Nonadiabatic transition probabilities for quantum systems in electromagnetic fields: Dephasing and population relaxation due to contact with a bath.

We contrast Dirac's theory of transition probabilities and the theory of nonadiabatic transition probabilities, applied to a perturbed system that is coupled to a bath. In Dirac's analysis, the presence of an excited state |k0⟩ in the time-dependent wave function constitutes a transition. In the nonadiabatic theory, a transition occurs when the wave function develops a term that is not adiabatically connected to the initial state. Landau and Lifshitz separated Dirac's excited-state coefficients into a term that follows the adiabatic theorem of Born and Fock and a nonadiabatic term that represents excitation across an energy gap. If the system remains coherent, the two approaches are equivalent. However, differences between the two approaches arise when coupling to a bath causes dephasing, a situation that was not treated by Dirac. For two-level model systems in static electric fields, we add relaxation terms to the Liouville equation for the time derivative of the density matrix. We contrast the results obtained from the two theories. In the analysis based on Dirac's transition probabilities, the steady state of the system is not an equilibrium state; also, the steady-state population ρkk,s increases with increasing strength of the perturbation and its value depends on the dephasing time T2. In the nonadiabatic theory, the system evolves to the thermal equilibrium with the bath. The difference is not simply due to the choice of basis because the difference remains when the results are transformed to a common basis.

Shannon and von Neumann entropies of multi-qubit Schrödinger's cat states.

Using IBM's publicly accessible quantum computers, we have analyzed the entropies of Schrödinger's cat states, which have the form Ψ = (1/2)1/2 [|0 0 0⋯0〉 + |1 1 1⋯1〉]. We have obtained the average Shannon entropy SSo of the distribution over measurement outcomes from 75 runs of 8192 shots, for each of the numbers of entangled qubits, on each of the quantum computers tested. For the distribution over N fault-free measurements on pure cat states, SSo would approach one as N → ∞, independent of the number of qubits; but we have found that SSo varies nearly linearly with the number of qubits n. The slope of SSoversus the number of qubits differs among computers with the same quantum volumes. We have developed a two-parameter model that reproduces the near-linear dependence of the entropy on the number of qubits, based on the probabilities of observing the output 0 when a qubit is set to |0〉 and 1 when it is set to |1〉. The slope increases as the error rate increases. The slope provides a sensitive measure of the accuracy of a quantum computer, so it serves as a quickly determinable index of performance. We have used tomographic methods with error mitigation as described in the qiskit documentation to find the density matrix ρ and evaluate the von Neumann entropies of the cat states. From the reduced density matrices for individual qubits, we have calculated the entanglement entropies. The reduced density matrices represent mixed states with approximately 50/50 probabilities for states |0〉 and |1〉. The entanglement entropies are very close to one.

Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers.

This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.

Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory.

The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.

Variance of the energy of a quantum system in a time-dependent perturbation: Determination by nonadiabatic transition probabilities.

For a quantum system in a time-dependent perturbation, we prove that the variance in the energy depends entirely on the nonadiabatic transition probability amplitudes bk(t). Landau and Lifshitz introduced the nonadiabatic coefficients for the excited states of a perturbed quantum system by integrating by parts in Dirac's expressions for the coefficients ck (1)(t) of the excited states to first order in the perturbation. This separates ck (1)(t) for each state into an adiabatic term ak (1)(t) and a nonadiabatic term bk (1)(t). The adiabatic term follows the adiabatic theorem of Born and Fock; it reflects the adjustment of the initial state to the perturbation without transitions. If the response to a time-dependent perturbation is entirely adiabatic, the variance in the energy is zero. The nonadiabatic term bk (1)(t) represents actual excitations away from the initial state. As a key result of the current work, we derive the variance in the energy of the quantum system and all of the higher moments of the energy distribution using the values of |bk(t)|2 for each of the excited states along with the energy differences between the excited states and the ground state. We prove that the same variance (through second order) is obtained in terms of Dirac's excited-state coefficients ck(t). We show that the results from a standard statistical analysis of the variance are consistent with the quantum results if the probability of excitation Pk is set equal to |bk(t)|2, but not if the probability of excitation is set equal to |ck(t)|2. We illustrate the differences between the variances calculated with the two different forms of Pk for vibration-rotation transitions of HCl in the gas phase.

The interaction-induced dipole of H2-H: New ab initio results and spherical tensor analysis.

