Vibrational perturbation theory is a commonly-used method for obtaining anharmonic corrections to harmonic zero-order wave functions and energies. Traditional approaches use analytic expressions for second order corrections derived from the Watson Hamiltonian expressed in normal modes constructed from displacements of Cartesian coordinates. Given that in the absence of resonances internal and Cartesian coordinates provide identical corrections to the energies and other properties, Cartesian coordinates provide a convenient choice. However, when the Hamiltonian is expressed in Cartesian coordinates, the corrections to the energies result from large cancellations of positive and negative contributions from cubic and quartic terms in the expansion of the Hamiltonian. In internal coordinates the amount of cancellation is significantly smaller. We present a recently-developed implementation of perturbation theory that allows for flexibility in coordinate choice, order of correction, and handling of degeneracies. This approach is straightforward and provides a route to obtain insights into the origins of spectral intensities among other applications. We apply this method to a fully ab initio potential energy surfaces for several polyatomic molecules as well as model systems.

Complexes of halide ions (Cl, Br and I) with water have provided a set of systems that allow us to explore spectral signatures of hydrogen bonding and how the frequencies and intensities map onto the strength of the hydrogen bond interactions. By substituting HOCl for HOD, we are able to further explore how the acidity of the hydrogen bonding partner is reflected in the spectroscopy. Building off of prior studies of X⁻…H₂O it is possible to provide tentative assignments for only a subset of the features of interest. Through vibrational perturbation theory (VPT), we can obtain a more complete assignment of the vibrational spectrum of X⁻…HOCl from 1200-4000 cm⁻¹. Applying VPT to these systems requires a flexible approach, where resonances are handled appropriately and state energies are tuned to correct for overbinding of the hydrogen to the halide ion at the MP2/aug-cc-pVTZ level of theory/basis used for this study. After including these corrections, the calculated spectra are in very good agreement with experimental spectra. This flexibility also allows for the interpretation of the origin of spectral intensity, making it possible to determine whether a transition obtains intensity through higher order terms in the expansion of the dipole moment (electrical anharmonicity), higher order terms in the expansion of the potential surface (mechanical anharmonicity), or state mixing through through couplings of nearly degenerate zero-order states. The X⁻…HOCl systems also provide the opportunity to explore spectral implications of halogen bonding and vibrational perturbation theory is applied to the differentiation of contributions to the spectra from the halogen- and hydrogen-bonded isomers of ClHOI⁻.

An argument can be made that the nitrate radical (NO₃) is the most complicated tetraatomic molecule in nature, an assertion that becomes undoubtedly correct when its quantum mechanical complexity is convolved with its environmental importance. The three lowest electronic states of this molecule (X²A₂^′, A²E^′′ and B²E^′) are separated by less than 2 eV, and considerable vibronic mixing between these states leads to the complicated spectral patterns observed experimentally for NO₃. This talk reviews the various (qualitative) coupling mechanisms responsible for the abundance of various Franck-Condon forbidden features in electronic spectra of this species, with particular emphasis given to: photodetachment of the (well-behaved) nitrate anion; the A−X absorption spectrum; and the B−X absorption and dispersed fluorescence spectra. Apart from the A-X absorption spectrum, all of the above can be qualitatively reproduced by an extremely simple vibronic Hamiltonian, and semi-quantitative agreement is achieved with a more elaborate but conceptually identical form. As time permits, a progress report will be given on the interpretation of the A−X spectrum, some features of which remain poorly understood.

The determination of molecular bond dissociation energies (BDE) is a fundamental pursuit of chemistry. This is an area where computational approaches have proved useful, especially when addressing molecules or environments that are difficult to study in the lab. High-accuracy composite methods can typically compute bond-energies to within one kJ \textmol⁻¹ via a series of additive energy increments, with corrections for relativistic effects, the vibrational zero-point energy, and the Born-Oppenheimer approximation. Recently, the present authors explored an extension to the HEAT composite method, currently named KS-HEAT, which routinely reproduces the Active Thermochemical Tables (ATcT) total-atomization energies of small molecules to within 20 cm⁻¹. F₂, however, differs from the ATcT value by nearly 30 cm⁻¹. While fluorine-containing species are historically challenging to model, disagreement of this magnitude is surprising given the considerable level of theory and size of basis sets employed here. To confound the issue, while the BDE predicted by KS-HEAT agrees closely with the combined ZEKE and IPP study of Yang et al. and the computational work of Csontos et al., a recent CIPP study by Matthíasson et al. and the FPD value calculated by Feller et al. agree with the current ATcT assignment. As the BDE of F₂ influences the ATcT enthalpies of formation of all fluorine containing molecules, this is an important quantity to get "right". The details of these calculations are presented, and the BDE of F₂ is discussed.

