Self-consistent molecular hartree—fock—slater calculations. IV. On electron densities,spectroscopic constants and proton affinities of some small molecules

The use of the Xα exchange approximation in calculations on small molecules is studied. Electron densities are very similar to Hartree—Fock densities, as judged from density difference maps. The statistical total energy, E_Xα, is used in order to calculate R_eB_e, ω₃ and D_e of a series of diatomic molecules. The agreement with experiment is again similar to that in Hartree—Fock calculations. Proton affinities can also be calculated very well. The Hartree—Fock—Slater and Hartree—Fock models show on the whole very analogous behaviour. These results are obtained by using accurate, unapproximated, potentials and densities.     

Perturbation treatment of the Hartree–Fock equations of 1s2p3s 4Pθ state of the lithium isoelectronic sequence

The first order Hartree–Fock equations of the 1s2p3s ⁴P⁰ state of the three-electron atomic systems have been solved exactly. These solutions are used to evaluate Hartree–Fock energy up to third order with high accuracy. The third order Hartree–Fock energies for Li to Ne⁷⁺ are compared with those derived from experiment and other theoretical calculations.     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

Atomic Xα calculations based on EHFS(α) = Eexp

The total energies and one-electron energies for first- and second-row atoms were calculated by using the Hartree–Fock and the Hartree–Fock-Slater Hamiltonian with X_α orbitals, u_i(α_exp); α was parametrized from E^HFS (α_exp) = E^exp. The E^HF (α_exp) total energies are always higher than the Hartree–Fock energies for the atoms. The relation of the calculated ionization potential to the experimental ionization potential depends on the α used to define u_i(α), α_exp, or α_HF.     

MRCI study on spectroscopic parameters and molecular constants of the ground state of AsP(X1Σ+) molecule

The potential energy curve (PEC) for the ground state of AsP(X¹Σ⁺) has been investigated by the highly accurate valence internally contracted multireference configuration interaction method in the Molpro2008 program package with the correlation consistent basis set. The PEC is fitted to the analytic Murrrell–Sorbie function (M–S function) from which the spectroscopic constants are determined. The present D_e, B_e, α_e, ω_eχ_e, R_e, and ω_e values are of 4.2823 eV, 0.188622 cm^?1, 0.000749 cm^?1, 1.984427 cm^?1, 2.0194 Å, and 598.60 cm^?1, respectively. In addition, by numerically solving the radial Schrödinger equation of nuclear motion in the adiabatic approximation, the total of 96 vibration states is predicted when the rotational quantum number J = 0. The complete vibration levels, classical turning points, inertial rotation, and centrifugal distortion constants are reproduced. Comparison has been made with recent theoretical and experimental data. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000     

150−230 nm Chemiluminescence from C,CN and CO and observation of C(3P, 1D) in the N/C2F4 and N/O2/C2F4 reactions

Addition of C₂F₄ to a flowing nitrogen afterglow gives rise to CN(E²ΣA²Π, X²Σ), CN(F² ΔA²Π) and C (156.1, 165.5 and 193.0 nm) chemiluminescence. Transitions have been observed from CN(E²Σ) up to ν′ = 2 from which vibrational constants for this state have been recalculated to be ω_eχ_e = 13.8 cm^?1 and ω_e = 1698.4 cm^?1. Ground state and metasrable C(³P, ¹D) have been detected and studied via resonance fluorescence. Addition of O₂ to the N/C₂F₄ reaction system reduces C and CN emission intensities and [C] while giving rise to CO(a³Π-X¹Σ), CO(A¹ΠX¹Σ) and NO(B²ΠX²Π) emission. Probable excitation mechanisms are discussed.     

Absorption spectrum of manganian andalusite: Cluster calculation by an ab initio method

The ground state and the first few excited states of an MnO₆^9? cluster are calculated in the unrestricted Hartree–Fock model. The state ordering is ⁵B_{1 g}, ⁵A_{1 g}, ⁵B_{2 g}, and ⁵E_g as can be expected from simpler models. Consistent with the results by the same method for copper complexes, we obtain d–d transition energies about one half or less of the experimental energies. The charge transfer spectrum is subject to a large spin polarization in the sense that the lowest charge transfer state (⁵E_u) has five unpaired spins on Mn.     

