Electron correlation in the GK state of the hydrogen molecule

The second excited (1)Sigma(g)(+) state of the hydrogen molecule, the so-called GK state, has a potential energy curve with double minima. At the united atom limit it converges to the 1s3d configuration of He. At large internuclear distances R, it dissociates to two separated atoms, one in the ground state and another in the 2p excited state. Radial pair density calculations and natural orbital analyses reveal unusual effect of electron correlation around the K minimum of the potential energy curve. As R>2.0 a.u., a natural orbital of sigma(u) symmetry joins the two natural orbitals of sigma(g) symmetry at smaller R. The average interelectronic distance decreases as the internuclear distance increases from R=2.0 to 3.0 a.u. Around R=3.0 a.u. the singly peaked pair density curve splits into two peaks. The inner peak can be attributed to the formation of the ionic electron configuration (1s)(2), where both 1s electrons are on the same nucleus. As the two 1s electrons run into different nuclei, one of the two 1s electrons is promoted to the 2p state, which results in the outer peak in the pair density curve. The Rydberg 1s2p configuration persists as the nuclei stretch, and becomes dominant at large R where four natural orbitals, two of sigma(g) and two of sigma(u) symmetry, become responsible.     

The Sigma(-) states of the molecular hydrogen

A class of doubly excited electronic states of the hydrogen molecule is reported. The states are of Sigma(-) symmetry and are located ca. 200,000 cm(-1) above the ground state and about 75,000 cm(-1) above the ionization threshold. The electronic wave functions employed to described these states have been expanded in the basis of exponentially correlated Gaussian (ECG) functions with the nonlinear parameters variationally optimized. The lowest (3)Sigma and (1)Sigma states dissociate into hydrogen atoms in the n = 2 state, whereas the lowest (3)Sigma and (1)Sigma states have H(n = 2) and H(n = 3) as the dissociation products. All the four states are attractive and accommodate vibrational levels. The location of the vibrational energy levels has been determined by solving the radial Schr?dinger equation within the Born-Oppenheimer approximation.     

A time-dependent wave packet study of the vibronic and spin-orbit interactions in the dynamics of Cl((2)P)+H(2)-->HCl(X (1)Sigma(g) (+))+H((2)S) reaction

We investigate the vibronic and spin-orbit (SO) coupling effects in the state-selected dynamics of the title reaction with the aid of a time-dependent wave packet approach. The ab initio potential energy surfaces of Capecchi and Werner [Science 296, 715 (2002)] have been employed for this purpose. Collinear approach of the Cl((2)P) atom to the H(2) molecule splits the degeneracy of the (2)P state and gives rise to (2)Sigma and (2)Pi electronic states. These two surfaces form a conical intersection at this geometry. These states transform as 1 (2)A('), 1 (2)A("), and 2 (2)A('), respectively, at the nonlinear configurations of the nuclei. In addition, the SO interaction due to Cl atom further splits these states into (2)Sigma(1/2), (2)Pi(3/2), and (2)Pi(1/2) components at the linear geometry. The ground-state reagent Cl((2)P(3/2))+H(2) correlates with (2)Sigma(1/2) and (2)Pi(3/2), where as the SO excited reagent Cl(*)((2)P(1/2))+H(2) correlates with (2)Pi(1/2) at the linear geometry. In order to elucidate the impact of the vibronic and SO coupling effects on the initial state-selected reactivity of these electronic states we carry out quantum scattering calculations based on a flux operator formalism and a time-dependent wave packet approach. In this work, total reaction probabilities and the time dependence of electronic population of the system by initiating the reaction on each of the above electronic states are presented. The role of conical intersection alone on the reaction dynamics is investigated with a coupled two-state model and for the total angular momentum J=0 (neglecting the electronic orbital angular momentum) both in a diabatic as well as in the adiabatic electronic representation. The SO interaction is then included and the dynamics is studied with a coupled three-state model comprising six diabatic surfaces for the total angular momentum J=0.5 neglecting the Coriolis Coupling terms of the Hamiltonian. Companion calculations are carried out for the uncoupled adiabatic and diabatic surfaces in order to explicitly reveal the impact of two different surface coupling mechanisms in the dynamics of this prototypical reaction.     