Diffusion Monte Carlo (DMC) is a stochastic method that is used to obtain the ground state energy and ground state wave function of a system of interest. DMC requires a potential energy surface (PES) that describes all degrees of freedom of the system. We have found that the use of guiding functions, functions that describe some of the vibrational degrees of freedom within the system, allow improved sampling of the ground state wave function if the guiding function is chosen carefully.Lee, V. G. M. and McCoy, A.B., J. Phys. Chem. A (2019), 123, 37, 8063-8070.Finney, J. M., DiRisio, R. J., McCoy, A.B., J. Phys. Chem. A (2020), 124, 45, 9567-9577 While this enables us to used DMC to study larger systems, to obtain spectra we will also need to calculate the excited state energies and matrix elements of the dipole moment operator involving the ground and excited state wave functions. In this work we explore the use of excited state guiding functions for the evaluation of vibrationally excited states. Specifically, we combine the approaches taken from previous work using ground state guided DMC simulations and fixed-node approaches, which we have used to obtain excited state wave functions from unguided DMC calculations. This approach has been applied to studies of OH stretching vibrations in H₂O and H₃O₂⁻ , where comparisons to previous studies can be made. Various approaches for obtaining the intensities from the ground and excited state DMC wave functions are explored.Barnett, R. N., Reynolds, P. J., Lester Jr., W. A., J. Chem. Phys. (1992), 96, 2141-2154html:<hr /><h3>Footnotes: Lee, V. G. M. and McCoy, A.B., J. Phys. Chem. A (2019), 123, 37, 8063-8070.

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Barnett, R. N., Reynolds, P. J., Lester Jr., W. A., J. Chem. Phys. (1992), 96, 2141-2154

Recently, Baba group found that ro-vibrationally averaged bond lengths of C-H and C-D are observed as being almost identical (r_0,eff(C-H) ≅ r_{0 ,eff}(C-D)) for planar aromatic hydrocarbons from high-resolution laser spectroscopy. ^aQuite recently, the reason of the same r_0,eff(C-H) and r_0,eff(C-D) bond lengths has been brilliantly unveiled by Hirano et al. by high-level ab initio molecular orbital calculations.^b They revealed that the experimental bond lengths derived from effective rotational constants are "not" the ro-vibrationally averaged bond lengths but their projected lengths on the principle axis. In this study, we have carried out the path integral molecular dynamics (PIMD) simulations for C₆ H₆ and C₆ D₆ to directly estimate the distribution of the C-H and C-D bond lengths projected onto the principle axis. Our PIMD simulation strongly supports the previous explanation by Hirano et al.^a for the experimentally observed fact (r _0,eff(C-H) ≅ r_{0 ,eff}(C-D)) in C₆ H₆ and C₆ D₆.

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Footnotes:
^aS. Kunishige, T. Katori, M. Baba, et al., J. Chem. Phys. 143, 244302 (2015).
^bT. Hirano, U. Nagashima, M. Baba, J. Mol. Struct. 1243, 130537 (2021).

We present a computational study of x-ray absorption spectra for CH₃Cl and CH₂ICl using relativistic equation-of-motion coupled-cluster methods with spin-orbit coupling. The 1:1 ratio of the peak intensities for the chlorine L₃ edge and L₂ edge in the experimental x-ray absorption spectrum of CH₂ICl [1] shows an interesting deviation from the ratio of 2:1 between 2p_3/2 and 2p_1/2 electrons. Here we study the origin of this phenomenon using high-accuracy ab initio calculations. Our computational results explain the relation between this anomaly in intensities and “multiplet effects” [2].

