Mapping spin contamination-free potential energy surfaces using restricted open-shell methods with Grassmannians.

The Lagrange-based Grassmann interpolation (G-Int) method has been extended for open-shell systems using restricted open-shell (RO) methods. The performance of this method was assessed in constructing potential energy surfaces (PESs) for vanadium(II) oxide, benzyl radical, and methanesulfenyl chloride radical cation. The density matrices generated by G-Int when used as initial guesses for self-consistent field (SCF) calculations, exhibit superior performance compared to other traditional SCF initial guess schemes, such as SADMO, GWH, and CORE. Additionally, the energy obtained from the G-Int scheme satisfies the variational principle and outperforms the direct energy-based Lagrange interpolation approach. In the case of methanesulfenyl chloride radical cation, a unique example with a flat PES at the end region along the H-C-S-Cl dihedral angle, the use of an equally-spaced grid sampling leads to significant oscillations near the end of the interval due to the effects of Runge's phenomenon. Introducing an unequally-spaced grid sampling based on a scaled Gauss-Chebyshev quadrature effectively mitigated the Runge's phenomenon, making it suitable for combining with G-Int in constructing PESs for general applications. Thus, G-Int provides an efficient and robust strategy for building spin contamination-free PESs with consistent accuracy.

Ab initio anharmonic analysis of complex vibrational spectra of phenylacetylene and fluorophenylacetylenes in the acetylenic and aromatic C-H stretching region.

Vibrational spectra in the acetylenic and aromatic C-H stretching regions of phenylacetylene and fluorophenylacetylenes, viz., 2-fluorophenylacetylene, 3-fluorophenylacetylene, and 4-fluorophenylacetylene, were measured using the IR-UV double resonance spectroscopic method. The spectra, in both acetylenic and aromatic C-H stretching regions, were complex exhibiting multiple bands. Ab-initio anharmonic calculations with quartic potential using B97D3/6-311++G(d,p) and vibrational configuration interaction were able to capture all important spectral features in both the regions of the experimentally observed spectra for all four molecules considered in the present work. Interestingly, for phenylacetylene, the spectrum in the acetylenic C-H stretching region emerges due to anharmonic coupling of modes localized on the acetylenic moiety along with the other ring modes, which also involve displacements on the acetylenic group, which is in contrast to what has been proposed and propagated in the literature. In general, this coupling scheme is invariant to the fluorine atom substitution. For the aromatic C-H stretching region, the observed spectrum emerges due to the coupling of the C-H stretching with C-C stretching and C-H in-plane bending modes.

An accurate and efficient fragmentation approach via the generalized many-body expansion for density matrices.

With relevant chemical space growing larger and larger by the day, the ability to extend computational tractability over that larger space is of paramount importance in virtually all fields of science. The solution we aim to provide here for this issue is in the form of the generalized many-body expansion for building density matrices (GMBE-DM) based on the set-theoretical derivation with overlapping fragments, through which the energy can be obtained by a single Fock build. In combination with the purification scheme and the truncation at the one-body level, the DM-based GMBE(1)-DM-P approach shows both highly accurate absolute and relative energies for medium-to-large size water clusters with about an order of magnitude better than the corresponding energy-based GMBE(1) scheme. Simultaneously, GMBE(1)-DM-P is about an order of magnitude faster than the previously proposed MBE-DM scheme [F. Ballesteros and K. U. Lao, J. Chem. Theory Comput. 18, 179 (2022)] and is even faster than a supersystem calculation without significant parallelization to rescue the fragmentation method. For even more challenging systems including ion-water and ion-pair clusters, GMBE(1)-DM-P also performs about 3 and 30 times better than the energy-based GMBE(1) approach, respectively. In addition, this work provides the first overlapping fragmentation algorithm with a robust and effective binning scheme implemented internally in a popular quantum chemistry software package. Thus, GMBE(1)-DM-P opens a new door to accurately and efficiently describe noncovalent clusters using quantum mechanics.

Approaching the "Zundel" Limit: Tuning the Vibrational Coupling in N2H+Ng, Ng = {He, Ne, Ar, Kr, Xe, and Rn}.