Full configuration interaction potential energy curves for the X (1)Sigma(g) (+), B (1)Delta(g), and B(') (1)Sigma(g) (+) states of C(2): a challenge for approximate methods

The C(2) molecule exhibits unusual bonding and several low-lying excited electronic states, making the prediction of its potential energy curves a challenging test for quantum chemical methods. We report full configuration interaction results for the X (1)Sigma(g) (+), B (1)Delta(g), and B(') (1)Sigma(g) (+) states of C(2), which exactly solve the electronic Schrodinger equation within the space spanned by a 6-31G( *) basis set. Within the D(2h) subgroup used by most electronic structure programs, these states all have the same symmetry ((1)A(g)), and all three states become energetically close for interatomic distances beyond 1.5 A. The quality of several single-reference ab initio methods is assessed by comparison to the benchmark results. Unfortunately, even coupled-cluster theory through perturbative triples using an unrestricted Hartree-Fock reference exhibits large nonparallelity errors (>20 kcal mol(-1)) for the ground state. The excited states are not accurately modeled by any commonly used single-reference method, nor by configuration interaction including full quadruple substitutions. The present benchmarks will be helpful in assessing theoretical methods designed to break bonds in ground and excited electronic states.     

Theoretical spectroscopy of the calcium dimer in the A 1Sigma(u)+, c3Pi(u), and a3Sigma(u)+ manifolds: an ab initio nonadiabatic treatment

Nonadiabatic theory of molecular spectra of diatomic molecules is presented. It is shown that in the fully nonadiabatic framework, the rovibrational wave functions describing the nuclear motions in diatomic molecules can be obtained from a system of coupled differential equations. The rovibrational wave functions corresponding to various electronic states are coupled through the relativistic spin-orbit coupling interaction and through different radial and angular coupling terms, while the transition intensities can be written in terms of the ground state rovibrational wave function and bound rovibrational wave functions of all excited electronic states that are electric dipole connected with the ground state. This theory was applied in the nearly exact nonadiabatic calculations of energy levels, line positions, and intensities of the calcium dimer in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states. The excited state potentials were computed using a combination of the linear response theory within the coupled-cluster singles and doubles framework for the core-core and core-valence electronic correlations and of the full configuration interaction for the valence-valence correlation, and corrected for the one-electron relativistic terms resulting from the first-order many-electron Breit theory. The electric transition dipole moment governing the A (1)Sigma(u) (+)<--X (1)Sigma(g) (+) transitions was obtained as the first residue of the frequency-dependent polarization propagator computed with the coupled-cluster method restricted to single and double excitations, while the spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction wave functions restricted to single and double excitations. Our theoretical results explain semiquantitatively all the features of the observed Ca(2) spectrum in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states.     

Ab initio calculations including electron correlation for the minimum energy path of the (1A1) CH2+(1Σ)H2→ (1A1) CH4 insertion reaction

Ab initio calculations on the SCF level and with the inclusion of valence shell electron correlation in the IEPA–PNO (independent electron pair approximation with pair natural orbitals), the PNO–CI (pair-natural-orbital configuration interaction) and the CEPA–PNO (coupled electron pair approximation with pair natural orbitals) schemes with Gaussian lobe functions of “double zeta quality” have been performed for the minimum energy path of the insertion of singlet (¹A₁) methylene to the (¹Σ)H₂ molecule to yield methane. The energy was minimized on the SCF level to all geometrical parameters for various values of the “approximate” reaction coordinate. The energy along the reaction path decreases monotonically without a barrier and the curves representing the total energy of the system as a function of approximate reaction coordinates obtained at different levels of approximations have the same shape. From the physical point of view three phases of the reaction can be distinguished (chemically two steps) with different geometrical arrangements and different internal geometries of the partners.     

Spin-orbit effect in the energy pooling reaction O2(a 1Delta)+O2(a 1Delta)-->O2(b 1Sigma)+O2(X 3Sigma)

Five-dimensional nonadiabatic quantum dynamics studies have been carried out on two new potential energy surfaces of S(2)((1)A(')) and T(7)((3)A(")) states for the title oxygen molecules collision with coplanar configurations, along with the spin-orbit coupling between them. The ab initio calculations are based on complete active state second-order perturbation theory with the 6-31+G(d) basis set. The calculated spin-orbit induced transition probability as a function of collision energy is found to be very small for this energy pooling reaction. The rate constant obtained from a uniform J-shifting approach is compared with the existing theoretical and experimental data, and the spin-orbit effect is also discussed in this electronic energy-transfer process.     

