VSCF/VCI theory based on the Podolsky Hamiltonian.

While the vibrational spectra of semi-rigid molecules can be computed on approaches relying on the Watson Hamiltonian, floppy molecules or molecular clusters are better described by Hamiltonians, which are capable of dealing with any curvilinear coordinates. It is the kinetic energy operator (KEO) of these Hamiltonians, which render the correlated calculations relying on them rather costly. Novel implementation of vibrational self-consistent field theory and vibrational configuration interaction theory on the basis of the Podolsky Hamiltonian are reported, in which the inverse of the metric tensor, i.e., the G matrix, is represented by an n-mode expansion expressed in terms of polynomials. An analysis of the importance of the individual terms of the KEO with respect to the truncation orders of the n-mode expansion is provided. Benchmark calculations have been performed for the cis-HOPO and methanimine, H2CNH, molecules and are compared to experimental data and to calculations based on the Watson Hamiltonian and the internal coordinate path Hamiltonian.

Quantum chemical rovibrational analysis of aminoborane and its isotopologues.

Aminoborane, H2 NBH2 and its isotopologues, H2 N10 BH2 , D2 NBD2 , and D2 N10 BD2 , have been studied by high-level ab initio methods. All calculations rely on multidimensional potential energy surfaces and dipole moment surfaces including high-order mode coupling terms, which have been obtained from electronic structure calculations at the level of explicitly correlated coupled-cluster theory, CCSD(T)-F12, or the distinguishable cluster approximation, DCSD. Subsequent vibrational structure calculations based on second-order vibrational perturbation theory, VPT2, and vibrational configuration interaction theory, VCI, were used to determine rotational constants, centrifugal distortion constants, vibrationally averaged geometrical parameters and (an)harmonic vibrational frequencies. The impact of core-correlation effects is discussed in detail. Rovibrational VCI calculations were used to simulate the gas phase spectra of these species and an in-depth analysis of the ν7 band of aminoborane is provided. Color-coding is used to reveal the identity of the individual progressions of the rovibrational transitions for this particular mode.

FP(µ-N)2 S: A Sulfur-Pnictogen Four-Membered Ring with 6π Electrons.

The new 6π-electron four-membered ring compound 3-fluoro-1λ2 ,2,4,3λ3 -thiadiazaphosphetidine, FP(µ-N)2 S, has been generated in the gas phase through high-vacuum flash pyrolysis (HVFP) of thiophosphoryl diazide, FP(S)(N3 )2 , at 1000 K. Subsequent isolation of FP(µ-N)2 S in cryogenic matrices (Ar, Ne, and N2 ) allows its characterization with matrix-isolation IR and UV-vis spectroscopy by combination with 15 N-isotope labeling and computations at the CCSD(T)-F12a/VTZ-F12 level of theory. Upon visible-light irradiation at 550 nm, this cyclic compound undergoes ring-opening to the thiazyl isomer FPNSN, followed by dissociation to FP and SN2 under subsequent UV-irradiation at 365 nm. In sharp contrast to the square planar structure for the isolobal four-membered ring S2 N2 , a puckered structure with significant biradical character has been found for FP(µ-N)2 S.

Positioning of grid points for spanning potential energy surfaces-How much effort is really needed?

The positions of grid points for representing a multidimensional potential energy surface (PES) have a non-negligible impact on its accuracy and the associated computational effort for its generation. Six different positioning schemes were studied for PESs represented by n-mode expansions as needed for the accurate calculation of anharmonic vibrational frequencies by means of vibrational configuration interaction theory. A static approach, which has successfully been used in many applications, and five adaptive schemes based on Gaussian process regression have been investigated with respect to the number of necessary grid points and the accuracy of the fundamental modes for a small set of test molecules. A comparison with a related, more sophisticated, and consistent approach by Christiansen et al. is provided. The impact of the positions of the ab initio grid points is discussed for multilevel PESs, for which the computational effort of the individual electronic structure calculations decreases for increasing orders of the n-mode expansion. As a result of that, the ultimate goal is not the maximal reduction of grid points but rather the computational cost, which is not directly related.