We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the exponential operator applied to a restricted Hartree-Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r, R). For the geometrical configurations that we have studied in this work, the most important coefficients DλL(r, R) in the series expansion are D01(r, R), D21(r, R), D23(r, R), D43(r, R), and D45(r, R). We show that the ab initio results for D23(r, R) and D45(r, R) converge to the classical induction forms at large R. The convergence of D45(r, R) to the hexadecapolar induction form is demonstrated for the first time. Close agreement between the long-range ab initio values of D01(r0 = 1.449 a.u., R) and the known analytical values due to van der Waals dispersion and back induction is also demonstrated for the first time. At shorter range, D01(r, R) characterizes isotropic overlap and exchange effects, as well as dispersion. The coefficients D21(r, R) and D43(r, R) represent anisotropic overlap effects. Our results for the DλL(r, R) coefficients are useful for calculations of the line shapes for collision-induced absorption and collision-induced emission in the infrared and far-infrared by gas mixtures containing both H2 molecules and H atoms.

Dependence of the multipole moments, static polarizabilities, and static hyperpolarizabilities of the hydrogen molecule on the H-H separation in the ground singlet state.

In this work, we provide values for the quadrupole moment Θ, the hexadecapole moment Φ, the dipole polarizability α, the quadrupole polarizability C, the dipole-octopole polarizability E, the second dipole hyperpolarizability γ, and the dipole-dipole-quadrupole hyperpolarizability B for the hydrogen molecule in the ground singlet state, evaluated by finite-field configuration interaction singles and doubles (CISD) and coupled-cluster singles and doubles (CCSD) methods for 26 different H-H separations r, ranging from 0.567 a.u. to 10.0 a.u. Results obtained with various large correlation-consistent basis sets are compared at the vibrationally averaged bond length r0 in the ground state. Results over the full range of r values are presented at the CISD/d-aug-cc-pV6Z level for all of the independent components of the property tensors. In general, our values agree well with previous ab initio results of high accuracy for the ranges of H-H distances that have been treated in common. To our knowledge, for H2 in the ground state, our results are the first to be reported in the literature for Φ for r > 7.0 a.u., γ and B for r > 6.0 a.u., and C and E for any H-H separation outside a narrow range around the potential minimum. Quantum Monte Carlo values of Θ have been given previously for H-H distances out to 10.0 a.u., but the statistical error is relatively large for r > 7.0 a.u. At the larger r values in this work, αxx and αzz show the expected functional forms, to leading order in r-1. As r increases further, Θ and Φ vanish, while α, γ, and the components of B converge to twice the isolated-atom values. Components of C and E diverge as r increases. Vibrationally averaged values of the properties are reported for all of the bound states (vibrational quantum numbers υ = 0-14) with rotational quantum numbers J = 0-3.

Nonadiabatic transition probabilities in a time-dependent Gaussian pulse or plateau pulse: Toward experimental tests of the differences from Dirac's transition probabilities.

For a quantum system subject to a time-dependent perturbing field, Dirac's analysis gives the probability of transition to an excited state |k⟩ in terms of the norm square of the entire excited-state coefficient ck(t) in the wave function. By integrating by parts in Dirac's equation for ck(t) at first order, Landau and Lifshitz separated ck (1)(t) into an adiabatic term ak (1)(t) that characterizes the gradual adjustment of the ground state to the perturbation without transitions and a nonadiabatic term bk (1)(t) that depends explicitly on the time derivative of the perturbation at times t' ≤ t. Landau and Lifshitz stated that the probability of transition in a pulsed perturbation is given by |bk(t)|2, rather than by |ck(t)|2. We use the term "transition probability" to refer to the probability that a true excited-state component is present in the time-evolved wave function, as opposed to a smooth modification of the initial state. In recent work, we have examined the differences between |bk(t)|2 and |ck(t)|2 when a system is perturbed by a harmonic wave in a Gaussian envelope. We showed that significant differences exist when the frequency of the harmonic wave is off-resonance with the transition frequency. In this paper, we consider Gaussian perturbations and pulses that rise via a half Gaussian shoulder to a level plateau and later return to zero via a down-going half Gaussian. While the perturbation is constant, the transition probability |bk(t)|2 does not change. By contrast, |ck(t)|2 continues to oscillate while the perturbation is constant, and its time averaged value differs from |bk(t)|2. We suggest a general type of experiment to prove that the transition probability is given by |bk(t)|2, not |ck(t)|2. We propose a ratio test that does not require accurate knowledge of transition matrix elements or absolute field intensities.

Quantum transition probabilities during a perturbing pulse: Differences between the nonadiabatic results and Fermi's golden rule forms.