The diazenylium ion (N2H+) is a ubiquitous ion in dense molecular clouds. This ion is often used as a dense gas tracer in outer space. Most of the previous works on diazenylium ion have focused on the shared-proton stretch band, νH+. In this work, we have performed reduced-dimensional calculations to investigate the vibrational structure of N2H+Ng, Ng = {He, Ne, Ar, Kr, Xe, and Rn}. We demonstrate a few interesting things about this system. First, the vibrational coupling in N2H+ can be tuned to switch on interesting anharmonic effects such as Fermi resonance or combination bands by tagging it with different noble gases. Second, a comparison of the vibrational spectrum from N2H+He to N2H+Rn shows that the νH+ can be swept from an "Eigen-like" to a "Zundel-like" limiting case. Anharmonic calculations were performed using a multilevel approach, which utilized the MP2 and CCSD(T) levels of theories. Binding energies for the elimination of Ng in N2H+Ng are also reported.

The Grassmann interpolation method for spin-unrestricted open-shell systems.

The recently reported Grassmann interpolation (G-Int) method [J. A. Tan and K. U. Lao, J. Chem. Phys. 158, 051101 (2023)] has been extended to spin-unrestricted open-shell systems. In contrast to closed-shell systems, where G-Int has to be performed only once since the α and ß density matrices are the same, spin-unrestricted open-shell systems require G-Int to be performed twice-one for the α spin and another for the ß spin density matrix. In this work, we tested the performance of G-Int to the carbon monoxide radical cation CO●+ and nickelocene complex, which have the doublet and triple ground states, respectively. We found that the Frobenius norm errors associated with the interpolations for the α and ß spin density matrices are comparable for a given molecular geometry. These G-Int density matrices, when used as an initial guess for a self-consistent field (SCF) calculation, outperform the conventional SCF guess schemes, such as the superposition of atomic densities, purified superposition of atomic densities, core Hamiltonian, and generalized Wolfsberg-Helmholtz approximation. Depending on the desired accuracy, these G-Int density matrices can be used to directly evaluate the SCF energy without performing SCF iterations. In addition, the spin-unrestricted G-Int density matrices have been used for the first time to directly calculate the atomic charges using the Mulliken and ChElPG population analysis.

Generating accurate density matrices on the tangent space of a Grassmann manifold.

Interpolating a density matrix from a set of known density matrices is not a trivial task. This is because a linear combination of density matrices does not necessarily correspond to another density matrix. In this Communication, density matrices are examined as objects of a Grassmann manifold. Although this manifold is not a vector space, its tangent space is a vector space. As a result, one can map the density matrices on this manifold to their corresponding vectors in the tangent space and then perform interpolations on that tangent space. The resulting interpolated vector can be mapped back to the Grassmann manifold, which can then be utilized (1) as an optimal initial guess for a self-consistent field (SCF) calculation or (2) to derive energy directly without time-consuming SCF iterations. Such a promising approach is denoted as Grassmann interpolation (G-Int). The hydrogen molecule has been used to illustrate that the described interpolated method in this work preserves the essential attributes of a density matrix. For phosphorus mononitride and ferrocene, it was demonstrated numerically that reference points for the definition of the corresponding tangent spaces can be chosen arbitrarily. In addition, the interpolated density matrices provide a superior and essentially converged initial guess for an SCF calculation to make the SCF procedure itself unnecessary. Finally, this accurate, efficient, robust, and systematically improved G-Int strategy has been used for the first time to generate highly accurate potential energy surfaces with fine details for the difficult case, ferrocene.

Spectral Signatures of Protonated Noble Gas Clusters of Ne, Ar, Kr, and Xe: From Monomers to Trimers.

The structures and spectral features of protonated noble gas clusters are examined using a first principles approach. Protonated noble gas monomers (NgH+) and dimers (NgH+Ng) have a linear structure, while the protonated noble gas trimers (Ng3H+) can have a T-shaped or linear structure. Successive binding energies for these complexes are calculated at the CCSD(T)/CBS level of theory. Anharmonic simulations for the dimers and trimers unveil interesting spectral features. The symmetric NgH+Ng are charactized by a set of progression bands, which involves one quantum of the asymmetric Ng-H+ stretch with multiple quanta of the symmetric Ng-H+ stretch. Such a spectral signature is very robust and is predicted to be observed in both T-shaped and linear isomers of Ng3H+. Meanwhile, for selected asymmetric NgH+Ng', a Fermi resonance interaction involving the first overtone of the proton bend with the proton stretch is predicted to occur in ArH+Kr and XeH+Kr.