Spectroscopic Identification of Diphosphene HPPH and Isomeric Diphosphinyldene PPH2.

The simplest diphosphene HPPH and isomeric diphosphinyldene PPH2 features prototype phosphorus-phosphorus multiple bonding properties that have been of long-standing interest in main-group chemistry. Herein, we report the observation of cis-HPPH, trans-HPPH, and PPH2 among the respective laser photolysis products of phosphine (PH3 ) and diphosphine (P2 H4 ) in solid N2 - and Ar-matrices at 10 K. The identification of these P2 H2 isomers with matrix-isolation IR and UV/Vis spectroscopy is supported by D-isotope labeling and the quantum chemical calculations at the CCSD(T)-F12a/cc-pVTZ-F12 level using configuration-selective vibrational configuration interaction theory (VCI). Bonding analyses suggest that the two conformers of HPPH contain standard PP double bonds, whereas, PPH2 resembles P2 in having partial PP triple bond due to the H2 P←P π bonding interaction.

Diazophosphane HPN2.

Diazophosphane HPN2, a heavy analogue of hydrazoic acid (HN3), has been synthesized at low temperature (10 K) through photolytic reactions of molecular nitrogen (N2) with phosphine (PH3) and phosphaketene (HPCO) under irradiations at 193 and 365 nm, respectively. The characterization of HPN2 and its isotopologues DPN2 and HP15N2 by matrix-isolation IR and UV-vis spectroscopy is supported by quantum chemical calculations at the CCSD(T)-F12a/cc-pVTZ-F12 level of theory. Upon irradiation at 266 nm, the P-N bond in HPN2 breaks, whereas its photolysis at 193 nm generates the elusive phosphinyl radical •PN2.

Advances in vibrational configuration interaction theory - part 2: Fast screening of the correlation space.

For larger molecules, the computational demands of configuration selective vibrational configuration interaction theory (cs-VCI) are usually dominated by the configuration selection process, which commonly is based on second order vibrational Møller-Plesset perturbation (VMP2) theory. Here we present two techniques, which lead to substantial accelerations of such calculations while retaining the desired high accuracy of the final results. The first one introduces the concept of configuration classes, which allows for a highly efficient exploitation of the analogs of the Slater-Condon rules in vibrational structure calculations with large correlation spaces. The second approach uses a VMP2 like vector for augmenting the targeted vibrational wavefunction within the selection of configurations and thus avoids any intermediate diagonalization steps. The underlying theory is outlined and benchmark calculations are provided for highly correlated vibrational states of several molecules.

Structure, energetics, and spectroscopy of the chromophores of HHe+n, H2He+n, and He+n clusters and their deuterated isotopologues.

