Toward spectroscopic accuracy for open-shell systems: molecular structure and hyperfine coupling constants of H2CN, H2CP, NH2, and PH2 as test cases

The Semiexperimental Approach at Work: Equilibrium Structure of Radical Species

The so-called semiexperimental (SE) approach is a powerful technique for obtaining highly accurate equilibrium structures for isolated systems. This Featured Article describes its extension to open-shell species, thus providing the first systematic investigation on radical equilibrium geometries to be used for benchmarking purposes. The small yet significant database obtained demonstrates that there is no reduction in accuracy when moving from closed-shell species to radicals. We also provide an extension of the applicability of the SE approach to medium-/large-sized radicals by exploiting the so-called "Lego-brick" approach, which is based on the assumption that a molecular system can be seen as formed by smaller fragments for which the SE equilibrium structure is available. In this Featured Article we show that this model can be successfully applied also to open-shell species.

Electron correlation and vibrational effects in predictions of paramagnetic NMR shifts

Electronic structure calculations are fundamentally important for the interpretation of nuclear magnetic resonance (NMR) spectra from paramagnetic systems that include organometallic and inorganic compounds, catalysts, or metal-binding sites in proteins. Prediction of induced paramagnetic NMR shifts requires knowledge of electron paramagnetic resonance (EPR) parameters: the electronic g tensor, zero-field splitting D tensor, and hyperfine A tensor. The isotropic part of A, called the hyperfine coupling constant (HFCC), is one of the most troublesome properties for quantum chemistry calculations. Yet, even relatively small errors in calculations of HFCC tend to propagate into large errors in the predicted NMR shifts. The poor quality of A tensors that are currently calculated using density functional theory (DFT) constitutes a bottleneck in improving the reliability of interpretation of the NMR spectra from paramagnetic systems. In this work, electron correlation effects in calculations of HFCCs with a hierarchy of ab initio methods were assessed, and the applicability of different levels of DFT approximations and the coupled cluster singles and doubles (CCSD) method was tested. These assessments were performed for the set of selected test systems comprising an organic radical, and complexes with transition metal and rare-earth ions, for which experimental data are available. Severe deficiencies of DFT were revealed but the CCSD method was able to deliver good agreement with experimental data for all systems considered, however, at substantial computational costs. We proposed a more computationally tractable alternative, where the A was computed with the coupled cluster theory exploiting locality of electron correlation. This alternative is based on the domain-based local pair natural orbital coupled cluster singles and doubles (DLPNO-CCSD) method. In this way the robustness and reliability of the coupled cluster theory were incorporated into the modern formalism for the prediction of induced paramagnetic NMR shifts, and became applicable to systems of chemical interest. This approach was verified for the bis(cyclopentadienyl)vanadium(II) complex (Cp₂V; vanadocene), and the metal-binding site of the Zn²⁺ → Co²⁺ substituted superoxide dismutase (SOD) metalloprotein. Excellent agreement with experimental NMR shifts was achieved, which represented a substantial improvement over previous theoretical attempts. The effects of vibrational corrections to orbital shielding and hyperfine tensor were evaluated and discussed within the second-order vibrational perturbation theory (VPT2) framework.

Photoelectron spectroscopy of low valent organophosphorus compounds, P-CH3, H-PCH2 and PCH2

We report the mass-selected slow photoelectron spectra of three reactive organophosphorus species, PCH₂, and the two isomers, methylenephosphine or phosphaethylene, HPCH₂ and methylphosphinidine, P-CH₃. All spectra were recorded by double imaging photoelectron-photoion coincidence spectroscopy (i²PEPICO) using synchrotron radiation and all species were generated in a flow reactor by the reaction of trimethyl phosphine with fluorine atoms. Adiabatic ionisation energies of 8.80 ± 0.02 eV (PCH₂), 10.07 ± 0.03 eV (H-PCH₂) and 8.91 ± 0.04 eV (P-CH₃) were determined and the vibronic structure was simulated by calculating Franck-Condon factors from optimised structures based on quantum chemical methods. Observation of biradicalic P-CH₃ isomer with its triplet ground state is surprising because it is less stable than H-PCH₂.

Ab Initio Study of Fine and Hyperfine Interactions in Triplet POH

Phosphorous-containing molecules have a great relevance in prebiotic chemistry in view of the fact that phosphorous is a fundamental constituent of biomolecules, such as RNA, DNA, and ATP. Its biogenic importance has led astrochemists to investigate the possibility that P-bearing species could have formed in the interstellar medium (ISM) and subsequently been delivered to early Earth by rocky bodies. However, only two P-bearing molecules have been detected so far in the ISM, with the chemistry of interstellar phosphorous remaining poorly understood. Here, in order to shed further light on P-carriers in space, we report a theoretical spectroscopic characterisation of the rotational spectrum of POH in its 3A″ ground electronic state. State-of-the-art coupled-cluster schemes have been employed to derive rotational constants, centrifugal distortion terms, and most of the fine and hyperfine interaction parameters, while the electron spin-spin dipolar coupling has been investigated using the multi-configuration self-consistent-field method. The computed spectroscopic parameters have been used to simulate the appearance of triplet POH rotational and ro-vibrational spectra in different conditions, from cold to warm environments, either in gas-phase experiments or in molecular clouds. Finally, we point out that the predicted hyperfine structures represent a key pattern for the recognition of POH in laboratory and interstellar spectra.

