In this work, an extension to diffusion Monte Carlo (DMC) is proposed, allowing for the simultaneous calculation of the energy and wave function of multiple rotationally excited states of floppy molecules.¹ The total wave function is expanded into a set of Dirac δ-functions called walkers, while the rotational portion of the wave function is expanded in a symmetric top basis set. Each walker is given a rotational state vector containing coefficients for all states of interest. The positions of the atoms and the coefficients in the state vector evolve according to the split operator approximation of the quantum propagator. The method was benchmarked by comparing calculated rotation-vibration energies for H₃⁺, H₂D⁺, and H₃O⁺ to experimental values. For low to moderate values of J, the resulting energies are within the statistical uncertainty of the calculation. Rotation-vibration coupling is captured through flexibility introduced in the form of the vibrational wave function. This coupling is found to increase with increasing J-values. Based on the success achieved through these systems, the method was applied to CH₅⁺ and its deuterated isotopologues for v = 0, J ≥ 10. Based on these calculations, the energy level structure of CH₅⁺ is found to resemble that for a of a spherical top, and excitations up to J = 10 displayed insignificant rotation-vibration coupling. Extensions of this approach that explicitly account for vibrations will also be discussed.
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¹A. S. Petit, J. E. Ford and A. B. McCoy, J. Phys. Chem. A, in press, K. D. Jordan Festschrift, DOI: 10.1021/jp408821a

Large amplitude vibrations of Van der Waals clusters are important because they reveal large regions of a potential energy surface (PES). To calculate spectra of Van der Waals clusters it is common to use an adiabatic approximation. When coupling between intra- and inter-molecular coordinates is important non-adiabatic coupling cannot be neglected and it is therefore critical to develop and test theoretical methods that couple both types of coordinates. We have developed new product basis and contracted basis Lanczos methods for Van der Waals complexes and tested them by computing rovibrational energy levels of Cl⁻H₂O. The new product basis is made of functions of the inter-monomer distance, Wigner functions that depend on Euler angles specifying the orientation of H₂O with respect to a frame attached to the inter-monomer Jacobi vector, basis functions for H₂O vibration, and Wigner functions that depend on Euler angles specifying the orientation of the inter-monomer Jacobi vector with respect to a space-fixed frame. An advantage of this product basis is that it can be used to make an efficient contracted basis by replacing the vibrational basis functions for the monomer with monomer vibrational wavefunctions. Due to weak coupling between intra- and inter-molecular coordinates, only a few tens of monomer vibrational wavefunctions are necessary. The validity of the two new methods is established by comparing energy levels with benchmark rovibrational levels obtained with polyspherical coordinates and spherical harmonic type basis functions. For all bases, product structure is exploited to calculate eigenvalues with the Lanczos algorithm. For Cl⁻H₂O, we are able, for the first time, to compute accurate splittings due to tunnelling between the two equivalent C_s minima. We use the PES of Rheinecker and Bowman (RB).¹ Our results are in good agreement with experiment for the five fundamental bands observed.²
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¹ J. Rheinecker and J. M. Bowman, J. Chem. Phys. 124 131102 (2006); J. Rheinecker and J. M. Bowman, J. Chem. Phys. 125 133206 (2006) ²S. Horvath, A. B. McCoy, B. M. Elliott, G. H. Weddle, J. R. Roscioli, and M. A. Johnson J. Phys. Chem. A 114 1556 (2010)

The derivation of analytic expressions for vibrational and rovibrational constants, for example the anharmonicity constants χ_ij and the vibration-rotation interaction constants α^B_r, from second-order vibrational perturbation theory (VPT2) can be accomplished with pen and paper and some practice. However, the corresponding quantities from fourth-order perturbation theory (VPT4) are considerably more complex, with the only known derivations by hand extensively using many layers of complicated intermediates and for rotational quantities requiring specialization to orthorhombic cases or the form of Watson's reduced Hamiltonian. We present an automatic computer program for generating these expressions with full generality based on the adaptation of an existing numerical program based on the sum-over-states representation of the energy to a computer algebra context. The measures taken to produce well-simplified and factored expressions in an efficient manner are discussed, as well as the framework for automatically checking the correctness of the generated equations.