The linear molecular ions H2He+, HHe+2, and He+3 are the central units (chromophores) of certain He-solvated complexes of the H2He+n, HHe+n, and He+n families, respectively. These are complexes which do exist, according to mass-spectrometry studies, up to very high n values. Apparently, for some of the H2He+n and He+n complexes, the linear symmetric tetratomic H2He+2 and the diatomic He+2 cations, respectively, may also be the central units. In this study, definitive structures, relative energies, zero-point vibrational energies, and (an)harmonic vibrational fundamentals, and, in some cases, overtones and combination bands, are established mostly for the triatomic chromophores. The study is also extended to the deuterated isotopologues D2He+, DHe+2, and D2He+2. To facilitate and improve the electronic-structure computations performed, new atom-centered, fixed-exponent, Gaussian-type basis sets called MAX, with X = T(3), Q(4), P(5), and H(6), are designed for the H and He atoms. The focal-point-analysis (FPA) technique is employed to determine definitive relative energies with tight uncertainties for reactions involving the molecular ions. The FPA results determined include the 0 K proton and deuteron affinities of the 4He atom, 14 875(9) cm-1 [177.95(11) kJ mol-1] and 15 229(8) cm-1 [182.18(10) kJ mol-1], respectively, the dissociation energies of the He+2 → He+ + He, HHe+2 → HHe+ + He, and He+3 → He+2 + He reactions, 19 099(13) cm-1 [228.48(16) kJ mol-1], 3948(7) cm-1 [47.23(8) kJ mol-1], and 1401(12) cm-1 [16.76(14) kJ mol-1], respectively, the dissociation energy of the DHe+2 → DHe+ + He reaction, 4033(6) cm-1 [48.25(7) kJ mol-1], the isomerization energy between the two linear isomers of the [H, He, He]+ system, 3828(40) cm-1 [45.79(48) kJ mol-1], and the dissociation energies of the H2He+ → H+2 + He and the H2He+2 → H2He+ + He reactions, 1789(4) cm-1 [21.40(5) kJ mol-1] and 435(6) cm-1 [5.20(7) kJ mol-1], respectively. The FPA estimates of the first dissociation energy of D2He+ and D2He+2 are 1986(4) cm-1 [23.76(5) kJ mol-1] and 474(5) cm-1 [5.67(6) kJ mol-1], respectively. Determining the vibrational fundamentals of the triatomic chromophores with second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) techniques, both built around the Eckart-Watson Hamiltonian, proved unusually challenging. For the species studied, VPT2 has difficulties yielding dependable results, in some cases even for the fundamentals of the H-containing molecular cations, while carefully executed VCI computations yield considerably improved spectroscopic results. In a few cases unusually large anharmonic corrections to the fundamentals, on the order of 15% of the harmonic value, have been observed.

Comparison of body definitions for incremental vibrational configuration interaction theory (iVCI).

Within incremental vibrational configuration interaction theory (iVCI), the vibrational state energy is determined by means of a many-body expansion, i.e., it is a sum of terms of increasing order, which allow for an embarrassingly parallel evaluation. The convergence of this expansion depends strongly on the definition of the underlying bodies, which essentially decompose the correlation space into fragments. The different definitions considered here comprise mode-based bodies, excitation level-based bodies, and energy-based bodies. An analysis of the convergence behavior revealed that accounting for resonances within these definitions is mandatory and leads to a substantial improvement of the convergence, that is, the expansions can be truncated at lower orders. Benchmark calculations and systematic comparisons of the different body definitions for a small set of molecules, i.e., ketene, ethene, and diborane, have been conducted to study the overall performance of these iVCI implementations with respect to accuracy and central processing unit time.

Convergence of series expansions in rovibrational configuration interaction (RVCI) calculations.

Rotational and rovibrational spectra are a key in astrophysical studies, atmospheric science, pollution monitoring, and other fields of active research. The ab initio calculation of such spectra is fairly sensitive with respect to a multitude of parameters and all of them must be carefully monitored in order to yield reliable results. Besides the most obvious ones, i.e., the quality of the multidimensional potential energy surface and the vibrational wavefunctions, it is the representation of the µ-tensor within the Watson Hamiltonian, which has a significant impact on the desired line lists or simulated spectra. Within this work, we studied the dependence of high-resolution rovibrational spectra with respect to the truncation order of the µ-tensor within the rotational contribution and the Coriolis coupling operator of the Watson operator. Moreover, the dependence of the infrared intensities of the rovibrational transitions on an n-mode expansion of the dipole moment surface has been investigated as well. Benchmark calculations are provided for thioformaldehyde, which has already served as a test molecule in other studies and whose rovibrational spectrum was found to be fairly sensitive. All calculations rely on rovibrational configuration interaction theory and the discussed high-order terms of the µ-tensor are a newly implemented feature, whose theoretical basics are briefly discussed.

Efficient and automated quantum chemical calculation of rovibrational nonresonant Raman spectra.

