Accurate spectroscopic constants of the lowest three electronic states in halonitrenes with multireference configuration interaction

Internally contracted multireference configuration interaction (icMRCI) calculations of the ground state (X³Σ⁻), the first excited state (a¹Δ) as well as the second excited state (b¹Σ⁺) have been performed for a series of halogenated nitrenes NXs (X = Cl, Br, and I). Accurate spectroscopic constants of these lowest three electronic states of each NX were obtained in this work using MRCI methods with aug‐cc‐pVXZ (X = T, Q, 5) basis sets and complete basis set (CBS) limit. In addition, various corrections, including the Davidson correction, scalar relativistic effect, core‐valence correlation, and spin‐orbit coupling effect, have been studied in calculating spectroscopic constants, especially for heavy‐atom nitrenes. Comparisons have been made with previous computational and experimental results where available. The icMRCI + Q calculations presented in this work provide a comprehensive series of results at a consistent high level of theory for all of the halogenated nitrenes.     

Long- and intermediate-range interaction between hydrogen atoms in the B 1Σ state

The energy of the hydrogen molecule in the B ¹Σ state, for internuclear separations 12 ≦ R ≦ 20 a.u., has been computed using an 80-term variational wave function depending explicitly on the interelectronic distance. The same type of wave function has been employed in the perturbation theory approach. Using the polarization approximation, and not expanding the interaction Hamiltonian, the first-, second- and third-order energies have been computed and higher-order corrections have been estimated. The results show that in the region under consideration E and E represent the dominant contributions to the interaction energy in the B state.     

The lowest electronic states of the benzoyl ion. A molecular orbital study with configuration interaction

A configuration interaction method of molecular orbital theory shown to be accurate for the calculation of excited state energies in several aromatic systems was applied to the problem of excited states of the benzoyl ion. The excited singlet and triplet states of the benzoyl ion lie at least 3.8 eV and 2.6 eV, respectively, above the ground state. These results are not in agreement with a postulated state 20 kcal above the ground state. On the other hand, the charge distribution in excited states does agree with that postulated for the 20 kcal state. The p-hydroxy and p-cyano substituents do not greatly influence the charge distribution between the ring and the carbonyl group in either the ground or lowest excited states.     

The lowest states of the O3+ ion

A CAS SCF calculation of the potential surfaces for the lowest states of the O₃⁺ ion is reported. An assignment of the bands in the HeI photoelectron spectrum is based upon calculated vibration profiles. This assignment shows the ground state of the ion to have ²B₂ symmetry. Also the weak bands at 15.6, 16.5 and 17.5 eV are reassigned.     

A configuration interaction study of the four lowest 1∑+ states of the LiH molecule

A configuration interaction study was completed on the ¹∑⁺ states of the LiH molecule using a nonorthogonal one-electron basis in elliptical coordinates. A few wave functions with highly optimized parameters were obtained for the X¹∑⁺ and A¹∑⁺ states and combined to construct a larger wave function which gave improved results for both states over a wide range of R values. The third and fourth roots are also reported since the wave function is extensive enough to give good upper bounds for the two states. Calculations were completed for 34 values R in the range 1 ≤ R ≤ 10 bohr (b). The calculated X¹∑⁺ curve has a minimum at Re = 3.060b (3.015b), with E(Re) = ?8.0556 Hartree (H) (?8.0704), μ(Re) = ?5.89 debye (d) (?5.88d) and μ/(R dμ/dR)|_Re = 1.75 (1.80 ± 0.3). For the A¹∑⁺ state, Re = 4.928b (4.906b), E(Re) = ?7.9372H(?7.9496H), μ(Re) = +3.96d and μ/(R dμ/dR)|_Re = ?-0.471. The values in parentheses are experimental results for comparison. The numerical vibrational and rotational analysis agreed well with experiment for both states. The A¹∑⁺ state exhibited a pronounced negative anharmonicity. Both states show strong interaction of three zeroth-order configurations, the nature of which changes considerably with R. The thus far unobserved second excited state has two minima, a metastable one at R = 3.70b and another at R ≈ 10.00b. The third excited state also appears to have a minimum at R ≈ 7.00b.     

Ab initio calculations on the three lowest states of HO+2

Ab initio calculations were performed for the three lowest lying states of HO⁺₂. The ground state was found to be a bend ³A″ state. The first excited ¹A′ state cannot appropriately be described by a single determinant, therefore a MC SCF calculation was employed.     

Molecular formation and electron correlation in HeH+

A one-centre CI wave function for HeH⁺ reported by Stuart and Matsen for 0.1 ? R ? 5.0 has been analysed in detail from the viewpoint of molecular formation. Further, by means of a natural orbital analysis, it was possible to obtain some measure of the electron correlation contained within such wave functions for various R values. These effects were illustrated by means of a series of difference maps for the electron density. One- and two-particle expectation values were obtained as a function of R. Thus, it was possible to study several aspects of the influence of the proton on the electron charge cloud as we pass from He through to the united atom Li⁺. The occupation numbers within the natural expansions were compared with those which arise from a similar analysis of a two-centre wave function for HeH⁺. The “character” of such wave functions for HeH⁺, and also for He and Li⁺, were analysed and compared.     