For a perturbed quantum system initially in the ground state, the coefficient ck(t) of excited state k in the time-dependent wave function separates into adiabatic and nonadiabatic terms. The adiabatic term ak(t) accounts for the adjustment of the original ground state to form the new ground state of the instantaneous Hamiltonian H(t), by incorporating excited states of the unperturbed Hamiltonian H0 without transitions; ak(t) follows the adiabatic theorem of Born and Fock. The nonadiabatic term bk(t) describes excitation into another quantum state k; bk(t) is obtained as an integral containing the time derivative of the perturbation. The true transition probability is given by bk(t) 2, as first stated by Landau and Lifshitz. In this work, we contrast bk(t) 2 and ck(t) 2. The latter is the norm-square of the entire excited-state coefficient which is used for the transition probability within Fermi's golden rule. Calculations are performed for a perturbing pulse consisting of a cosine or sine wave in a Gaussian envelope. When the transition frequency ωk0 is on resonance with the frequency ω of the cosine wave, bk(t) 2 and ck(t) 2 rise almost monotonically to the same final value; the two are intertwined, but they are out of phase with each other. Off resonance (when ωk0 ≠ ω), bk(t) 2 and ck(t) 2 differ significantly during the pulse. They oscillate out of phase and reach different maxima but then fall off to equal final values after the pulse has ended, when ak(t) ≡ 0. If ωk0 < ω, bk(t) 2 generally exceeds ck(t) 2, while the opposite is true when ωk0 > ω. While the transition probability is rising, the midpoints between successive maxima and minima fit Gaussian functions of the form a exp[-b(t - d)2]. To our knowledge, this is the first analysis of nonadiabatic transition probabilities during a perturbing pulse.

Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field.

In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gauge dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels identically with a gauge-dependent term in the usual form of the field Hamiltonian. We treat the electromagnetic field classically and treat the molecule quantum mechanically, but nonrelativistically. Our derivation starts from the Lagrangian for a set of charged particles and an electromagnetic field, with the particle coordinates, the vector potential, the scalar potential, and their time derivatives treated as the variables in the Lagrangian. We construct the full Hamiltonian using a Lagrange multiplier method originally suggested by Dirac, partition this Hamiltonian into a molecular term Hm and a field term Hf, and show that both Hm and Hf have gauge-independent expectation values. Any gauge may be chosen for the calculations; but following our partitioning, the expectation values of the molecular Hamiltonian are identical to those obtained directly in the Coulomb gauge. As a corollary of this result, the power absorbed by a molecule from a time-dependent, applied electromagnetic field is equal to the time derivative of the non-adiabatic term in the molecular energy, in any gauge.

Non-adiabatic current densities, transitions, and power absorbed by a molecule in a time-dependent electromagnetic field.

The energy of a molecule subject to a time-dependent perturbation separates completely into adiabatic and non-adiabatic terms, where the adiabatic term reflects the adjustment of the ground state to the perturbation, while the non-adiabatic term accounts for the transition energy [A. Mandal and K. L. C. Hunt, J. Chem. Phys. 137, 164109 (2012)]. For a molecule perturbed by a time-dependent electromagnetic field, in this work, we show that the expectation value of the power absorbed by the molecule is equal to the time rate of change of the non-adiabatic term in the energy. The non-adiabatic term is given by the transition probability to an excited state k, multiplied by the transition energy from the ground state to k, and then summed over the excited states. The expectation value of the power absorbed by the molecule is derived from the integral over space of the scalar product of the applied electric field and the non-adiabatic current density induced in the molecule by the field. No net power is absorbed due to the action of the applied electric field on the adiabatic current density. The work done on the molecule by the applied field is the time integral of the power absorbed. The result established here shows that work done on the molecule by the applied field changes the populations of the molecular states.

Quantum mechanical calculation of the collision-induced absorption spectra of N2-N2 with anisotropic interactions.

We present quantum mechanical calculations of the collision-induced absorption spectra of nitrogen molecules, using ab initio dipole moment and potential energy surfaces. Collision-induced spectra are first calculated using the isotropic interaction approximation. Then, we improve upon these results by considering the full anisotropic interaction potential. We also develop the computationally less expensive coupled-states approximation for calculating collision-induced spectra and validate this approximation by comparing the results to numerically exact close-coupling calculations for low energies. Angular localization of the scattering wave functions due to anisotropic interactions affects the line strength at low energies by two orders of magnitude. The effect of anisotropy decreases at higher energy, which validates the isotropic interaction approximation as a high-temperature approximation for calculating collision-induced spectra. Agreement with experimental data is reasonable in the isotropic interaction approximation, and improves when the full anisotropic potential is considered. Calculated absorption coefficients are tabulated for application in atmospheric modeling.