An outline of a newly developed program for the simulation of rovibrational nonresonant Raman spectra is presented. This program is an extension of our recently developed code for rovibrational infrared spectra [Erfort et al., J. Chem Phys. 152, 244104 (2020)] and relies on vibrational wavefunctions from variational configuration interaction theory to allow for an almost fully automated calculation of such spectra in a pure ab initio fashion. Due to efficient contraction schemes, this program requires modest computational resources, and it can be controlled by only a few lines of input. As the required polarizability surfaces are also computed in an automated fashion, this implementation enables the routine application to small molecules. For demonstrating its capabilities, benchmark calculations for water H2 16O are compared to reference data, and spectra for the beryllium dihydride dimer, Be2H4 (D2h), are predicted. The inversion symmetry of the D2h systems lead to complementary infrared and Raman spectra, which are both needed for a comprehensive investigation of this system.

Determination of spectroscopic constants from rovibrational configuration interaction calculations.

Rotational constants and centrifugal distortion constants of a molecule are the essence of its rotational or rovibrational spectrum (e.g., from microwave, millimeter wave, and infrared experiments). These parameters condense the spectroscopic characteristics of a molecule and, thus, are a valuable resource in terms of presenting and communicating spectroscopic observations. While spectroscopic parameters are obtained from experimental spectra by fitting an effective rovibrational Hamiltonian to transition frequencies, the ab initio calculation of these parameters is usually done within vibrational perturbation theory. In the present work, we investigate an approach related to the experimental fitting procedure, but relying solely on ab initio data obtained from variational calculations, i.e., we perform a nonlinear least squares fit of Watson's A- and S-reduced rotation-vibration Hamiltonian to rovibrational state energies (resp. transition frequencies) from rotational-vibrational configuration interaction calculations. We include up to sextic centrifugal distortion constants. By relying on an educated guess of spectroscopic parameters from vibrational configuration interaction and vibrational perturbation theory, the fitting procedure is very efficient. We observe excellent agreement with experimentally derived parameters.

Advances in vibrational configuration interaction theory - part 1: Efficient calculation of vibrational angular momentum terms.

Finite basis vibrational configuration interaction theory (VCI) is a highly accurate method for the variational calculation of state energies and related properties, but suffers from fast growing computational costs in dependence of the size of the correlation space. In this series of papers, concepts and techniques will be presented, which diminish the computational demands and thus broaden the applicability of this method to larger molecules or more complex situations. This first part focuses on a highly efficient implementation of the vibrational angular momentum (VAM) terms as occurring in the Watson Hamiltonian and the prediagonalization of initial subspaces within an iterative configuration selective VCI implementation. Working equations and benchmark calculations are provided, the latter demonstrating the increased performance of the new algorithm.

Vibrational spectrum and photochemistry of phosphaketene HPCO.

The vibrational spectra of the simplest phosphaketene HPCO and its isotopologue DPCO in solid Ar-matrices at 12.0 K have been analyzed with the aid of the computations at the CCSD(T)-F12a/cc-pVTZ-F12 level using configuration-selective vibrational configuration interaction (VCI). In addition to the four IR fundamentals, four overtone and ten combination bands have been unambiguously identified. Furthermore, the photochemistry of HPCO in the matrix has been investigated for the first time. Upon UV-light irradiation (365 or 266 nm), CO-elimination occurs by forming the parent phosphinidene HP that can be trapped by ˙NO to yield the elusive phosphinimine-N-oxyl radical HPNO˙. In contrast, an excimer laser (193 nm) irradiation of HPCO causes additional decomposition to H˙ and ˙PCO with concomitant formation of the long-sought phosphaethyne HOCP.

VCI Calculations Based on Canonical and Localized Normal Coordinates for Non-Abelian Molecules: Accurate Assignment of the Vibrational Overtones of Allene.

Vibrational configuration interaction calculations (VCI) have been performed to study the impact of the nature of the underlying coordinate systems, i.e., canonical vs localized normal coordinates, on accurate vibrational structure calculations for non-Abelian molecules. Once the correlation space is represented by real-valued primitive Hartree products, the assignment of vibrational states beyond the fundamentals is usually a tedious task and is further complicated by the use of non-symmetry-adapted coordinates. Our recently presented approach based on sparse grid integration of overlap integrals of the VCI wave function with the corresponding harmonic oscillator wave function has been used to determine and assign all fundamentals and vibrational overtones of allene and its deuterated isotopologue. Excellent agreement with available experimental results is observed in all cases.