On the ground-state properties of the germanium dimer

A theoretical evaluation of the bond length, vibrational frequency and dissociation energy of the Ge₂ molecule is reported. The effective core-potential Hartree—Fock calculations followed by extensive Cl give the following values: R_e = 4.60 bohr, ω_e = 217 cm^?1, D_e = 2.54 eV. These values are discussed and compared with those or previous theoretical work and with the available experimental data.     

The first two excited 1Σg+ states of Cs2

Laser-induced fluorescence Of Cs₂ molecules in the infrared region (4000–9000 cm^?1) has been observed using several exciting wavelengths from an argon-ion laser and from a ring dye laser. Accurate molecular constants for the first two excited ¹Σ_g⁺ electronic states are derived from spectra recorded at high resolution by Fourier transform spectroscopy. Main molecular constants are: (2)¹Σ_g⁺: T_c = 12114.090 cm^?1, ω_e = 23.350 cm^?1, B_c = 7.4.5 × 10^?3 cm^?1, R_c = 5.8316 Å; (3)¹Σ_g⁺: T_e = 15975.450 cm^?1, ω_e = 22.423 cm^?1 , B_e = 8.23 × 10^?3 cm^?1, R_c = 5.5569 Å.     

Interatomic potential for the X1Σ state of Be2, revisited

An extended geminal model has been applied to determine the interatomic potential for the X¹Σ state of Be₂. By adopting a (23s, 10p, 8d, 6f, 3g, 2h) uncontracted Gaussian‐type basis, the following spectroscopic parameters are obtained: R_e = 4.633 a.u. (4.63 a.u.), D_e = 945 ± 15 cm (790 ± 30 cm), G(1)–G(0) = 221.7 cm^?1 (223.8 ± 2 cm^?1), G(2)–G(1) = 175.0 cm^?1 (169 ± 3 cm^?1), G(3)–G(2) = 123.1 cm^?1 (122 ± 3 cm^?1), and G(4)–G(3) = 80.8 cm^?1 (79 ± 3 cm^?1), experimental values in parentheses. The calculated binding energy is substantially higher than the accepted experimental value. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Inexpensive vibrational anharmonicities from estimated derivatives: Diatomic molecules

Four alternatives are compared for estimating vibrational anharmonicity constants without explicitly calculating the expensive fourth derivatives of the potential curves. In the first, semiempirical approach, fourth derivatives for 53 diatomic molecules are estimated from ab initio second and third derivatives by using the Morse model potential. Vibrational anharmonicities ω_ex_e are then computed from the third and fourth derivatives. The second approach invokes a purely empirical linear correlation between ω_ex_e and the harmonic frequencies ω_e. The third and fourth empirical approaches suppose that the effective harmonic and anharmonic force constants are proportional (with an additive constant in the fourth approach). Experimental values for ω_ex_e are compared with empirical predictions and with semiempirical estimates based upon Hartree–Fock (HF), Møller–Plesset (MP2), and local, nonlocal, and hybrid density-functional theories (DFT), using the small 6-31G* basis set. Ab initio values of ω_e and bond lengths r_e are also compared against experiment. The (U)MP2 results are the worst and include several anomalies. The other semiempirical methods yield results of comparable accuracy for ω_ex_e of hydrides, although the DFT methods are markedly better for ω_e and r_e and for ω_ex_e of nonhydrides. The empirical estimates are nearly as good as the semiempirical ones. We conclude that: (1) both empirical and semiempirical approximations are useful for predicting stretching anharmonicity constants ω_ex_e to precisions of σ≈5 cm⁻¹ for hydrides and σ≈1.5 cm⁻¹ for nonhydrides; and (2) MP2 theory is relatively unreliable for such calculations. In addition, we find the following tests to be useful when evaluating the reliability of vibrational constants calculated at the UMP2 level: (a) the calculated values of ω_e and ω_ex_e should not deviate substantially from the empirical relations; (b) harmonic frequencies and intensities calculated at the MP2 level should be smaller than those calculated at the corresponding HF level; (c) a large distance-dependence of the spin contamination, d〈S²〉/dR≳0.05 Å⁻¹, suggests that calculated constants are too large. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1315–1324, 1998     

