Accurate variational calculations for line lists to model the vibration-rotation spectra of hot astrophysical atmospheres

Picking up Good Vibrations through Quartic Force Fields and Vibrational Perturbation Theory

Quartic force fields (QFFs) define sparse potential energy surfaces (compared to semiglobal surfaces) that are the cheapest and easiest means of computing anharmonic vibrational frequencies, especially when utilized with second-order vibrational perturbation theory (VPT2). However, flat and shallow potential surfaces are exceedingly difficult for QFFs to treat through a combination of numerical noise in the often numerically computed derivatives and in competing energy factors in the composite energies often utilized to provide high-level spectroscopic predictions. While some of these issues can be alleviated with analytic derivatives, hybrid QFFs, and intelligent choices in coordinate systems, the best practice is for predicting good molecular vibrations via QFFs is to understand what they cannot do, and this manuscript documents such cases where QFFs may fail.

Performance of EOM-CCSD(T)(a)*-Based Quartic Force Fields in Computing Fundamental, Anharmonic Vibrational Frequencies of Molecular Electronically Excited States with Application to the Ã1A″ State of :CCH2 (Vinylidene)

Highly accurate anharmonic vibrational frequencies of electronically excited states are not as easily computed as their ground electronic state counterparts, but recently developed approximate triple excited state methods may be changing that. One emerging excited state method is equation of motion coupled cluster theory at the singles and doubles level with perturbative triples computed via the (a)* formalism, EOMEE-CCSD(T)(a)*. One of the most employed means for the ready computation of vibrational anharmonic frequencies for ground electronic states is second-order vibrational perturbation theory (VPT2), a theory based on quartic force fields (QFFs),fourth-order Taylor series expansions of the potential portion of the internuclear Watson Hamiltonian. The combination of these two is herein benchmarked for its performance for use as a means of computing rovibrational spectra of electronically excited states. Specifically, the EOMEE-CCSD(T)(a)* approach employing a complete basis set extrapolation along with core electron inclusion and relativity (the so-called "CcCR" approach) defining the QFF produces anharmonic fundamental vibrational frequencies within 2.83%, on the average, of reported gas-phase experimentally assigned values for the test set including the A ~ 1 A ″ states of HCF, HCCl, HSiF, HNO, and HPO. However, some states have exceptional accuracy in the fundamentals, most notably for ν2 of A ~ 1 A ″ HCCl in which the CcCR QFF value is within 1.8 cm-1 at 927.9 cm-1 (or 0.2%) of the experiment. Additionally, this approach produces rotational constants to, on the absolute average, within 0.41% of available experimental data, showcasing notable accuracy in the computation of rovibronic spectral data. Furthermore, utilizing a hybrid approach composed of harmonic CcCR force constants along with a set of simple EOMEE-CCSD(T)(a)*/aug-cc-pVQZ QFF cubic and quartic force constants is faster than using pure CcCR and better represents those modes that suffer from numerical instability in the anharmonic portion of the QFF, implying that this so-called "CcCR + QZ" QFF approach may be the best for future applications. Finally, complete, rovibrational spectral data are provided for A ~ 1 A 2 :CCH2, a molecule of potential astrochemical interest, in order to aid in its potential future experimental rovibronic characterization.

Dipole Moment Calculations Using Multiconfiguration Pair-Density Functional Theory and Hybrid Multiconfiguration Pair-Density Functional Theory