A global CHIPR potential energy surface of PH2(X2B1) via extrapolation to the complete basis set limit and the dynamics of P(2D) + H2(X1Σ+g) → PH(X3Σ−) + H(2S)

A global PEC of the ground state PH2 was constructed using the CHIPR method based on accurate MRCI(Q)/CBS(T, Q) energy points. The ICS and k(T) of P(2D) + H2(X1Σ+g) → PH(X3Σ−) + H(2S) were calculated based on the QCT method.

A Joint Venture of Ab Initio Molecular Dynamics, Coupled Cluster Electronic Structure Methods, and Liquid-State Theory to Compute Accurate Isotropic Hyperfine Constants of Nitroxide Probes in Water

The isotropic hyperfine coupling constant (HFCC, Aiso) of a pH-sensitive spin probe in a solution, HMI (2,2,3,4,5,5-hexamethylimidazolidin-1-oxyl, C9H19N2O) in water, is computed using an ensemble of state-of-the-art computational techniques and is gauged against X-band continuous wave electron paramagnetic resonance (EPR) measurement spectra at room temperature. Fundamentally, the investigation aims to delineate the cutting edge of current first-principles-based calculations of EPR parameters in aqueous solutions based on using rigorous statistical mechanics combined with correlated electronic structure techniques. In particular, the impact of solvation is described by exploiting fully atomistic, RISM integral equation, and implicit solvation approaches as offered by ab initio molecular dynamics (AIMD) of the periodic bulk solution (using the spin-polarized revPBE0-D3 hybrid functional), embedded cluster reference interaction site model integral equation theory (EC-RISM), and polarizable continuum embedding (using CPCM) of microsolvated complexes, respectively. HFCCs are obtained from efficient coupled cluster calculations (using open-shell DLPNO-CCSD theory) as well as from hybrid density functional theory (using revPBE0-D3). Re-solvation of "vertically desolvated" spin probe configuration snapshots by EC-RISM embedding is shown to provide significantly improved results compared to CPCM since only the former captures the inherent structural heterogeneity of the solvent close to the spin probe. The average values of the Aiso parameter obtained based on configurational statistics using explicit water within AIMD and from EC-RISM solvation are found to be satisfactorily close. Using either such explicit or RISM solvation in conjunction with DLPNO-CCSD calculations of the HFCCs provides an average Aiso parameter for HMI in aqueous solution at 300 K and 1 bar that is in good agreement with the experimentally determined one. The developed computational strategy is general in the sense that it can be readily applied to other spin probes of similar molecular complexity, to aqueous solutions beyond ambient conditions, as well as to other solvents in the longer run.

Performance of the DLPNO-CCSD and recent DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals

In the present study, the performance of a set of density functionals: BP86, PBE, OLYP, BEEF, PBEpow, TPSS, SCAN, PBEGXPBE, M06L, MN15L, B3LYP, PBE0, mPW1PW, B97, BHandHLYP, mPW1PW, B98, TPSS0, PBE1KCIS, SCAN0, M06, M06-2X, MN15, CAM-B3LYP, ωB97x, B2PLYP, and the B3LYP/N07D and PBE/N07D schemes in the calculation of the ¹⁴N anisotropic hyperfine coupling (HFC) constants of a set of 23 nitroxide radicals is evaluated. The results are compared with those obtained with the DLPNO-CCSD method and experimental HFC values. Harmonic contribution to the ¹⁴N HFC vibrational correction was calculated at the revPBE0/def2-TZVPP level and included in the evaluation. With the vibrational correction, the DLPNO-CCSD method yielded HFC values in good agreement with the experiment (mean absolute deviation (MAD) = 0.3 G for the dipole-dipole contribution and MAD = 0.8 G for the contact coupling contribution). The best DFT results are obtained using the M06 functional with MAD = 0.2 G for the dipole-dipole contribution and MAD = 0.7 G for the contact coupling contribution. In general, vibrational correction significantly improved most DFT functionals' performance but did not change its overall ranking.