A study of interaction in the lowest singlet and triplet states of H2

The potential energy curves of the ground state and the first excited state of H₂ are examined in terms of the electronic force acting on each nucleus. The results reveal the detailed course of events that occur when two hydrogen atoms with parallel and antiparallel electron spins approach one another from a large internuclear separation.     

OOCO+ cation I: characterization of its isomers and lowest electronic states

Accurate ab initio calculations are performed in order to investigate the stable isomers of OOCO+ and its electronic states at both the molecular and asymptotic regions. These calculations are done using large basis sets and configuration interaction methods. Our theoretical computations predict the presence of four stable forms: A global minimum where a weakly bound charge transfer complex (OOOC+) may be found. Few tenths of cm(-1) above in energy, the OOCO+ very weakly bound isomer is predicted. At 1.75 eV above OOCO+, a strongly bound centrosymmetric isomer (c-CO3+) is located. For energies >8 eV, a third isomer of C(2v) symmetry is found where one oxygen is in the center. The one-dimensional potential energy surface cuts of these electronic states reveal the existence of shallow potential wells for OOCO+ and OOOC+ and of deep potential wells for the two other forms, where electronically excited molecules can be formed at least transiently. Finally, the electronic states of each isomer should interact by spin-orbit, vibronic, Renner-Teller, and Jahn-Teller couplings in competition with isomerization processes converting one form to another.     

Vibrational motion in isotopomers of the HeH+ molecular ion: An application of the electron nuclear dynamics method

The importance of isotopic substitution as a tool for elucidation of chemical reaction events originates in the fact that the Coulombic Hamiltonian is isotopically invariant except for the nuclear kinetic energy term. Thus, in theories of isotope effects based on the Born-Oppenheimer scheme, the basic presumption is the invariance of the potential energy surface (PES). We use, however, a fully dynamic approach, called Electron Nuclear Dynamics (END), which does not require a preconstructed PES. Since the END formalism is rather different from commonly used procedures, we study the anharmonic nuclear vibration in isotopic species of the HeH⁺ molecular ion as a model problem. A single time-dependent complex parametrized determinantal wave function is used for the electrons and the nuclei are treated classically. The time evolution of the nuclear and electronic dynamical variables obtained by integration of equations of motion are reported as bond length, nuclear kinetic energy, and Mulliken populations. The molecule vibrates as a classical object. The product of the reduced mass and the square of the vibrational frequency is isotopomer invariant for any common total energy. The difference between the total energy and the nuclear kinetic energy as a function of the internuclear distance is interpreted as the average dynamic potential. © 1997 John Wiley & Sons, Inc.     

The B 1sigma+ and X 1sigma+ electronic states of hydrogen fluoride: a direct potential fit analysis

All literature pure rotational and vibration-rotational spectroscopic data on the ground X (1)Sigma(+) electronic state of HF and DF, together with the entire set of spectroscopic line positions from analyses of the B (1)Sigma(+) --> X (1)Sigma(+) emission band systems of HF and DF, have been used in a global least-squares fit to the radial Hamiltonian operators, in compact analytic form, for both electronic states. With a data set consisting of 6157 spectroscopic line positions, the reduced standard deviation of the fit was sigma = 1.028. Sets of quantum mechanically significant rotational and centrifugal distortion constants were calculated for both electronic states using Rayleigh-Schr?dinger perturbation theory.     

Accurate ab initio based multisheeted double many-body expansion potential energy surface for the three lowest electronic singlet states of H3+

The authors present diabatic and adiabatic potential energy surfaces for the three lowest electronic singlet states of H3+. The modeling of the surfaces is based on the multi-sheeted double many-body expansion method which consists of dressing the various matrix elements of the diatomics-in-molecules potential matrix with three-body terms. The avoided crossing between the two lowest states and the conical intersection between the second and the third state are accurately represented by construction.     

Current‐density functional study of the HeH+ molecular ion under a strong ultrashort magnetic field

The HeH⁺ molecular ion under an ultrashort magnetic field on the order of 10⁹ G is investigated through quantum fluid dynamics and a current‐density functional theory (CDFT) based approach, employing a vector exchange–correlation (XC) potential which depends on the electronic charge‐density as well as on the current‐density. The behavior of the exchange and correlation energies of the HeH⁺ ion is analyzed and compared with those obtained using an approach based on the time‐dependent density functional theory (TD‐DFT) under similar computational constraints but employing a scalar XC potential dependent only on the electronic charge‐density. The CDFT‐based approach yields exchange and correlation energies as well as TD electronic charge‐densities drastically different from those obtained using the TD‐DFT‐based approach particularly, at typical TD magnetic field strengths. This is attributed to the nonadiabatic effects induced by the vector XC potential of the CDFT in the oscillating charge‐density of the HeH⁺ ion, which are further explained in the terminology of quantum fluid dynamics. The vector XC potential of the CDFT‐based approach is observed to augment the magnetic interactions in the H₂ molecule and in the He ion, whereas it opposes the magnetic interactions in the HeH⁺ ion particularly, at the intermediate magnetic field strengths. © 2012 Wiley Periodicals, Inc.     