The dipole moment is the molecular property that most directly indicates molecular polarity. The accuracy of computed dipole moments depends strongly on the quality of the calculated electron density, and the breakdown of single-reference methods for strongly correlated systems can lead to poor predictions of the dipole moments in those cases. Here, we derive the analytical expression for obtaining the electric dipole moment by multiconfiguration pair-density functional theory (MC-PDFT), and we assess the accuracy of MC-PDFT for predicting dipole moments at equilibrium and nonequilibrium geometries. We show that MC-PDFT dipole moment curves have reasonable behavior even for stretched geometries, and they significantly improve upon the CASSCF results by capturing more electron correlation. The analysis of a dataset consisting of 18 first-row transition-metal diatomics and 6 main-group polyatomic molecules with a multireference character suggests that MC-PDFT and its hybrid extension (HMC-PDFT) perform comparably to CASPT2 and MRCISD+Q methods and have a mean unsigned deviation of 0.2-0.3 D with respect to the best available dipole moment reference values. We explored the dependence of the predicted dipole moments upon the choice of the on-top density functional and active space, and we recommend the tPBE and hybrid tPBE0 on-top choices for the functionals combined with the moderate correlated-participating-orbitals scheme for selecting the active space. With these choices, the mean unsigned deviations (in debyes) of the calculated equilibrium dipole moments from the best estimates are 0.77 for CASSCF, 0.29 for MC-PDFT, 0.24 for HMC-PDFT, 0.28 for CASPT2, and 0.25 for MRCISD+Q. These results are encouraging because the computational cost of MC-PDFT or HMC-PDFT is largely reduced compared to the CASPT2 and MRCISD+Q methods.

Rovibrational Quantum Chemical Treatment of Inorganic and Organometallic Astrochemicals

ConspectusOur two groups have both independently and collaboratively been pushing quantum-chemical techniques to produce highly accurate predictions of anharmonic vibrational frequencies and spectroscopic constants for molecules containing atoms outside of the typical upper p block. Methodologies employ composite approaches, relying on various levels of coupled cluster theory-most often at the singles, doubles, and perturbative triples level-and quartic force field constructions of the potential portion of the intramolecular Watson Hamiltonian. Such methods are known to perform well for organic species, and we have extended this to molecules containing atoms outside of this realm.One notable atom that has received much attention in this application is magnesium. Mg is the second-most-abundant element in the Earth's mantle, and while molecules containing this element are among the confirmed astrochemicals, its further atomic abundance in the galaxy implies that many more molecules (both purely inorganic and organometallic) containing element 12 exist in astrophysical regions in chemical sizes between those of atoms and dust-sized nanocrystals. Our approach discussed herein is producing quality benchmarks and predicting novel data for magnesium-bearing molecules.The story is similar for Al and Si, which are also notably abundant in both rocky bodies and the universe at large. While Na, Sc, and Cu may not be as abundant as Mg, Al, and Si, molecules containing Na and transition metals have also previously been reported to be detected beyond the Earth. Consequently, the need to produce spectral reference data for molecules containing such atoms is growing. While several experimental groups (including, notably, the groups in Arizona, Boston, and France/Spain) have clearly led the way in detection of inorganic/organometallic molecules in space, computational support and even rational design can provide novel avenues for the detection of molecules containing atoms not typically studied in most laboratories. The application of quantum chemistry to other elements beyond carbon and its cronies at the top right of the periodic table promises a better understanding of the observable universe. It will also provide novel and fundamental chemical insights pushing the "central science" into new molecular territory.

Empirical Line Lists in the ExoMol Database

The ExoMol database aims to provide comprehensive molecular line lists for exoplanetary and other hot atmospheres. The data are expanded by inclusion of empirically derived line lists taken from the literature for a series of diatomic molecules, namely CH, NH, OH, AlCl, AlF, OH + , CaF, MgF, KF, NaF, LiCl, LiF, MgH, TiH, CrH, FeH, C 2 , CP, CN, CaH, and triplet N 2 . Generally, these line lists are constructed from measured spectra using a combination of effective rotational Hamiltonian models for the line positions and ab initio (transition) dipole moments to provide intensities. This work results in the inclusion of 22 new molecules (36 new isotopologues) in the ExoMol database.

Anharmonic vibrational analysis of s-trans and s-cis conformers of acryloyl fluoride using numerical-analytic Van Vleck operator perturbation theory

