The C₄H molecule is of significant astronomical interest. It represents one of the smallest "carbon chain” radicals, is abundantly distributed in astronomical sources, and C₄H⁻ was the one of the first molecular anions to be detected in space. The acetylenic radicals H(C₂)_n form an interesting sequence in which low-lying excited electronic states are conspicuous. The simplest radical (C₂H) has a ²Σ ground state, with the ²Π excited state just below 0.5 eV higher. As the length of the carbon chain increases, the delocalization present in the ²Π state (relative to ²Σ, which is acetylenic in nature with the unpaired spin localized on the terminal carbon) leads to its preferential stabilization, and ²Π lies comfortably below ²Σ for C₆H and larger members of the series. In this regard, C₄H sits essentially on the frontier: the most recent experiments place the ²Σ lowest, but by only < 30 meV, and a clear picture of its low-level vibronic level structure has yet to emerge. This talk discusses all three of the low-lying states (²Σ and the two components of ²Π), which in fact display a low-lying three-state conical intersection within 150 meV of the minimum on the adiabatic surface, and undergo profound vibronic pseudo-Jahn-Teller (²Σ/²Π) and Renner-Teller (²Π) mixing. High-level calculations are performed to identify the various principal stationary points and conical intersections on the potential, and this information is used to construct a three-state vibronic Hamiltonian of the Köppel-Cederbaum-Domcke variety. These results are used to present a view of the electronic structure of this molecule that goes beyond the simple description of simple ²Σ and Renner-Teller distorted ²Π states that has typically been invoked in the past, and to carry out a simulation of the photoelectron spectrum.  

While scalar-relativistic core-valence separated equation-of-motion coupled-cluster [1] methods can provide quantitative description of core ionization energies [2,3], the necessity of including higher excitations (full triples and quadruples) limits the applicability to small molecules. Here we explore the use of delta-coupled-cluster (∆CC) methods as an efficient alternative that is applicable to larger molecules. The ∆CC methods perform CC calculations separately for the neutral and core ionized states and thus fully account for the orbital relaxation induced by the core hole in the core ionized state. The convergence difficulty in ∆CC equations [4] is solved by adapting the generic idea of core-valence separation (CVS) [5] to ∆CC. In benchmark calculations of chemical shifts for the core ionization energies for second-row elements, ∆CCSD(T) is shown to be as accurate as EOM-CCSDTQ, which is by far a more expensive method. It is also shown that the errors introduced by CVS within ∆CC for the absolute values of core ionization energies is around 0.5 eV and should be taken care of when aming at high-accuracy calculations of the absolute values.

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R. H. Myhre, T. J. A. Wolf, L. Cheng, S. Nandi, S. Coriani, M. Gühr and H. Koch, J. Chem. Phys. 148, 064106 (2018).

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J. Liu, D. Matthews, S. Coriani, and L. Cheng, J. Chem. Theory Comp. (2019). DOI:10.1021/acs.jctc.8b01160.

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Jahn Teller active molecules are a convenient tool for understanding various nonadiabatic effects due to a conical intersection in the potential energy surface (PES), whether its position is determined by symmetry or accidentally along a reaction path. Computing PES, including the nonadiabatic coupling parameters, helps us to interpret the vibronic spectra of these molecules. Vibronic eigenfunctions are calculable either by utilizing fit data obtained from these vibronic spectra or electronic structure methods. In this talk we discuss the application and efficacy of these eigenvectors for calculating rovibronic parameters that characterize eigenstates in Jahn-Teller active molecules. Methods have been developed to plot spin vibronic eigenfunctions for multimode calculations. These plots give us considerable insight and enhance our understanding by visualizing Jahn-Teller interactions, multimode effects, and potentially the dynamics around a conical intersection.