Large-Z and -N dependence of atomic energies from renormalization of the large-dimension limit

By combining Hartree–Fock results for nonrelativistic ground-state energies of N-electron atoms with analytic expressions for the large-dimension limit, we have obtained a simple renormalization procedure. For neutral atoms, this yields energies typically threefold more accurate than the Hartree–Fock approximation. Here, we examine the dependence on Z and N of the renormalized energies E(N, Z) for atoms and cations over the range Z, N = 2 → 290. We find that this gives for large Z = N an expansion of the same form as the Thomas–Fermi statistical model, E → Z^7/2(C₀ + C₁Z^?1/3 + C₂Z^?2/3 + C₃Z^?3/3 + ?), with similar values of the coefficients for the three leading terms. Use of the renormalized large-D limit enables us to derive three further terms. This provides an analogous expansion for the correlation energy of the form δE δZ^4/3(δC₃ + δC₅Z^?2/3 + δC₆Z^?3/3 + ?); comparison with accurate values of δE available for the range Z ? 36 indicates the mean error is only about 10%. Oscillatory terms in E and δE are also evaluated. © 1994 John Wiley & Sons, Inc.     

Methods for the calculation of spherically averaged Compton profiles with GTOs

For the first time, an analytical and efficient algorithm for the evaluation of spherically averaged reciprocal form factors B(s)=〈B( s )〉_Ω using Gauss-type basis functions is presented. The spherically averaged Compton profile is available by Fourier transformation of the reciprocal form factor. The algorithm has been successfully implemented in connection with the quantum chemistry codes GAMESS and CRYSTAL92, which perform Hartree–Fock calculations for molecules and solids. In addition, an analytical algorithm for the direct evaluation of spherically averaged Compton profiles and the moments 〈p^ν〉 (ν≥−1) via the momentum density is proposed for Gauss-type basis functions. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 213–223, 1997     

Fast calculation of excited-state potentials for rare-gas diatomic molecules: Ne2 and Ar2

A fast method for obtaining excited-state potentials of rare-gas diatomic molecules is described. Two types of excited orbitals are used: molecular orbitals calculated in the field of a singly charged molecular ion, and atomic orbitals (properly symmetrized) obtained in a similar atomic system. The RPA equations are solved within the manifold of excitations from the highest occupied orbital in each symmetry to the lowest excited orbital of either type in each symmetry. A simple model for estimating the dynamic correlation correction to excitation (and ionization) energies is given. Applications to excited states of Ne₂(^1,3Σ⁺_{g, u}, ^1,3Π_{g, u}) and Ar₂(^1,3Σ⁺_{g, u}) are described. Two-electron integral transformations involve only three orbitals of each symmetry, and the RPA matrices are four-dimensional. The computational effort required for all excited-state potentials adds less than one-tenths (in terms of computer time) to the effort involved in the preliminary ground state Hartree—Fock calculations. The resulting potentials compare favorably with more elaborate CI calculations and give good agreement with spectroscopic and scattering data. Potential curves for the molecular ions are also given.     

An accurate analytical formula for the van der Waals potentials of homonuclear rare-gas dimers with one adjustable parameter

In the present article, the Tang–Toennies–Yiu (TTY) potential model is modified by introducing one adjustable parameter. Then, the van der Waals potentials of He₂, Ne₂, Ar₂, Kr₂, and Xe₂ are calculated by this model with the adjustable parameter being determined by the well determined well depth D_e of these systems. Based on the derived potentials, the vibrational energy spacings of these systems are also calculated. It is shown that the present derived potentials and vibrational energy spacings agree well with experiment and other theoretical calculations. Finally, the normalization constant A in the asymptotic wave function of rare-gas atoms is estimated. The present derived normalization constant A is very close to the one by calculating the ratio between the Hartree–Fock function and the asymptotic wave function. The results confirm that absorbing the first-order polarization energy into the exchange energy expression is a well approximation for the present systems.     

