. I. Calculations of the potential energy curves and molecular constants of the ground and ionized states of N2

The self-consistent-field molecular-orbital method in LCAO (linear combination of atomic orbitals) approximation is applied to the ground and three ionized states of N₂ at a number of internuclear distances for the computation of the potential energy curves. In these calculations both the linear coefficients and the screening constants of the atomic orbitals have been optimized. The molecular constants ω_e, ω_ex_e, B_e, α_e, and R_e have also been calculated for the above states from the computed potential energy curves. The computed spectral results are compared with the experimental data as well as with the results reported by others from ab initio 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.     

Bond functions in molecular excited states: MRD CI calculations for the A3Σ+u,B3Πg and W3Δu states of N2

Using double-zeta plus polarization (DZP) basis sets systematically augmented with a variety of bond functions, the term dissociation energies are calculated for the A³Σ⁺_u, B³Π_g and W³Δ_u states of N₂. 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 B³Π_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_ey_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.     

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.     

On the equilibrium structure of MgC2 and AlC2

In order to find such unknown molecules as MgC₂ and AlC₂ in interstellar space, accurate calculations to determine the equilibrium structures of these molecules were carried out. The ab initio MCSCF and MRSDCI methods were employed in the calculations. MgNC whose rotational constant has been observed was used to check the reliability of the computational scheme. The predicted geometrical structures of MgC₂ and AlC₂ were equilateral triangles and their rotational constants were A_e = 51.55, B_e = 11.52 and C_e = 9.413 GHz for MgC₂ and A_e = 50.76, B_e = 12.00 and C_e = 9.705 GHz for AlC₂.     

Theoretical study of the static Jahn-Teller effect—I. Two-mode vibronic coupling in octahedral halocomplexes with doubly degenerate electronic states

A two-mode E_g-(a_1g+e_g) vibronic coupling is analyzed for octahedral systems. Analytic formula for the adiabatic potential surface (APS) is obtained considering quadratic vibronic terms and anharmonicities of normal vibrations as well. Potential constants, viz. five elastic force constants and three vibronic constants, are evaluated from the numerical map of the APS applying the non-linear regression analysis. Numerical values are obtained for hexahalocomplexes on the CNDO/INDO level of total energy calculations.     

Theoretical electronic studies of aluminum monobromide and aluminum monoiodide

By using CASSCF/MRCI methods, theoretical molecular calculations have been performed for 12 electronic states for AlBr molecule and 12 electronic states for AlI molecule in the representation ^2s+1Λ (neglecting spin‐orbit effects). Calculated potential energy curves are displayed. Spectroscopic constants including the harmonic vibrational wave number ω_e, the electronic energy T_e referred to the ground state and the equilibrium internuclear distance R_e are predicted for these singlet and triplet electronic states for both AlBr and AlI molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Diagrammatic perturbation theory: Potential curves for the ground state of the carbon monoxide molecule

Diagrammatic many-body perturbation theory is used to calculate the potential energy function for the X¹ σ+ state of the CO molecule near the equilibrium nuclear configuration. Spectroscopic constants are derived from a number of curves which are obtained from calculations taken through third order in the energy. By forming [2/1] Padé approximants to the constants we obtain: r_e = 1.125 Å (1.128 Å), B_e = 1.943 cm^?1 (1.9312 cm^?1), a^B_e = 0.0156 cm^?1 (0.0175 cm^?1), W_e = 2247 cm^?1 (2170 cm^?1), W_eX_e = 12.16 cm^?1 (13.29 cm^?1), where the experimental values are given in parenthesis.     

An ab initio calculation of the potential surface and rotation—vibration energies of the silyl radical

We have calculated 64 points on the ground electronic state potential energy surface of the silyl radical (SiH₃) using the MRD CI technique. This potential surface gives an inversion barrier of 1951 cm^?1 and an equilibrium geometry of r_e = 1.480 Å and α_e(HSiH) = 111.2°. Using the non-rigid invertor Hamiltonian with this potential we determine for SiH₃ that ν₁ = 2424 cm^?1, ν₂ = 778 cm^?1, ν₃ = 2106 cm^?1, and ν₄ = 976 cm^?1; the inversion splitting is calculated to be 0.11 cm^?1. Rotational constants and centrifugal distortion constants have also been calculated.     