Hyperfine structures of the 2 (3)Sigma(g) (+), 3 (3)Sigma(g) (+), and 4 (3)Sigma(g) (+) states of Na(2)

The hyperfine structures of the 2 (3)Sigma(g) (+), 3 (3)Sigma(g) (+), and 4 (3)Sigma(g) (+) states of Na(2) have been resolved with sub-Doppler continuous wave perturbation facilitated optical-optical double resonance spectroscopy via A (1)Sigma(u) (+) approximately b (3)Pi(u) mixed intermediate levels. The hyperfine patterns of these three states are similar. The hyperfine splittings of the low rotational levels are all very close to the case b(betaS) limit. As the rotational quantum number increases, the hyperfine splittings become more complicated and the coupling cases become intermediate between cases b(betaS) and b(beta J) due to spin-rotation interaction. We present a detailed analysis of the hyperfine structures of these three (3)Sigma(g) (+) states, employing both case b(betaS) and b(beta J) coupling basis sets. The results show that the hyperfine splittings of the (3)Sigma(g) (+) states are mainly due to the Fermi-contact interaction. The Fermi contact constants for the two d sigma Rydberg states, the 2 (3)Sigma(g) (+) and 4 (3)Sigma(g) (+), are 245+/-5 MHz and 225+/-5 MHz, respectively, while the Fermi contact constant of the s sigma 3 (3)Sigma(g) (+) Rydberg state is 210+/-5 MHz. The diagonal spin-spin and spin-rotation constants, and nuclear spin-electronic spin dipolar interaction parameters of the 3 (3)Sigma(g) (+) and 4 (3)Sigma(g) (+) states are also obtained.     

The 39K(2) 2(3)Sigma(g)+ state: observation and analysis

The (39)K(2) 2 (3)Sigma(g) (+) state has been observed by perturbation-facilitated infrared-infrared double resonance spectroscopy and two-photon excitation. Resolved fluorescence spectra into the a (3)Sigma(u) (+) state have been recorded. The observed vibrational levels have been assigned as the v=23-25, 27, 28, 31-33, 38-45, 47, and 53 levels by comparing the observed and calculated spectra of the 2 (3)Sigma(g) (+)-->a (3)Sigma(u) (+) transitions. Molecular constants have been obtained using a global fitting procedure with a comprehensive set of experimental data. Fine and hyperfine splittings have been resolved in the excitation spectra. Perturbations between the 2 (3)Sigma(g) (+) and 2 (3)Pi(g) states were observed. The hyperfine patterns of the 2 (3)Sigma(g) (+) levels are strongly affected by the perturbation. The perturbation-free and weakly perturbed levels follow the case b(betaS) coupling scheme, while the perturbed levels follow case b(beta J) coupling. A Fermi contact constant, b(F)=65+/-10 MHz, has been obtained. Intensity anomalies of rotational lines appeared both in the 2 (3)Sigma(g) (+) approximately 2 (3)Pi(g)<--b (3)Pi(u) excitation spectra and in the 2 (3)Sigma(g) (+) approximately 2 (3)Pi(g)-->a (3)Sigma(u) (+) resolved fluorescence spectra. These intensity anomalies can be explained in terms of a quantum-mechanical interference effect.     

Identification and analysis of the perturbed c3Pi(v=1)-X 1Sigma+ and k 3Pi(v=5)-X 1Sigma+ absorption bands of carbon monoxide

Two new red-degraded bands in the room-temperature vacuum-ultraviolet absorption spectrum of carbon monoxide have been identified in the 94,000-94,500 cm(-1) energy region and analyzed. One of the bands at approximately 94,225 cm(-1) (106.1 nm) has three observable bandheads and is partially overlapped with the strong C 1Sigma+-X 1Sigma+ (1-0) transition at lower energy. It is assigned to the c 3Pi-X 1Sigma+ (1-0) transition. The other band at approximately 94,437 cm(-1) (105.9 nm) with one clear bandhead is assigned to the k 3Pi-X 1Sigma+ (5-0) transition. A strong homogeneous perturbation was found to exist between the two upper states that strongly influences the line positions and shapes of these bands. A rotational deperturbation analysis was performed and molecular rotational constants for both upper states were determined. These deperturbed molecular constants are entirely consistent with the expected values for the k 3Pi valence and c 3Pi Rydberg states. The Hamiltonian interaction term between these two states is found to be separable into vibrational and electronic factors and the electronic factor is determined to be H(e)=323+/-40 cm(-1). A discrepancy in the literature regarding the location of the c 3Pi (v=1) state is identified and discussed.     