Ground and excited states of vanadium hydroxide isomers and their cations, VOH(0,+) and HVO(0,+).

Employing correlation consistent basis sets of quadruple-zeta quality and applying both multireference configuration interaction and single-reference coupled cluster methodologies, we studied the electronic and geometrical structure of the [V,O,H](0,+) species. The electronic structure of HVO(0,+) is explained by considering a hydrogen atom approaching VO(0,+), while VOH(0,+) molecules are viewed in terms of the interaction of V(+,2+) with OH(-). The potential energy curves for H-VO(0,+) and V(0,+)-OH have been constructed as functions of the distance between the interacting subunits, and the potential energy curves have also been determined as functions of the H-V-O angle. For the stationary points that we have located, we report energies, geometries, harmonic frequencies, and dipole moments. We find that the most stable bent HVO(0,+) structure is lower in energy than any of the linear HVO(0,+) structures. Similarly, the most stable state of bent VOH is lower in energy than the linear structures, but linear VOH(+) is lower in energy than bent VOH(+). The global minimum on the potential energy surface for the neutral species is the X(3)A" state of bent HVO, although the X(5)A" state of bent VOH is less than 5 kcal/mol higher in energy. The global minimum on the potential surface for the cation is the X(4)Σ(-) state of linear VOH(+), with bent VOH(+) and bent HVO(+) both more than 10 kcal/mol higher in energy. For the neutral species, the bent geometries exhibit significantly higher dipole moments than the linear structures.

Adiabatic and nonadiabatic contributions to the energy of a system subject to a time-dependent perturbation: complete separation and physical interpretation.

When a time-dependent perturbation acts on a quantum system that is initially in the nondegenerate ground state ∣0> of an unperturbed Hamiltonian H(0), the wave function acquires excited-state components ∣k> with coefficients c(k)(t) exp(-iE(k)t/ℏ), where E(k) denotes the energy of the unperturbed state ∣k>. It is well known that each coefficient c(k)(t) separates into an adiabatic term a(k)(t) that reflects the adjustment of the ground state to the perturbation--without actual transitions--and a nonadiabatic term b(k)(t) that yields the probability amplitude for a transition to the excited state. In this work, we prove that the energy at any time t also separates completely into adiabatic and nonadiabatic components, after accounting for the secular and normalization terms that appear in the solution of the time-dependent Schrödinger equation via Dirac's method of variation of constants. This result is derived explicitly through third order in the perturbation. We prove that the cross-terms between the adiabatic and nonadiabatic parts of c(k)(t) vanish, when the energy at time t is determined as an expectation value. The adiabatic term in the energy is identical to the total energy obtained from static perturbation theory, for a system exposed to the instantaneous perturbation λH'(t). The nonadiabatic term is a sum over excited states ∣k> of the transition probability multiplied by the transition energy. By evaluating the probabilities of transition to the excited eigenstates ∣k'(t)> of the instantaneous Hamiltonian H(t), we provide a physically transparent explanation of the result for E(t). To lowest order in the perturbation parameter λ, the probability of finding the system in state ∣k'(t)> is given by λ(2) ∣b(k)(t)∣(2). At third order, the transition probability depends on a second-order transition coefficient, derived in this work. We indicate expected differences between the results for transition probabilities obtained from this work and from Fermi's golden rule.

Infrared absorption by collisional H2-He complexes at temperatures up to 9000 K and frequencies from 0 to 20,000 cm(-1).

Quantum chemical methods have been used elsewhere to obtain the potential energy surface (PES) and the induced dipole surface (IDS) of H(2)-He collisional complexes at eight different H-H bond distances, fifteen atom-molecule separations, and 19 angular orientations each [X. Li, A. Mandal, E. Miliordos, and K. L. C. Hunt, J. Chem. Phys. 136, 044320 (2012)]. An atom-molecule state-to-state scattering formalism is employed, which couples the collisional molecular complex to the electromagnetic radiation field. In this way, we obtain theoretical collision-induced absorption (CIA) spectra of H(2)-He complexes for frequencies from 0 to 20,000 cm(-1) and temperatures up to 9000 K. The work is based on the fundamental theory and is motivated by current research of certain astronomical objects, such as cool white dwarf stars, cool main sequence stars, M dwarfs, exoplanets, so-called "first" stars. We compare our theoretical results to existing laboratory measurements of CIA spectra; very close agreement of theory and measurement is observed. We also discuss similar previous theoretical efforts.