H.T. Clarke,A handbook of organic analysis,qualitative and quantitative, (Fifth Edition), Edward Arnold,London (1975), Revised by B. Haynes,with E.C. Brick and G.G. Shone,pp. x + 291, price £12.00 (clothbound), 4.95 (paperback)

Ab initio calculations at minimal (STO-3G) and extended (4-31G) basis levels have been carried out for the cyclopropylcarbinyl radical using the unrestricted Hartree-Fock procedure. It is found that the ordering of the long-range proton isotropic hyperfine coupling constants are opposite to the results obtained from semi-empirical INDO calculations. The coupling constants for the extended basis set are a_exo = ?1.71 G, a_endo = ?4.25 G, a_β= 11.41 G, a_α1 = ?66.01 G and a_α2 = ?64.73 G.     

Sensitivity of the H + CH3 → CH4 recombination rate constant to the shape of the CH stretching potential

Using a potential-energy surface obtained in part from ab initio calculations, the H + CH₃ → CH₄ bimolecular rate constant at T = 300 K is determined from a Monte Carlo classical trajectory study. Representing the CH stretching potential with a standard Morse function instead ofthe ab initio curve increases the calculated rate constant by an order of magnitude. The experimental recombination rate constant is intermediate of the rate constants calculated with the Morse and ab initio stretching potentials.Two properties of the H + CH₃ α CH₄ potential-energy surface which significantly affect the recombination rate constant are the shape of the CH stretching potential and the attenuation of the H₃CH bending frequencies. Ab initio calculations with a hierarchy of basis sets and treatment of electron correlation indicate the latter is properly described [13]. The exact shape of the CH stretching potential is not delineated by the ab initio calculations, since the ab initio calculations are not converged for bond lengths of 2.0–3.0 Å [12]. However, the form of this stretching potential deduced from the highest-level ab initio calculations, and fit analytically by eq. (2), is significantly different from a Morse function. The experimental recombination rate constant is intermediate of the rate constants calculated with the Morse and ab initio CH stretching potentials. This indicates that the actual CH potential energy curve lies between the Morse and ab initio curves. This is consistent with the finding that potential energy curves for diatomics are not well described by a Morse function [12].     

Internal Rotation and Equilibrium Structure of the Bromonitromethane Molecule According to Gas Electron Diffraction Data and Quantum Chemical Calculations

The structure and internal rotation of the bromonitromethane molecule are studied using electron diffraction analysis and quantum chemical calculations. The electron diffraction data are analyzed within the models of a general intramolecular anharmonic force field and quantum chemical pseudoconformers to account for the adiabatic separation of a large amplitude motion associated with the internal rotation of the NO₂ group. The following experimental bond lengths and valence angles are obtained for the equilibrium orthogonal configuration of the molecule with C_s symmetry: r_e(N=O) = 1.217(5) Å, r_e(C–N) = 1.48(2) Å, r_e(C–Br) = 1.919(5) Å, ∠_еBr–C–N = 109.6(9)°, ∠_еO=N=O = 125.9(9)°. The equilibrium geometry parameters are in good agreement with CCSD(T)/cc-pVTZ calculations. Thermally averaged parameters are calculated using the equilibrium geometry and quadratic and cubic quantum chemical force constants. The barrier to internal rotation cannot be determined reliably based on the electron diffraction data used in this work. There is a 82% probability that the equilibrium configuration with orthogonal C–Br and N=O bonds is most preferable, and internal rotation barrier does not exceed 280 cm^-1, which agrees with CCSD(T)/cc-pVTZ calculations.     