High resolution vacuum ultraviolet emission spectrum of D(2) from 78 to 103 nm: The D (1)Pi(u)-->X (1)Sigma(g) (+) and D(') (1)Pi(u) (-)-->X (1)Sigma(g) (+) band systems

The emission spectrum of the D(2) molecule has been studied at high resolution in the vacuum ultraviolet region 78.5-102.7 nm. A detailed analysis of the two D (1)Pi(u)-->X (1)Sigma(g) (+) and D(') (1)Pi(u) (-)-->X (1)Sigma(g) (+) electronic band systems is reported. New and improved values of the level energies of the two upper states have been derived with the help of the program IDEN [V. I. Azarov, Phys. Scr. 44, 528 (1991); 48, 656 (1993)], originally developed for atomic spectral analysis. A detailed comparison is made between the observed energy levels and solutions of coupled equations using the newest ab initio potentials by Wolniewicz and co-workers [J. Chem. Phys. 103, 1792 (1995); 99, 1851 (1993); J. Mol. Spectros. 212, 208 (2002); 220, 45 (2003)] taking into account the nonadiabatic coupling terms for the D (1)Pi(u) state with the lowest electronic states B (1)Sigma(u) (+), C (1)Pi(u), and B(') (1)Sigma(u) (+). A satisfactory agreement has been found for most of the level energies belonging to the D and D(') states. The remaining differences between observation and theory are probably due to nonadiabatic couplings with other higher electronic states which were neglected in the calculations.     

Ab initio configuration interaction study of the low-lying 1Sigma+ electronic states of LiCl

Ab initio configuration interaction calculations have been performed for the X 1Sigma+ and B 1Sigma+ electronic states of LiCl. Potential energy curves, dipole moment functions, and dipole transition moments have been computed for internuclear distances between R = 2.5a0 and 50a0. Single- and double-excitation configuration interaction wave functions were constructed using molecular orbitals obtained from a two-state averaged multiconfiguration self-consistent-field calculation. This procedure yielded an accurate energy splitting between the covalent and ionic separated-atom limits. The calculated avoided crossing of the X and B state curves occurs at R = 16.2a0, in close agreement with previous calculations using a semiempirical covalent-ionic resonance model. X 1Sigma+ state spectroscopic constants are in excellent agreement with experimental values.     

A regularized inverted perturbation approach method: potential energy curve of the 4 (1)Sigma(u) (+) state in Na(2)

We describe a modification of the inverted perturbation approach method allowing to construct physically sensible potential energy curves for electronic states of diatomic molecules even when some parts of the potential are not adequately characterized by the experimental data. The method is based on a simple regularization procedure, imposing an additional constraint on the constructed potential curve. In the present work it is applied to the double minimum 4 (1)Sigma(u) (+) state of Na(2), observed experimentally by polarization labeling spectroscopy technique.     

Reaction dynamics of Si(3PJ)+O2-->SiO(X 1 Sigma+)+O studied by a crossed-beam laser-induced fluorescence technique

Oxidation reaction of the ground state Si atom was studied by using a crossed molecular beam technique at 13.0 kJ/mol of collision energy. The Si atomic beam was generated by laser vaporization and crossed with the oxygen molecular beam at right angle. Products at the crossing region were detected by the laser-induced fluorescence (LIF). The LIF of SiO(A 1 Pi-X 1 Sigma+) was used to determine the vibrational state distribution of the electronic ground state, SiO(X 1 Sigma+). The determined distribution was inverted with the maximum population at v"=4, and in good agreement with the recent quasiclassical trajectory calculation on the singlet potential energy surface. The agreement suggested that an abstraction mechanism is dominant at the collision energy studied here. One of the counterproducts, O(3PJ), was also observed by the vacuum ultraviolet LIF and the distribution of the spin-orbit levels were determined. The formation of O(3PJ) was consistent with the significant population of v"=7 and 8 states of SiO, which could be explained by the presence of the triplet product channel with higher exothermicity.     