Ab initio potential curves for the lowest 1Σ+ and 3Π states of the ion CN+

Ab initio configuration-interaction calculations using a 9s5p|3s2p gaussian basis supplemented with polarization functions are presented for potential curves for the a ¹Σ⁺ and the lowest ³Π state of CN⁺. The two states are very close in energy and calculations at this level do not give an unequivocal indication of the identity of the ground state.     

Rates of radiative recombination to form HD+ and HeH+

The rates of radiative recombination to form HD⁺ and HeH⁺ along the ground electronic state potential surface have been calculated from known potentials. These exact quantum calculations are compared with a classical model. For the formation HD⁺, the classical model predicts the rate in the range of 100–1000 K. Below 100 K, the rate is dominated by the effect of low energy shape resonances. For the formation of HeH⁺, the classical model predicts the correct temperature dependence.     

Approximate wave functions for excited states: Energies and dipole moments of the 2pσ state of HeH+2

The problem of calculating approximate wave functions for an excited state, which is not the lowest of a symmetry species, has been investigated for the first excited -state of the HeH²⁺ ion. The results of calculations using explicitly orthogonalized variational trial functions are compared with results based on the linear combination of molecular Orbitals (LCMO) procedure, and with the exact values. Our values of the electronic energy and of the dipole moment are in good agreement with the exact values.

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Zusammenfassung Das Problem der Berechnung eines angeregten Zustands, der nicht der niedrigste seiner Rasse ist, wird am Beispiel des ersten angeregten -Zustands von HeH⁺² diskutiert. Energien, Dipolmomente und Übergangsmomente, erhalten mit nichtorthogonalisierten und orthogonalisierten Variationsstörungsfunktionen 0. und 1. Ordnung und mit LCMO-Funktionen, werden mit den exakten Werten verglichen.

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Résumé On étudie le problème du calcul d'une fonction d'onde approchée pour un état excité qui n'est pas le plus bas pour sa classe de symétrie, sur l'exemple du premier état excité de l'ion HeH⁺². Les résultats du calcul par utilisation de fonctions d'essai variationnelles explicitement orthogonalisées sont comparés à ceux fondés sur un procédé de combinaison linéaire des orbitales moléculaires (LCMO) et aux valeurs exactes. Nos valeurs pour l'énergie électronique et le moment dipolaire sont en bon accord avec les valeurs exactes.

     

Ab initio adiabatic and quasidiabatic potential energy surfaces of lowest four electronic states of the H+ + O2 system

Ab initio global adiabatic and quasidiabatic potential energy surfaces of lowest four electronic (1-4 (3)A(")) states of the H(+)+O(2) system have been computed in the Jacobi coordinates (R,r,γ) using Dunning's cc-pVTZ basis set at the internally contracted multireference (single and double) configuration interaction level of accuracy, which are relevant to the dynamics studies of inelastic vibrational and charge transfer processes observed in the scattering experiments. The computed equilibrium geometry parameters of the bound [HO(2)](+) ion in the ground electronic state and other parameters for the transition state for the isomerization process, HOO(+)?OOH(+) are in good quantitative agreement with those available from the high level ab initio calculations, thus lending credence to the accuracy of the potential energy surfaces. The nonadiabatic couplings between the electronic states have been analyzed in both the adiabatic and quasidiabatic frameworks by computing the nonadiabatic coupling matrix elements and the coupling potentials, respectively. It is inferred that the dynamics of energy transfer processes in the scattering experiments carried out in the range of 9.5-23 eV would involve all the four electronic states.     

Non-Born-Oppenheimer calculations of the pure vibrational spectrum of HeH+

Very accurate calculations of the pure vibrational spectrum of the HeH(+) ion are reported. The method used does not assume the Born-Oppenheimer approximation, and the motion of both the electrons and the nuclei are treated on equal footing. In such an approach the vibrational motion cannot be decoupled from the motion of electrons, and thus the pure vibrational states are calculated as the states of the system with zero total angular momentum. The wave functions of the states are expanded in terms of explicitly correlated Gaussian basis functions multipled by even powers of the internuclear distance. The calculations yielded twelve bound states and corresponding eleven transition energies. Those are compared with the pure vibrational transition energies extracted from the experimental rovibrational spectrum.     

Combined CI-HY studies of atomic states. IV. The four lowest 1S and four lowest 1P states of He and the lowest 1S and 1P states of H−1

Combined CI -HY method calculations are reported for the ground and first three excited S states of He with an error on the order of 10^?7 a.u. within the same 120-term basis. For He ¹P, the four lowest states are obtained with an error ≤2 × 10^?6 a.u. within the same 102-term basis. H^?1 S and ¹P states are also treated by the same CI -HY technique. The utility of an spd Slater-type orbital, r, v = 0, 1 basis is investigated, with indications that it might be an excellent basis for states of first row atoms.