The nuclear Schrödinger equation forms the basis for vibrational perturbation theory. However, the canonical "∧HΨ = EΨ" form is shown to be insufficient for computing elements of the rotational effective Hamiltonian and ultimately the various rovibrational and vibrationally-averaged rotational molecular properties. The necessary modifications are shown to be a natural result of derivation of the Schrödinger equation in a non-commutative algebra. The resulting equation is also compared to the contact transformation approach (CVVPT) and the two are shown to be equivalent (as is well known in the pure vibrational case). Lastly, equations for various rovibrational constants using this corrected approach and fourth-order perturbation theory (VPT4) are presented and compared to the available literature results.

Fourth-Order Rayleigh-Schrodinger Perturbation Theory (VPT4) is applied to a series of small molecules. The quality of results have been shown to be heavily dependent on the quality of the quintic and sextic force constants used and that numerical sextic force constants converge poorly and are unreliable for VPT4. Using analytic Hartree-Fock force constants, it is shown that these analytic higher-order force constants are comparable to corresponding force constants from numerical calculations at a higher level of theory. Calculations show that analytic Hartree-Fock sextic force constants are reliable and can provide good results with Fourth-Order Rayleigh-Schrodinger Perturbation Theory.

The structure of the purely rotational spectrum of sulphur trioxide SO₃ is investigated using a new synthetic line list. The list combines line positions from an empirical model with line intensities determined, in the form of Einstein coefficients, from variationally computed ro-vibrational wavefunctions in conjunction with an ab initio dipole moment surface. The empirical model providing the line positions involves an effective, Watsonian-type rotational Hamiltonian with literature parameter values resulting from least-squares fittings to observed transition frequencies. The formation of so-called rotational energy clusters at high rotational excitation are investigated. The SO₃ molecule is planar at equilibrium and exhibits a unique type of rotational-energy clustering associated with unusual stabilization axes perpendicular to the S-O bonds. This behaviour is characterized theoretically in the J range from 100 through 250. The wavefunctions for these cluster states are analysed, and the results are compared to those of a classical analysis in terms of the rotational-energy-surface formalism.

When disubstituted benzene molecules are considered the relative position of the substituents must be defined. The three possible forms are ortho-, meta-, and para- where the latter is investigated in this work by consideration of the effect para positioned substituents will have on the vibrational modes. The consistency of the labelling and assignment of the vibrational frequencies of the para disubstituted benzene molecules is investigated in their ground states (S₀) and first electronically excited states (S₁). The work extends a previously published nomenclature where ring-localised vibrations are compared straightforwardly across different monosubstituted benzene species and given the label M_i.^1,2,3 The assignments of the frequencies include previous work but also the calculated wavenumbers for both hydrogenated disubstituted benzenes (-h₄) and the deuterated isotopologues (-d₄) employing density functional theory (DFT) and time-dependent density functional theory (TDDFT).
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¹A. M. Gardner and T. G. Wright, J. Chem. Phys., 135, 114305 (2011) ²A. M. Gardner, A. M. Green, V. M. Tame-Reyes, V. H. K. Wilton and T. G. Wright, 138, 134303 (2013) ³A. M. Gardner, A. M. Green, V. M. Tame-Reyes, K. L. Reid, J. A. Davies, V. H. K. Wilton and T. G. Wright, manuscript accepted

Advances in hardware performance and the availability of efficient and reliable computational models have made possible the application of computational spectroscopy to ever larger molecular systems. The systematic interpretation of experimental data and the full characterization of complex molecules can then be facilitated. Focusing on vibrational spectroscopy, several approaches have been proposed to simulate spectra beyond the double harmonic approximation, so that more details become available. However, a routine use of such tools requires the preliminary definition of a valid protocol with the most appropriate combination of electronic structure and nuclear calculation models. Several benchmark of anharmonic calculations frequency have been realized on organic molecules. Nevertheless, benchmarks of organometallics or inorganic metal complexes at this level are strongly lacking despite the interest of these systems due to their strong emission and vibrational properties. Herein we report the benchmark study realized with anharmonic calculations on simple metal complexes, along with some pilot applications on systems of direct technological or biological interest.