Structural and vibrational characterization of HCO+ and Rg-HCO+, Rg = {He, Ne, Ar, Kr, and Xe}.

The structures of the formyl ion (HCO+) and its rare gas tagged counterparts (Rg-HCO+, Rg = He, Ne, Ar, Kr, and Xe) were studied at the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)]/aug-cc-pVTZ level of theory and basis set. A linear structure for these tagged complexes was predicted. The Rg binding energies for Rg-HCO+ are also examined at the CCSD(T) level. It was found that the binding interaction increases from He-HCO+ to Xe-HCO+. A multilevel potential energy surface built at the CCSD(T) and second-order Møller-Plesset perturbation levels of theory were used to study these species' vibrational spectra. By changing the Rg in the first-solvation shell for HCO+, the Fermi resonance interaction between the first H+ bend overtone and the asymmetric and symmetric H-C-O stretches can be modulated. This Fermi resonance modulation is demonstrated by examining a series of rare gas solvated HCO+.

Fermi resonance switching in KrH+Rg and XeH+Rg (Rg = Ne, Ar, Kr, and Xe).

Matrix isolation experiments have been successfully employed to extensively study the infrared spectrum of several proton-bound rare gas complexes. Most of these studies have focused on the spectral signature for the H+ stretch (ν3) and its combination bands with the intermolecular stretch coordinate (ν1). However, little attention has been paid to the Fermi resonance interaction between the H+ stretch (ν3) and H+ bend overtone (2ν2) in the asymmetric proton-bound rare gas dimers, RgH+Rg'. In this work, we have investigated this interaction on KrH+Rg and XeH+Rg with Rg = (Ne, Ar, Kr, and Xe). A multilevel potential energy surface (PES) was used to simulate the vibrational structure of these complexes. This PES is a dual-level comprising of second-order Møller-Plesset perturbation theory and coupled-cluster singles doubles with perturbative triples [CCSD(T)] levels of ab initio theories. We found that when both the combination bands (nν1 + ν3) and bend overtone 2ν2 compete to borrow intensity from the ν3 band, the latter wins over the former, which then results in the suppression of the nν1 + ν3 bands. The current simulations offer new assignments for the ArH+Xe and KrH+Xe spectra. Complete basis set (CBS) binding energies for these complexes were also calculated at the CCSD(T)/CBS level.

Strong Fermi Resonance Associated with Proton Motions Revealed by Vibrational Spectra of Asymmetric Proton-Bound Dimers.

Infrared spectra for a series of asymmetric proton-bound dimers with protonated trimethylamine (TMA-H+ ) as the proton donor were recorded and analyzed. The frequency of the N-H+ stretching mode is expected to red shift as the proton affinity of proton acceptors increases. The observed band, however, shows a peculiar splitting of approximately 300 cm-1 with the intensity shifting pattern resembling a two-level system. Theoretical investigation reveals that the observed band splitting and its extraordinarily large gap of around 300 cm-1 is a result of strong coupling between the fundamental of the proton stretching mode and overtone states of the two proton bending modes, that is commonly known as Fermi resonance (FR). We also provide a general theoretical model to link the strong FR coupling to the quasi-two-level system. Since the model does not depend on the molecular specification of TMA-H+ , the strong coupling we observed is an intrinsic property associated with proton motions.

Structure and Vibrational Spectra of ArnH+ (n = 2-3).