Interaction-induced dipoles of hydrogen molecules colliding with helium atoms: a new ab initio dipole surface for high-temperature applications.

We report new ab initio results for the interaction-induced dipole moments Δµ of hydrogen molecules colliding with helium atoms. These results are needed in order to calculate collision-induced absorption spectra at high temperatures; applications include modeling the radiative profiles of very cool white dwarf stars, with temperatures from 3500 K to 9000 K. We have evaluated the dipoles based on finite-field calculations, with coupled cluster methods in MOLPRO 2006 and aug-cc-pV5Z (spdfg) basis sets for both the H and He centers. We have obtained values of Δµ for eight H(2) bond lengths ranging from 0.942 a.u. to 2.801 a.u., for 15 intermolecular separations R ranging from 2.0 a.u. to 10.0 a.u., and for 19 different relative orientations. In general, our values agree well with earlier ab initio results, for the geometrical configurations that are treated in common, but we have determined more points on the collision-induced dipole surface by an order of magnitude. These results make it possible to calculate transition probabilities for molecules in excited vibrational states, overtones, and rotational transitions with ΔJ > 4. We have cast our results in the symmetry-adapted form needed for absorption line shape calculations, by expressing Δµ as a series in the spherical harmonics of the orientation angles of the intermolecular vector and of a unit vector along the H(2) bond axis. The expansion coefficients depend on the H(2) bond length and the intermolecular distance R. For large separations R, we show that the ab initio values of the leading coefficients converge to the predictions from perturbation theory, including both classical multipole polarization and dispersion effects.

Ab initio investigation of titanium hydroxide isomers and their cations, TiOH(0,+) and HTiO(0,+).

We studied the electronic and geometrical structure of the [Ti, O, H](0,+) species, using large basis sets and both single-reference coupled cluster and multireference configuration interaction methodologies. The electronic structure of HTiO(0,+) is interpreted qualitatively in terms of a hydrogen atom bonding to TiO(0,+), while the structure of TiOH(0,+) is interpreted in terms of Ti(+,2+) bonding to OH(-). Potential energy profiles are reported as functions of the Ti-OH and H-TiO bond lengths, and of the H-Ti-O angle. For a total of 33 stationary points on the potential energy surfaces, we report absolute energies, geometries, and harmonic frequencies. For the neutral species, dipole moments are also given.

First-principles calculations of the electronic and geometrical structures of neutral [Sc,O,H] molecules and the monocations, ScOH(0,+) and HScO(0,+).

Using multireference configuration interaction and coupled-cluster methodologies, with quadruple-ζ basis sets, we explored the potential energy surfaces of the ground and excited states of the neutral and cationic triatomics [Sc,O,H](0,+). In its ground state, the neutral species is trapped into either a linear ScOH or a bent HScO conformation; these two minima are approximately equal in energy and separated by a barrier of 40 kcal/mol. The linear ScOH structure is preferred by the excited states of the neutral species and by all of the electronic states of the charged molecular systems that we studied in this work. Both ScOH and ScOH(+) present ionic characters, Sc(+)OH(-) and Sc(2+)OH(-), similar to those found for the isovalent ScF(0,+) species. The HScO(0,+) structures are obtained by covalent or dative interaction of hydrogen and ScO(0,+). For most of the minima located in this work, we calculated geometries, vibrational frequencies, binding energies, excitation energies, and dipole moments. Our numerical results agree well with existing experimental data.

Collision-induced absorption by H2 pairs: from hundreds to thousands of kelvin.

An interaction-induced dipole surface (IDS) and a potential energy surface (PES) of collisionally interacting molecular hydrogen pairs H(2)-H(2) was recently obtained using quantum chemical methods (Li, X.; et al. Computational Methods in Science and Engineering, ICCMSE. AIP Conf. Proc. 2009, ; see also Li, X.; et al. Int. J. Spectrosc. 2010, ID 371201). The data account for substantial rotovibrational excitations of the H(2) molecules, as encountered at temperatures of thousands of kelvin (e.g., in the atmospheres of "cool" stars). In this work we use these results to compute the binary collision-induced absorption (CIA) spectra of dense hydrogen gas in the infrared at temperatures up to several thousand kelvin. The principal interest of the work is in the spectra at such higher temperatures, but we also compare our computations with existing laboratory measurements of CIA spectra of dense hydrogen gas and find agreement.