Incremental vibrational configuration interaction theory, iVCI: Implementation and benchmark calculations.

The implementation of an algorithm for the determination of vibrational state energies based on a many-body expansion within the framework of configuration interaction theory is presented. An efficient evaluation of the increments within this approach is realized by an iterative configuration selection scheme. The new algorithm is characterized by low memory demands and an embarassingly parallel workload. The convergence of the expansion has been studied for a series of small molecules of increasing size, namely, formaldehyde, ketene, ethylene, and diborane. A threshold function has been employed to reduce the number of increments for high orders of the expansion. Benchmark calculations with respect to customary configuration-selective vibrational configuration interaction calculations are provided.

Hydrogen-Atom Tunneling in Metaphosphorous Acid.

Invited for the cover of this issue is X. Zeng and co-workers at Soochow University, University of Stuttgart, and Max-Planck Institute for Solid State Research. The image depicts the fast tunneling transformation of the highly elusive metaphosphorous acid (HOPO). Read the full text of the article at 10.1002/chem.202000844.

Hydrogen-Atom Tunneling in Metaphosphorous Acid.

Metaphosphorous acid (HOPO), a key intermediate in phosphorus chemistry, has been generated in syn- and anti-conformations in the gas phase by high-vacuum flash pyrolysis (HVFP) of a molecular precursor ethoxyphosphinidene oxide (EtOPO→C2 H4 +HOPO) at ca. 1000 K and subsequently trapped in an N2 -matrix at 2.8 K. Unlike the two conformers of the nitrogen analogue HONO, the anti-conformer of HOPO undergoes spontaneous rotamerization at 2.8 K via hydrogen-atom tunneling (HAT) with noticeable kinetic isotope effects for H/D (>104 for DOPO) and 16 O/18 O (1.19 for H18 OPO and 1.06 for HOP18 O) in N2 -matrices.

Assignment of vibrational states within configuration interaction calculations.

The assignment of vibrational states is an integral part of quantum chemical calculations, which supports the analysis of experimental infrared spectra. In variational calculations, usually, it is the leading coefficient of the configuration interaction vector, which provides the state identity. However, this concept will possibly fail in case of special coordinate systems, such as, for example, localized normal coordinates, or within calculations for overtones of non-Abelian molecules, when a real valued configuration basis has been employed. A combination of both renders a proper assignment fairly tedious. We present a route to overcome this problem by using a highly efficient calculation of multidimensional overlap integrals based on the Smolyak quadrature. Beside this, a general protocol for the symmetry assignment of vibrational states will be discussed, which completes a general assignment. Extensive benchmark calculations are provided for the fundamental modes and overtones of chloromethane, CH3Cl, in canonical and localized normal coordinates based on accurate potential energy surfaces obtained from explicitly correlated coupled-cluster theory. In addition, the linear CNNC molecule has been studied, for which hardly any reference data do exist.

Account of non-Condon effects in time-independent Raman wavefunction theory: Calculation of the S1← S0 vibronic absorption spectrum of formaldehyde.

The time-independent eigenstate-free Raman wavefunction approach for calculating anharmonic vibronic spectra has been extended for the calculation of Herzberg-Teller contributions on the basis of an n-mode expansion of the transition electric dipole moment surface. This allows for the efficient simulation of Franck-Condon dark vibronic spectra. In addition, vibrational angular momentum terms have been implemented into this formalism, as they are important for an accurate description of vibrational wavefunctions spanning double-well potentials. This approach has been used to compute the FC-forbidden vibronic spectrum of the n → π* transition of formaldehyde based on a potential energy and transition dipole moment surfaces obtained from explicitly correlated multi-reference configuration interaction calculations. An extensive analysis of the resulting vibronic structure is provided, which allows for a detailed assignment and interpretation of the experimental spectrum.