The free O-H stretching modes of H⁺(CH₃OH)₁₋₃ clusters with/without argon have been unraveled by combining Infrared Pre-Dissociation (IR-PD) spectra and multidimensional normal mode analysis by Density Functional Theory (DFT) methods. Experimental IR-PD spectra have shown sharp peaks between 3200 and 3800 cm⁻¹, and these peaks shift when the size of cluster is varied, as well as increasing the number of argon attachment. We benchmarked several DFT and ab initio methods and the results shown that the free O-H stretching modes can well described by using a few selected normal mode coordinates with standard DFT methods.

A proton under a tug of war between two competing Lewis bases is a common motif in biological systems and proton transfer processes^{1 − 2} . Over the past decades, model compounds for such motifs can be prepared by delicate stoichiometric control of salt solutions ³ . Unfortunately, condensed phase studies, which aims to identify the key vibrational signatures are complicated to analyze. As a result, gas-phase studies do provide promising insights on the behavior of the shared proton. This study attempts to understand the quantum nature of the shared proton under theoretical paradigms. Proton bound symmetric dimers of (MeOH)₂H⁺ and (Me₂O)₂H⁺ are chosen as the model compounds. The simulation is performed using Density Functional Theory (DFT) at the B3LYP level with 6-311+G(d,p) as the basis set. It was found out that stretching mode of shared proton couples with several other normal modes and its corresponding oscillator strength do distribute to other normal modes.
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¹J.R. Roscioli, L.R. McCunn and M.A. Johnson. Science 2007, 316, 249 ²T.E. DeCoursey. Physiol. Rev., 2003, 83, 475 ³E.S. Stoyanov. Psys. Chem. Phys., 2000,2,1137

Computational spectroscopy techniques have become in the last years effective means to predict and characterize spectra, such as infrared, for molecular systems of increasing dimensions with account for different environments. We are actively developing a comprehensive and robust computational protocol, set within a perturbative vibrational framework [1], aimed at a quantitative reproduction of the spectra of biomolecules. In order to model the vibrational spectra of weakly bound molecular complexes, dispersion interactions should be taken into proper account. In this work, we present critical assessment of dispersion-corrected DFT approaches for anharmonic vibrational frequency calculations. It is shown that fully anharmonic IR spectra, simulated through full and reduced-dimensionality generalized second-order vibrational perturbation theory (GVPT2)[1] with the potential energy surfaces computed with the B3LYP-D3 approach, may be used to interpret experimental data of nucleobases and their complexes[2] by the direct comparison of experimental IR spectra with their theoretical anharmonic counterpart, taking into account also overtones and combination bands. [1] V. Barone, M. Biczysko, J. Bloino, Phys. Chem. Chem. Phys., 2014,16, 1759-1787 [2] T. Fornaro, M. Biczysko, S. Monti, V. Barone , Phys. Chem. Chem. Phys., 2014, DOI: 10.1039/C3CP54724H

Accurate structures of aminoacids in the gas phase have been obtained by joint microwave and quantum-chemical investigations. However, the structure and conformational behavior of α-aminoacids once incorporated into peptide chains are completely different and have not yet been characterized with the same accuracy. To fill this gap, we present here an accurate characterization of the simplest dipeptide analogue (N-acetylglycinamide) involving peptidic bonds. State-of-the-art quantum-chemical computations are complemented by a comprehensive study of the rotational spectrum using a combination of Fourier transform microwave spectroscopy with laser ablation. The coexistence of the C₇ and C₅ conformers has been proved and energetically as well as spectroscopically characterized. This joint theoretical-experimental investigation demonstrated the feasibility of obtaining accurate structures for flexible small biomolecules, thus paving the route to the elucidation of the inherent behavior of peptides.