Spin-orbit coupling in O2(v)+O2 collisions: a new energy transfer mechanism

A reduced dimensionality model is used to study the relaxation of highly vibrationally excited O(2)(X (3)Sigma(g) (-),v>/=20) in collisions with O(2)(X (3)Sigma(g) (-),v=0). Spin-orbit coupled potential energy surfaces are employed to incorporate the vibrational-to-electronic energy transfer mechanism involving the O(2)(a (1)Delta(g)) and O(2)(b (1)Sigma(g) (+)) excited states. The transition probabilities obtained show a sharp increase for v>/=26 providing the first direct evidence of the important role played by the electronic energy transfer processes in the depletion of O(2)(X (3)Sigma(g) (-),v>/=26).     

The D 1Sigma+ state of 7LiH: comparison of observations with vibronic theory

The excited D (1)Sigma(+) electronic state of (7)LiH has been observed up to near its dissociation limit by a pulsed optical-optical double resonance fluorescence depletion spectroscopic technique. An extensive vibronic calculation has been performed with a diabatic approach with purely potential couplings involving a set of eight diabatic states of (1)Sigma(+) symmetry, corresponding to seven neutral states and one ionic state. Twenty-six new vibrational levels have been observed. Both the derived vibrational energy spacings and the vibronic ones are similarly irregular. The observed spectral linewidths and vibronic resonance widths are found to vary similarly with increasing energy. Observed asymmetric spectral lineshapes may be attributed to the strong radial couplings between the discrete levels of the D (1)Sigma(+) electronic state and the continuum states of the C (1)Sigma(+) electronic state. The mutual agreement between the spectral results and the vibronic results demonstrates that the D (1)Sigma(+) electronic state of (7)LiH is better characterized by the vibronic approach.     

Evidence for the production of N4 via the N2 A3Sigma(u)+ + N2 A3Sigma(u)+ energy pooling reaction

We report mass spectrometric evidence supporting our proposed mechanistic pathway for the production of N4 through the energy pooling reaction N2 A3Sigma(u)+ + N2 A3Sigma(u)+. N2 A3Sigma(u)+ is generated from the quenching of resonantly excited xenon in a mixture of xenon, 15N2, and 14N2 that is illuminated with xenon resonant lamps (147 nm). Mass spectra are periodically taken of the mixture. Over time, we observe significant isotopic scrambling of the 15N2 and 14N2, generating 15N14N in concentrations approaching 10% (approximately 2 Torr) of the initial 15N2 concentration. Though we do not observe the direct formation of N4, the isotopic ratios indicate that an excited complex (15N2(14)N2) exists long enough so that scrambling of the nitrogen atoms can occur, offering a possible route to the formation of tetrahedral nitrogen (1Td N4).     

Spin-forbidden transitions in the vicinity of the 2 (1)pi(u) <-- X (1)sigma(g)+ band system of Rb2

We have investigated the Rb2 475 nm system by resonance enhanced two-photon ionization spectroscopy in a pulsed molecular beam. Strong extra bands accompanying the 2 (1)Pi(u) v' = 5 - 8 <-- X (1)Sigma(g)(+) v' = 0 bands were newly observed. Rotational analysis of the main and extra bands reveals that the 2 (1)Pi(u) v' = 5 - 8 levels are significantly perturbed, mainly by the 3 (3)Sigma(u)(+)(1 u) state and also by the 2 (3)Pi(u)(1 u) state. For the major perturber, 3 (3)Sigma(u)(+)(1 u), the intensity borrowing has been found to be facilitated by the 2 (1)Pi(u)-3 (3)Sigma(u)(+)(1 u) potential energy curve crossing near 21,100 cm(-1). For the vibronic-band intensities of the 2 (3)Pi(u)(1 u) v' <-- X (1)Sigma(g)(+) v' = 0 transitions observed in this spectral region, intensity borrowing was most effective when the 2 (3)Pi(u)(1 u) levels were close to the 3 (3)Sigma(u)(+)(1 u) levels. A deperturbation fit for the perturbing bands has provided the 2 (1)Pi(u)-3 (3)Sigma(u)(+)(1 u) coupling constants.