Accurate potential energy curves for the group 12 dimers Zn2, Cd2, and Hg2

Potential energy curves of the electronic ground states of the group 12 dimers Zn₂ and Cd₂ were computed at the CCSD(T) level of theory, including full triple corrections $\Updelta$ T in the coupled-cluster procedure, and spin-orbit (SO) contributions from four-component coupled-cluster calculations, extrapolated to the complete basis set (CBS) limit. For Hg₂, the potential energy curve published recently (Pahl et al. in J Chem Phys 132:114301, 2010] is complemented in this work by non-relativistic calculations to quantify and discuss relativistic effects. We obtain very accurate fits of our CBS/CCSD(T) and CBS/CCSD(T)+ $\Updelta$ T data points to an analytically simple and computationally efficient extended Lennard Jones form. For the CBS/CCSD(T)+ $\Updelta$ T+SO curves, we obtain dissociation energies of D _e?=?226?cm^?1 and D _e?=?319?cm^?1 for Zn₂ and Cd₂ respectively, in very good agreement with recent theoretical calculations and experimental data. We also present equilibrium distances and rotational and vibrational spectroscopic constants to compare with available theoretical and experimental data. The results obtained for non-relativistically treated Hg₂ continue nicely the trends with increasing atom number preset by Zn₂ and Cd₂, confirming that indeed, relativistic effects account for the known peculiarities for the mercury dimer.     

Hydrogen bond studies : 79. Correlation curves for properties of hydrogen bonded water molecules based on ab initio calculations

Correlation curves have been derived from previous ab initio MO-LCAO-SCF calculations made on water molecules in hydrates. The OH-stretching frequency shifts have been correlated with: (a) ratios of the intensity of v?v_OH for bonded water to that for free water, (b) shifts in the OH-distances and (c) quadrupole coupling constants for deuterium in D₂O. Shifts in quadrupole coupling constants are also correlated with shifts in OH-distances. Comparisons have been made with experimental data and the agreement is found to be satisfactory.     

Vibrational force constants from generalized X-ray scattering factors

Generalized X-ray scattering factors have been extracted from an accurate one-electron density function of molecular hydrogen. With the approximation that the atomic densities perfectly follow the nuclei, vibrational force constants are given in terms of sum rules for the generalized X-ray scattering factors. Calculated (experimental) results for H₂ are k_e = 5.76 (5.73) mdyne Å^?1, l_e = -38.7 (~36.9) mdyne Å^?2 and m_e = 246 (235) mdyne Å^?3.     

The nature of the bonding of Li+ to H2O and NH3; A3 initio studies

Ab initio wavefunctions have been calculated for the complex of Li⁺ with NH₃ and H₂O in order to better characterize the nature of the bonding. Hartree—Fock and generalized valence bond calculations were performed using a double zeta basis plus polarization functions. The binding energies obtained at the GVB level are D_e (Li⁺ — NH₃) = 40.4 kcal/mol and D_e (Li⁺ ? H₂O) = 37.6 kcal/mol, in reasonable agreement with experimental values. Model calculations indicate that the Li⁺ ? base bond is basically electrostatic. Small basis sets were found to lead to D_e as large as 75 kcal/mol for Li⁺ — NH₃, a significant overestimation. Repulsions due to the Li⁺ core are responsible for keeping the Li⁺ too far away for significant relaxation effects.     

Ab initio calculations for the potential curves and spin–orbit coupling of Mg2

 The ground state and several low-lying excited states of the Mg₂ dimer have been studied by means of a combination of the complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) method and coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] scheme. Reasonably good agreement with experiment has been obtained for the CCSD(T) ground-state potential curve but the dissociation energy of the only experimentally known A¹Σ _u ⁺ excited state of Mg₂ is somewhat overestimated at the CASSCF/CASPT2 level. The spectroscopic constants D _e, R _e and ω_e deduced from the calculated potential curves for other states are also reported. In addition, some spin–orbit matrix elements between the excited singlet and triplet states of Mg₂ have been evaluated as a function of internuclear separation. Received: 10 May 2001 / Accepted: 15 August 2001 / Published online: 30 October 2001     

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.     

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.