From the precise measurement of the ionization energy of H₂ its dissociation energy can be determinedN. Hölsch, M. Beyer, E.J. Salumbides, K.S.E. Eikema, W. Ubachs, Ch. Jungen, and F. Merkt, Phys. Rev. Lett., 122(10), 103003 (2019) which serves as a benchmark quantity for QED calculationsM. Puchalski, J. Komasa, P. Czachorowski, and K. Pachucki, Phys. Rev. Lett., 122(10), 103003 (2019) The most precise determinations of the ionization energies of molecular hydrogen currently rely on the extrapolation of Rydberg series using multichannel quantum-defect theory (MQDT)D. Sprecher, Ch. Jungen and F. Merkt, J. Chem. Phys. 140, 104303:1-18 (2014) Nonpenetrating high-l states offer significant advantages for these extrapolations: they have small quantum defects and are much less perturbed by channel interactions than low-l states. Their high polarisabilities are a disadvantage in zero-field measurements, but can be exploited to our advantage in Stark measurements. We show that the combination of a 3-photon excitation scheme with application of relatively weak electric fields (10 - 250 mV/cm) provides easy optical access to the linear Stark manifolds associated with near-degenerate high-l states. We perform spectroscopy of the high-Rydberg Stark manifold with both continuous-wave millimeter-wave and near-infrared (NIR) radiation. The manifold states are desirable as spectroscopic targets because their positions are less sensitive to errors in the quantum defects, a limiting factor in the determination of ionization energies by Rydberg series extrapolation. Extrapolating the linear Stark manifold to zero field yields accurate values of the zero-quantum-defect positions, given by −R_H2/n² relative to the ionization thresholds. These positions constitute references for the respective l = 3 states and provide an assessment of multichannel-quantum-defect-theory calculations at a precision on the order of 100 kHz. We show that this method can contribute to a one-order-of-magnitude improvement in the determination of ionization energies in molecular hydrogen and that, by using narrow-band NIR laser light, it can be extended beyond the ground state of para-H₂⁺.

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Footnotes:

N. Hölsch, M. Beyer, E.J. Salumbides, K.S.E. Eikema, W. Ubachs, Ch. Jungen, and F. Merkt, Phys. Rev. Lett., 122(10), 103003 (2019), M. Puchalski, J. Komasa, P. Czachorowski, and K. Pachucki, Phys. Rev. Lett., 122(10), 103003 (2019). D. Sprecher, Ch. Jungen and F. Merkt, J. Chem. Phys. 140, 104303:1-18 (2014).

Atoms and molecules in a Rydberg state with a large principal or orbital-angular-momentum quantum number (n ≥ 100 or l ≥ 10) have an ion core that, to a good approximation, is isolated from the Rydberg electron and behaves as the bare ion. Properties of cations, such as their rovibronic structure, can thus be spectroscopically determined by studying the ion core within the orbit of a Rydberg electron. This led to the development of the isolated-core-excitation (ICE) technique [1] and isolated-core multiphoton Rydberg dissociation spectroscopy [2]. Until now, the photoexcitation of the ion core relied on electric-dipole transitions. We report the first observation of an electric-quadrupole ICE transition observed in the Sr atom and attributed to the one-photon excitation of the ion core from the Sr⁺(5d_5/2) state to the Sr⁺(5g_{7/2, 9/2}) states. Photoexcitation spectra from Sr(5d_5/2nl) states (n=16 − 21, l=12), located high in energy in the Sr⁺ continuum, to an energy region between the Sr⁺(5f) and Sr⁺(5g) ionization thresholds were studied in a joint experimental and theoretical investigation. They show series of lines attributed to Sr(5gn"l") states, which cannot be reached by electric-dipole ICE from Sr(5d_5/2nl) states. We have identified two mechanisms responsible for these lines: (i) the direct electric-quadrupole excitation from Sr(5d_5/2nl) to Sr(5gn′l) states, and (ii) the electric-dipole excitation to the weak Sr(5fnl) component of the Sr(5gn′l′) states, this mixing being caused by the Coulomb interaction between the two excited electrons. The two excitation mechanisms can be unambiguously identified because they lead to spectra with different line-intensity distributions. A detailed analysis of the spectra is under way.

Pt⁺(C₂H₂)_n (n = 1 – 9) complexes are studied with tunable infrared laser photodissociation spectroscopy. These complexes are produced with laser vaporization of a platinum rod in a pulsed supersonic expansion of argon seeded with acetylene. Argon-tagged and tag-free complexes are then mass-selected in a specially made reflectron time-of-flight mass spectrometer, and their spectra are measured in the C – H stretching region (2800 – 3400 cm⁻¹) with infrared laser photodissociation spectroscopy. A coordination number of three acetylenes is found for platinum-cation. The experimental spectra are assigned using B3LYP/DEF2TZVP with an effective core potential on platinum. Peaks for the asymmetric and normally forbidden symmetric stretch of acetylene are red shifted from free acetylene molecules. The presence of cation – pi complexes and reacted structures is investigated by comparing experiment to theory.