A U (3) algebraic approach is proposed to describe 2D systems for effective potentials. Our approach is based on the 2D vibron model where the addition of a scalar boson is introduced into the 2D harmonic oscillator space. As a crucial ingredient of our approach an algebraic realization of the coordinates and momenta is obtained. This feature provides the tools to obtain the algebraic representation of a 2D Hamiltonian in terms of similitude transformation of a diagonal matrix. As an application of our approach the rotation-bending energy levels of carbon suboxide C₃O₂ are described in good agreement with experimental data [1].
[1] M. Rodriguez-Arcos, R. Lemus, Chem. Phys. Lett., 713 (2018) 266–271

An algebraic approach based on the unitary U(4) algebra is proposed to describe 3D systems for effective potentials. Our approach is based on the 3D vibron model where the addition of a scalar boson is introduced into the space of a 3D harmonic oscillator keeping constant the total number of bosons N. However instead of dealing directly with the dynamical symmetries we proceed to identify the coordinates and momenta in the algebraic space. Our approach is based on the mapping between the U(4) ⊃ U(3) ⊃ O(3) dynamical symmetry and the harmonic oscillator states. A minimization procedure is used in order to determine the coefficients involved in the algebraic expansion of the coordinates and momenta. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations. This identification provides useful tools to obtain the matrix representation of 3D Hamiltonians in a simple form through the use of the transformation brackets connecting the different bases. The exact energy and wave functions are obtained in the N large limit. As an application of this approach the eigensystem of the 3D-Morse potential is analyzed, whose wave functions are contrasted with the approximate analytical solutions for null angular momentum. The analyses of inertia moments as well as the dipole moment strengths are also included. This approach provides results which contrasts to the 3D-vibron model where the Morse functions are identified with a dynamical symmetry.

Computer spectrometers have recently been used to `measure' the energy associated with the C → C<sup>+</sup> ionizationNike Dattani (2018) "0.06 cm<sup>−1</sup> Discrepancy for Li<sub>2</sub> → 2Li and 0.994 cm<sup>−1</sup> for C → C<sup>+</sup> between Laboratory and Computer Spectrometers" Proceedings of the 73rd International Symposium on Molecular Spectroscopy. the Li<sub>2</sub>(1<sup>3</sup>Σ<sub>u</sub><sup>+</sup>)→ 2Li separation<sup>a</sup>, and the vibrational levels and vibrational spacings of Li<sub>2</sub>(1<sup>3</sup>Σ<sub>u</sub><sup>+</sup>)Nike Dattani (2017) "Computer Spectrometers". Proceedings of the 72nd International Symposium on Molecular Spectroscopy.Nike Dattani, Sandeep Sharma, Ali Alavi (2016) "Full CI Benchmark Potentials for the 6e<sup>−</sup> System Li<sub>2</sub> with a CBS Extrapolation from aug-cc-pCV5Z and aug-cc-pCV6Z Basis Sets Using FCIQMC and DMRG". Proceedings of the 71st International Symposium on Molecular Spectroscopy.. These were all cases involving up to 6 electrons. Up to at least 6 electrons, computer spectroscopy has been as accurate, almost as accurate, or in some cases even more accurate, than the best laboratory spectrometers, for measuring quantities such as ionization energies and dissociation energies, but we lag behind laboratory experimentalists when it comes to assigning uncertainties on our `measurements': There is no easy way to do it accurately. Typically basis set incompleteness is the biggest source of uncertainty in computer spectroscopy. Energies are calculated with larger and larger basis sets, and then an extrapolation is done to approximate a CBS (complete basis set) energy. The uncertainty associated with this approximation can be estimated based on doing multiple extrapolations, with slightly different models, and looking at the spread of extrapolated values, but this is still a rather ad hoc way to estimate the uncertainty. Similar extrapolation schemes are also starting to become popular for estimating the correlation energy at a given basis set size. My proposal is to develop a way to assign uncertainties to computer spectroscopy measurements in a way more similar to how it is done for laboratory instruments. Instruments often have a `precision rating' based on the likelihood that the true value of the measured quantity is outside a specified window of precision around the number reported by the instrument. The measurement uncertainties reported in NIST's atomic spectra database are 1σ uncertainties, meaning that there is approximately a 1/3 chance of the true value being outside of the reported error bar. The precision rating can therefore be calibrated by doing many measurements, but for computer spectrometers we rely on building a big database and doing machine learning. I discuss the determination of uncertainties both for CBS extrapolations and for FCI energy estimations.