The structure and vibrational spectra of protonated Ar clusters ArnH+ (n = 2-3) are studied using potential energy surfaces at the CCSD(T)/aug-cc-pVTZ level and basis set. Ar binding energies, as well as position isomerism in Ar3H+, were investigated. In our previous work, the spectra of Ar2H+ reveal a strong progression of combination bands, which involves the asymmetric Ar-H+ stretch with multiple quanta of the symmetric Ar-H+ stretch. In this work, insights on the origin of such progression were examined using an adiabatic model. In addition, contributions from mechanical and electrical anharmonicity on the progressions' intensities were also examined. Comparison of the calculated spectrum for the bare and Ar-tagged ions reveals that the reduction of the symmetry group, from D∞h to either C∞v or C2v, results in a richer vibrational structure in the 500-1700 cm-1 region. When compared with previously reported action spectra (D. C. McDonald III, D. T. Mauney, D. Leicht, J. H. Marks, J. A. Tan, J.-L. Kuo, and M. A. Duncan, J. Chem. Phys., 2016, 145, 231,101), it appears that the position isomers, because of the binding of the weakly bound Ar messenger, are needed to account for the additional bands in the infrared photodissociation spectrum for Ar3H+. These findings demonstrate the active role of the messenger atom in relaxing some of the selection rules for the bare ion's vibrational transitions - resulting in an augmentation of the bands in the action spectrum.

A theoretical study on the infrared signatures of proton-bound rare gas dimers (Rg-H+-Rg), Rg = {Ne, Ar, Kr, and Xe}.

The infrared spectrum of proton-bound rare gas dimers has been extensively studied via matrix isolation spectroscopy. However, little attention has been paid on their spectrum in the gas phase. Most of the Rg2H+ has not been detected outside the matrix environment. Recently, ArnH+ (n = 3-7) has been first detected in the gas-phase [D. C. McDonald et al., J. Chem. Phys. 145, 231101 (2016)]. In that work, anharmonic theory can reproduce the observed vibrational structure. In this paper, we extend the existing theory to examine the vibrational signatures of Rg2H+, Rg = {Ne, Ar, Kr, and Xe}. The successive binding of Rg to H+ was investigated through the calculation of stepwise formation energies. It was found that this binding is anti-cooperative. High-level full-dimensional potential energy surfaces at the CCSD(T)/aug-cc-pVQZ//MP2/aug-cc-pVQZ were constructed and used in the anharmonic calculation via discrete variable representation. We found that the potential coupling between the symmetric and asymmetric Rg-H+ stretch (ν1 and ν3 respectively) causes a series of bright n1ν1 + ν3 progressions. From Ne2H+ to Xe2H+, an enhancement of intensities for these bands was observed.

Multilevel Approach for Direct VSCF/VCI MULTIMODE Calculations with Applications to Large "Zundel" Cations.

We test existing efficient schemes for the "direct-dynamics" approach in building a potential energy surface (PES) in the code MULTIMODE. These are (1) the n-mode representation (nMR) approach to the PES, (2) the exploitation of the normal mode's symmetry to reduce the computational effort in constructing the PES, (3) the use of sparse grids for fitting the n-mode potentials, and (4) different levels of ab initio theory for these potentials. These schemes are applied to a four-dimensional calculation for the proton-bound methanol dimer (CH3OH)2H+. In addition to the major reduction in complexity obtained by considering only four modes, the combination of these schemes leads to a significant reduction in the computational effort without any major loss of accuracy. VSCF/VCI test calculations are presented for (CH3OH)2H+.

Infrared spectra and anharmonic coupling of proton-bound nitrogen dimers N2-H+-N2, N2-D+-N2, and 15N2-H+-15N2 in solid para-hydrogen.

The proton-bound nitrogen dimer, N2-H+-N2, and its isotopologues were investigated by means of vibrational spectroscopy. These species were produced upon electron bombardment of mixtures of N2 (or 15N2) and para-hydrogen (p-H2) or normal-D2 (n-D2) during deposition at 3.2 K. Reduced-dimension anharmonic vibrational Schrödinger equations were constructed to account for the strong anharmonic effects in these protonated species. The fundamental lines of proton motions in N2-H+-N2 were observed at 715.0 (NH+N antisymmetric stretch, ν4), 1129.6 (NH+N bend, ν6), and 2352.7 (antisymmetric NN/NN stretch, ν3) cm-1, in agreement with values of 763, 1144, and 2423 cm-1 predicted with anharmonic calculations using the discrete-variable representation (DVR) method at the CCSD/aug-cc-pVDZ level. The lines at 1030.2 and 1395.5 cm-1 were assigned to combination bands involving nν2 + ν4 (n = 1 and 2) according to theoretical calculations; ν2 is the N2N2 stretching mode. For 15N2-H+-15N2 in solid p-H2, the corresponding major lines were observed at 710.0 (ν4), 1016.7 (ν2 + ν4), 1124.3 (ν6), 1384.8 (2ν2 + ν4), and 2274.9 (ν3) cm-1. For N2-D+-N2 in solid n-D2, the corresponding major lines were observed at 494.0 (ν4), 840.7 (ν2 + ν4), 825.5 (ν6), and 2356.2 (ν3) cm-1. In addition, two lines at 762.0 (weak) and 808.3 cm-1 were tentatively assigned to be some modes of N2-H+-N2 perturbed or activated by a third N2 near the proton.