A new gas-phase infrared (IR) spectrum of acryloyl fluoride (ACRF, CH₂CHCFO) with a resolution of 0.1cm^-1 in the range 4000-450cm^-1 was measured. Theoretical ab initio molecular structures, full quartic potential energy surfaces (PES), and cubic surfaces of dipole moments and polarizability tensor components (electro-optical properties, EOP) of the s-trans and s-cis conformers of the ACRF were calculated by the second-order Møller-Plesset electronic perturbation theory with a correlation consistent Dunning triple-ζ basis set. The numerical-analytic implementation of the second-order operator canonical Van Vleck perturbation theory was employed for predicting anharmonic IR and Raman scattering (RS) spectra of ACRF. To improve the anharmonic predictions, harmonic frequencies were replaced by their counterparts evaluated with the higher-level CCSD(T)/cc-pVTZ model, to form a "hybrid" PES. The original operator representation of the Hamiltonian is analytically reduced to a quasi-diagonal form, integrated in the harmonic oscillator basis and diagonalized to account for strong resonance couplings. Double canonical transformations of EOP expansions enabled prediction of integral intensities of both fundamental and multi-quanta transitions in IR/RS spectra. Enhanced band shape analysis reinforced the assignments. A thorough interpretation of the new IR experimental spectra and existing matrix-isolation literature data for the mixture of two conformers of ACRF was accomplished, and a number of assignments clarified.

A Modular Implementation for the Simulation of 1D and 2D Solid-State NMR Spectra of Quadrupolar Nuclei in the Virtual Multifrequency Spectrometer-Draw Graphical Interface

We present the implementation of the solid state (SoS)NMR module for the simulation of several 1D and 2D NMR spectra of all the elements in the periodic table in the virtual multifrequency spectrometer (VMS). This module is fully integrated with the graphical user interface of VMS (VMS-Draw) [Licari et al., J. Comput. Chem. 36, 2015, 321-334], a freeware tool which allows a user-friendly handling of structures and analyses of advanced spectroscopical properties of chemical compounds-from model systems to real-world applications. Besides the numerous modules already available in VMS for the study of electronic, optical, vibrational, vibronic, and EPR properties, here the simulation of NMR spectra is presented with a particular emphasis on those techniques usually employed to investigate solid state systems. The SoSNMR module benefits from its ability to work under both periodic and nonperiodic conditions, such that small molecules/molecular clusters can be treated, as well as extended three-dimensional systems enforcing (or not) translational periodicity. These features allow VMS to simulate spectra resulting from NMR calculations by some popular quantum chemistry codes, namely Gaussian09/16, Castep, and Quantum Espresso. The effectiveness of the SoSNMR module of VMS is examined throughout the manuscript, and applied to simulate 1D static, MAS, and VAS NMR spectra as well as 2D correlation (90°, MAS) and MQMAS spectra of active NMR nuclei embedded in different amorphous and crystalline systems of actual interest in chemistry and material science. Finally, the program is able to simulate the spectra of both the total ensemble of spin-active nuclei present in the system and of subensembles differentiated depending on the chemical environment of the first and second coordination sphere in a very general way applicable to any kind of systems.

Simulating electric field interactions with polar molecules using spectroscopic databases

Ro-vibrational Stark-associated phenomena of small polyatomic molecules are modelled using extensive spectroscopic data generated as part of the ExoMol project. The external field Hamiltonian is built from the computed ro-vibrational line list of the molecule in question. The Hamiltonian we propose is general and suitable for any polar molecule in the presence of an electric field. By exploiting precomputed data, the often prohibitively expensive computations associated with high accuracy simulations of molecule-field interactions are avoided. Applications to strong terahertz field-induced ro-vibrational dynamics of PH₃ and NH₃, and spontaneous emission data for optoelectrical Sisyphus cooling of H₂CO and CH₃Cl are discussed.