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Footnotes:

Nike Dattani (2018) "0.06 cm⁻¹ Discrepancy for Li₂ → 2Li and 0.994 cm⁻¹ for C → C⁺ between Laboratory and Computer Spectrometers" Proceedings of the 73rd International Symposium on Molecular Spectroscopy., Nike Dattani (2017) "Computer Spectrometers". Proceedings of the 72nd International Symposium on Molecular Spectroscopy.

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Footnotes:

Ethanol dehydrogenation dimerization to form ethyl acetate (EA) and hydrogen is, in principle, the best atomically economic reaction and is also considered to be an environmentallly friendly process in EA synthesis. Even though the copper-based catalysts have been utilized as commercial catalysts they still have some disadvantages such as low productivity and difficult separation from the by-products. Density functional theory was used to investigate the ethanol dehydrogenation dimerization over Cu(111) catalyst. In this work, we calculated and analysed the reaction network on Cu(111) along different dehydrogenation pathways. In addition, to improve the performance of Cu-based catalyst, we investigated the activities over Cu₃Pt(111) and Cu₃Pd(111). By comparsion, the introduction of Pt or Pd is beneficial for the improvement of catalytic activity. The analysis of density of eletronic states was used to explain how these electron transfers were proceeded over different catalysts. Through calculating the entire frequencies of each intermediate, the Infrared and Raman spectra for each intermediate were predicted that will be useful to experimental detection of intermediates.

Franck Condon factors (FCFs) among low-lying electronic states of a molecule are of paramount importance in the study of laser cooling based on optical cycles. The accurate calculation of potential energy surfaces for these electronic states is key to obtaining accurate FCFs. Multireference configuration interaction as a standard approach for computing potential energy surfaces has been the method of choice in many applications. Since the laser cooling procedure focuses on the low-lying vibrational states, only the local potential energy surfaces, for which the multi-reference character is often not pronounced and it is the treatment of dynamic correlation that determines the accuracy of the calculation, are relevant. Therefore, we advocate the use of coupled-cluster (CC) techniques, which provide systematic treatments of dynamic electron correlation, to obtain accurate computational results for FCFs. The yttrium oxide molecule that is subject to active experimental studies [1-3] is adopted here as an example to demonstrate the accuracy of the FCFs using CC potential energy surfaces.

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M. T. Hummon, M. Yeo, B. K. Stuhl, A. L. Collopy, Y. Xia, and J. Ye, Phys. Rev. Lett. 110, 143001 (2013).

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A. L. Collopy, M. T. Hummon, M. Yeo, B. Yan, J. Ye, New J. Phys. 17, 055008 (2015).

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A. L. Collopy, S. Ding, Y. Wu, lan A. Finneran, L. Anderegg, B. L. Augenbraun, J. M. Doyle, and J. Ye, Phys. Rev. Lett. 121, 213201 (2018).

DFT calculations were carried out to obtain the absorption and fluorescence spectra of 4-vinyl-N,N-di(p-toyly)aniline derivatives denoted as MTPAs, in different solvents to understand the correlation between the functional groups and solvent effects. In this presentation, we will discuss DFT results on six MTPAs in two solvents, dichloromethane and toluene, and the solvent impact on the structures of electronically excited states. We will also briefly discuss the choice of functional of the DFT results with comparison to the experimental measurements of these derivatives.

Recently developed two dimensional THz-THz-Raman (TTR) spectroscopy applied to liquids is an excellent tool for probing dynamics which takes place at room temperature and drives processes such as solvation, protein folding, and ion diffusion. The TTR spectrum packs rich information about the systems under study, such as the degree of anharmonicity and mechanical coupling of the low energy modes, and the nonlinearity of the dipole and polarizability surfaces. However, these properties are difficult to interpret, being convoluted into a three point correlation function. We develop a computational procedure based on Reduced Density Matrix (RDM) dynamics, which allows us to calculate the microscopic properties of a molecule by fitting to the experimental signal measured in the condensed phase. We apply RDM to liquid bromoform and we obtain parameters of the same order of magnitude with values computed ab initio. This paves the road to a more general protocol that could be extended to other molecules in order to measure and fit electric and mechanical molecular properties. These parameters could further be used to develop more reliable force fields for solvation liquids and biomolecules.