Tuning the vibrational coupling of H3O+ by changing its solvation environment.

This study demonstrates how the intermode coupling in the hydronium ion (H3O+) is modulated by the composition of the first solvation shell. A series of rare gas solvated hydronium ions (H3O+Rg3, where Rg = Ne, Ar, Kr, and Xe) is examined via reduced-dimensional anharmonic vibrational (RDAV) ab initio calculations. We considered six key vibrational normal modes, namely: a hindered rotation, two H-O-H bends, and three O-H stretches. Between the O-H stretches and the H-O-H bends, the first is more sensitive to solvation strength. Our calculations revealed that the Fermi resonance between the first overtones of O-H bends and the fundamentals of O-H stretches led to complex spectral features from 3000 to 3500 cm-1. Such an interaction is not only sensitive to the type of rare gas messengers surrounding the H3O+ ion, it also exhibits an anomalous H → D isotope effect. Although it is accepted that visible combination tones (∼1900 cm-1) arise from the complex coupling between the hindered rotation and the H-O-H bends, the origin of their intensities is not yet clearly understood. We found that the intensity of these combination tones could be much stronger than their fundamental H-O-H bends. Within our theoretical framework, we tracked the combination tone's intensity back to the asymmetric O-H stretches. This simple notion of intensity borrowing is confirmed by examining eight complexes (H3O+·Rg3 and D3O+·Rg3) with spectral features awaiting experimental confirmations.

A closer examination of the coupling between ionic hydrogen bond (IHB) stretching and flanking group motions in (CH3OH)2H(+): the strong isotope effects.

The intermode coupling between shared proton (O-H(+)-O) fundamental stretching and flanking modes in (CH3OH)2H(+) was revisited in the following contexts: (1) evaluation of Hamiltonian matrix elements represented in a "pure state" (PS) basis and (2) tuning of coupling strengths using H/D isotopic substitution. We considered four experimentally accessible isotopologues for this study. These are: (CH3OH)2H(+), (CD3OH)2H(+), (CH3OD)2D(+), and (CD3OD)2D(+). Potential energy surfaces (PESs), as well as dipole moment surfaces (DMSs), were constructed at the MP2/aug-cc-pVDZ level. Multidimensional vibrational calculations were conducted by solving a reduced dimensional Schrödinger equation using a discrete variable representation (DVR). We found that vibrational states in (CH3OH)2H(+) and (CD3OH)2H(+) are much more heavily mixed than those in (CH3OD)2D(+) and (CD3OD)2D(+). Furthermore, each isotopologue chooses to strongly couple between out-of-phase in-plane CH3 rocking and its out-of-plane counterpart. Lastly, the interaction between O-O stretching and O-H(+)-O stretching was explored. We found that between the first overtone of O-O stretching and its combination tone with O-H(+)-O fundamental stretching, only the second couples with O-H(+)-O fundamental stretching. We hope that our isotopologue calculations would motivate experimentalists to measure them in the future.

Strong Quantum Coupling in the Vibrational Signatures of a Symmetric Ionic Hydrogen Bond: The Case of (CH3OH)2H(.).

Vibrational coupling between proton and flanking group motions in the ionic hydrogen bond (IHB) of (CH3OH)2H(+) were studied by solving reduced-dimension vibrational Schrödinger equations. Potential energy and dipole surfaces along a few key normal modes were constructed with high-level ab initio methods. It was found that the IHB stretch parallel to O-O axis strongly couples with the out-of-phase C-O stretch and out-of-phase in-plane CH3 rock with COH deformation. Such strong quantum coupling leads to a complex triplet at 850-1100 cm(-1) region. Furthermore, we have investigated the possible active role of torsional motion in intensity redistribution.