Small Molecules-Big Data

Quantum mechanics builds large-scale graphs (networks): the vertices are the discrete energy levels the quantum system possesses, and the edges are the (quantum-mechanically allowed) transitions. Parts of the complete quantum mechanical networks can be probed experimentally via high-resolution, energy-resolved spectroscopic techniques. The complete rovibronic line list information for a given molecule can only be obtained through sophisticated quantum-chemical computations. Experiments as well as computations yield what we call spectroscopic networks (SN). First-principles SNs of even small, three to five atomic molecules can be huge, qualifying for the big data description. Besides helping to interpret high-resolution spectra, the network-theoretical view offers several ideas for improving the accuracy and robustness of the increasingly important information systems containing line-by-line spectroscopic data. For example, the smallest number of measurements necessary to perform to obtain the complete list of energy levels is given by the minimum-weight spanning tree of the SN and network clustering studies may call attention to "weakest links" of a spectroscopic database. A present-day application of spectroscopic networks is within the MARVEL (Measured Active Rotational-Vibrational Energy Levels) approach, whereby the transitions information on a measured SN is turned into experimental energy levels via a weighted linear least-squares refinement. MARVEL has been used successfully for 15 molecules and allowed to validate most of the transitions measured and come up with energy levels with well-defined and realistic uncertainties. Accurate knowledge of the energy levels with computed transition intensities allows the realistic prediction of spectra under many different circumstances, e.g., for widely different temperatures. Detailed knowledge of the energy level structure of a molecule coming from a MARVEL analysis is important for a considerable number of modeling efforts in chemistry, physics, and engineering.

Saddle point localization of molecular wavefunctions

The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN ↔ HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, ℓ) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states.

The Virtual Multifrequency Spectrometer: a new paradigm for spectroscopy

On going developments of hardware and software are changing computational spectroscopy from a strongly specialized research area to a general tool in the inventory of most researchers. Increased interactions between experimentally-oriented users and theoretically-oriented developers of new methods and models would result in more robust, flexible and reliable tools and studies for the systems of increasing complexity, which are of current scientific and technological interest. This is the philosophy behind this review, which presents the development of a so-called virtual multi-frequency spectrometer (VMS) including state-of-the-art approaches in a user-friendly frame. The current status of the VMS tool will be illustrated by a number of case studies with special reference to infrared and UV-vis regions of the electro-magnetic spectrum including also chiral spectroscopies. Only the basic theoretical background will be provided avoiding explicit equations as far as possible, and pointing out the most recent advancements beyond the standard rigid-rotor harmonic-oscillator model coupled to vertical electronic excitation energies.

Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems

Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods.

New developments of a multifrequency virtual spectrometer: stereo-electronic, dynamical, and environmental effects on chiroptical spectra

Computational spectroscopy has recently evolved from a field reserved for specialists toward a general tool allowing interpretations and analyses of experimental results. However, the current practice of providing tables of transitions for rigid geometries, possibly tuned by phenomenological broadening, is by far too naive. In order to improve this situation in the last few years we have been developing a general, robust, and user-friendly virtual spectrometer (VS) able to complement experimental studies for complex systems in condensed phases. The VS is based on flexible graphical pre- and postprocessing tools interfaced with general number-crunching software. This last tool is rooted in several electronic structure methodologies (DFT, TD-DFT, post-Hartree-Fock), powerful discrete/continuum models for describing environmental effects, and general vibrational and vibronic models. These last topics are the main focus of this work, which sketches our latest developments related to effective inclusion of anharmonic contributions, together with time-independent and/or time-dependent descriptions of vibronic transitions including Franck-Condon, Herzberg-Teller, and Duschinsky effects. Some test cases are described in some detail with the aim of showing the role of different effects in ruling vibrational (VCD) and electronic (ECD, CPL) chiral spectroscopies.

Accurate structure, thermodynamics, and spectroscopy of medium-sized radicals by hybrid coupled cluster/density functional theory approaches: the case of phenyl radical

The coupled-cluster singles doubles model with perturbative treatment of triples (CCSD(T)) coupled with extrapolation to the complete basis-set limit and additive approaches represent the "golden standard" for the structural and spectroscopic characterization of building blocks of biomolecules and nanosystems. However, when open-shell systems are considered, additional problems related to both specific computational difficulties and the need of obtaining spin-dependent properties appear. In this contribution, we present a comprehensive study of the molecular structure and spectroscopic (IR, Raman, EPR) properties of the phenyl radical with the aim of validating an accurate computational protocol able to deal with conjugated open-shell species. We succeeded in obtaining reliable and accurate results, thus confirming and, partly, extending the available experimental data. The main issue to be pointed out is the need of going beyond the CCSD(T) level by including a full treatment of triple excitations in order to fulfil the accuracy requirements. On the other hand, the reliability of density functional theory in properly treating open-shell systems has been further confirmed.