Theoretical electronic structure of the molecule ScI

Theoretical investigation of the 18 lowest electronic states of the molecule ScI in the representation ^2S+1Λ^(±) has been performed via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. To the best of our knowledge these calculated electronic states are the first ones from ab initio methods. Thirteen electronic states between 4,500 cm^?1 and 21,000 cm^?1 have been studied for the first time and have not yet been observed experimentally. The harmonic frequency ω_e, the internuclear distance R_e, the electronic transition energy with respect to the ground state T_e, and the rotational constant B_e have been calculated for the considered electronic states. By using the canonical functions approach the eigenvalues E_υ and the rotational constants B_υ have also been calculated for the six lowest‐lying electronic states. The comparison of these results with the theoretical and the experimental data available in the literature shows a good agreement. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Theoretical study of the low‐lying electronic states of the molecular ion KRb+

The potential energy curves of the molecular ion KRb⁺ have been investigated for the 60 lowest molecular states of symmetry ²Σ⁺, ²Π, ²Δ, and Ω = 1/2, 3/2, and 5/2. Using an ab initio method, the calculation has been done in a one active electron approach based on nonempirical pseudopotentials with core valence effects taken into account through parameterized l‐dependent polarization potentials. Using the canonicals functions approach a rovibrational study is done by calculating the eigenvalues E_v, the rotational constants B_v, the centrifugal distortion constants D_v (up to 135 vibrational levels), and the spectroscopic constants ω_e and B_e for the five electronic states (1)²Σ⁺, (3)²Σ⁺, (1)²Π, (1)Ω = 1/2, and (1)Ω = 3/2. No comparison of these values with other results is yet possible because they are given here for the first time. Extensive tables of energy values of E_v, B_v, and D_v are displayed at http://hplasim2.univ‐lyon1.fr/allouche . © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

The absorption spectrum of carbon monoxide in the CO(3Π r,a) state between 215 nm and 285 nm

Bye-beam excitation of a He/CO mixture the CO(³Π _r ,a) state was sufficiently populated to allow the measurement of the absorption spectrum. The (0, 0), (1, 1), (2, 2) and (0, 1) bands of thec ³Π←a ³Π system of CO have been observed and the molecular constantsT _e =92036.0 cm^?1 (for the band head), ω _e =2249.5 cm^?1, ω _e x _e =29.5 cm^?1 have been derived for CO(c). A new electronic state withT _e =91854.3 cm^?1, ω _e =848.4 cm^?1, ω _e x _e =9.8 cm^?1,B _e =1.351 cm^?1, and α _e =0.021 cm^?1 was identified to be a³Σ state. It seems to be very likely that this state is the CO (3pσ,³Σ,j) state discussed in the literature. The results indicate a perturbation of the υ=1 levels of the new state by the CO (c,υ=0) levels. Another strong perturbation is found in the υ=4 levels. The three CO(³Σ,b,υ′=0,1,2)←CO (a,υ″=0) bands were also investigated yielding for CO(b):T _e =83778 cm^?1, ω _e =2335 cm^?1, ω _e x _e =59 cm^?1 andB _e =1.86 cm^?1.     

OH自由基的高精度量子化学研究

采用内收缩MRCI方法(Internally Contracted Multiconfiguration-Reference Configuration Interaction)研究了OH自由基, 计算得到其基态稳定构型的键长是0.09708 nm, 对应的实验值是0.096966 nm, 第一激发态的键长是0.10137 nm,实验值是0.10121 nm. 同时得到势能曲线PECs (Potential Energy Curve), 再分别由Murrell-Sorbie势能函数拟合计算和POLFIT程序计算得到OH自由基在基态X²Π和第一激发态A²Σ⁺时的光谱数据：平衡振动频率ω_e, 非谐性常数ω_eχ_e以及高阶修正ω_eY_e, 平衡转动常数B_e, 振转耦合系数α_e, 解离能D₀和垂直跃迁能量ν₀₀. 这些理论计算结果与最新的实验值非常吻合, 精确度比前人也有很大提高. 其中我们计算得到基态OH(X²Π)的解离能D₀＝35568.86 cm^－1, 第一激发态OH (A²Σ⁺)的解离能D₀＝18953.93 cm^－1, 从第一激发态A²Σ⁺ (ν＝0)到基态X²Π (v＝0)的垂直跃迁能ν₀₀＝32496.42 cm^－1.