Description of the Methylene Amidogene Radical and Its Anion with an Economical Treatment of Correlation Effects Using Density Functional Theory Orbitals

The ground and low-lying excited state electronic structural properties (such as equilibrium geometries, harmonic frequencies, excitation energies, barrier energy, and so on) of the methylene amidogene radical (H₂CN) and its anion (H₂CN^-) have been studied using the CASCI (complete active space configuration interaction) and SSMRPT (state-specific multireference Møller-Plesset perturbation theory) methods with density function theory (DFT) orbitals. Here, the span of the active orbitals have been obtained from Kohn-Sham DFT using B3LYP exchange-correlation functionals in the CASCI (DFT-CASCI) approximation to describe nondynamic correlation associated with electronic degeneracies. The DFT-SSMRPT protocol provides an attractive way to deal with both dynamical and nondynamical correlation effects in strongly correlated systems such as H₂CN and H₂CN^-. The present work clearly indicates that the electronic absorption band near 35,050 cm^-1 corresponds to the B̃²A₁ ← X̃²B₂ transition. DFT-SSMRPT findings are in close agreement with high-level theoretical estimates. It is concluded that the transition at 1725 cm^-1 could be due to the CN stretching of the trans-HCNH isomer which is originally assigned to the CN stretch of H₂CN in the experiment. The present results confirm most of the previous vibrational assignments. It is not possible to definitively assign a transition to the 35,600 cm^-1 band with the present estimations, suggesting further experiment is urgently called for.

Hyperfine-Coupling Tensors from Projected Hartree-Fock Theory

We assess the calculation of hyperfine coupling (HFC) tensors by different variants of Projected Hartree-Fock (PHF) theory. For a set of small main-group S = 1/2 radicals (BO, CO⁺, CN, AlO, vinyl, methyl, ethynyl), spin-symmetry as well as complex-conjugation and point-group symmetry are first broken in a reference determinant, and then variationally restored, in the frame of the modern formulation of PHF theory. Historically, PHF theory was basically restricted to the restoration of spin symmetry from an unrestricted HF determinant (conserving S_z symmetry). This afforded unsatisfactory HFCs. We obtain far better results for isotropic (and anisotropic) HFCs when the variational energy is further lowered by working with generalized determinants that completely break spin symmetry, and when additional symmetries are used. Specifically, complex-conjugation projection recovers a substantial fraction of the dynamical correlation energy in small molecules, and the detailed equations for combined complex-conjugation, spin- and point-group projection in the density-matrix/diagonalization formulation of PHF theory are here reported for the first time. The compact representation of the PHF wave function allows for a straightforward evaluation of the spin-density matrix and of HFC tensors with little effort. The promising performance of PHF theory may motivate the application of post-PHF methods to the calculation of HFC tensors.

Magnetic Properties and Electronic Structure of the S = 2 Complex [MnIII{(OPPh2)2N}3] Showing Field-Induced Slow Magnetization Relaxation

The high-spin S = 2 Mn(III) complex [Mn{(OPPh₂)₂N}₃] (1_Mn) exhibits field-induced slow relaxation of magnetization (Inorg. Chem. 2013, 52, 12869). Magnetic susceptibility and dual-mode X-band electron paramagnetic resonance (EPR) studies revealed a negative value of the zero-field-splitting (zfs) parameter D. In order to explore the magnetic and electronic properties of 1_Mn in detail, a combination of experimental and computational studies is presented herein. Alternating-current magnetometry on magnetically diluted samples (1_Mn/1_Ga) of 1_Mn in the diamagnetic gallium analogue, [Ga{(OPPh₂)₂N}₃], indicates that the slow relaxation behavior of 1_Mn is due to the intrinsic properties of the individual molecules of 1_Mn. Investigation of the single-crystal magnetization of both 1_Mn and 1_Mn/1_Ga by a micro-SQUID device reveals hysteresis loops below 1 K. Closed hysteresis loops at a zero direct-current magnetic field are observed and attributed to fast quantum tunneling of magnetization. High-frequency and -field EPR (HFEPR) spectroscopic studies reveal that, apart from the second-order zfs terms (D and E), fourth-order terms (B₄^m) are required in order to appropriately describe the magnetic properties of 1_Mn. These studies provide accurate spin-Hamiltonian (sH) parameters of 1_Mn, i.e., zfs parameters |D| = 3.917(5) cm^-1, |E| = 0.018(4) cm^-1, B⁰₄ = B₄² = 0, and B₄⁴ = (3.6 ± 1.7) × 10^-3 cm^-1 and g = [1.994(5), 1.996(4), 1.985(4)], and confirm the negative sign of D. Parallel-mode X-band EPR studies on 1_Mn/1_Ga and CH₂Cl₂ solutions of 1_Mn probe the electronic-nuclear hyperfine interactions in the solid state and solution. The electronic structure of 1_Mn is investigated by quantum-chemical calculations by employing recently developed computational protocols that are grounded on ab initio wave function theory. From computational analysis, the contributions of spin-spin and spin-orbit coupling to the magnitude of D are obtained. The calculations provide also computed values of the fourth-order zfs terms B₄^m, as well as those of the g and hyperfine interaction tensor components. In all cases, a very good agreement between the computed and experimentally determined sH parameters is observed. The magnetization relaxation properties of 1_Mn are rationalized on the basis of the composition of the ground-state wave functions in the absence or presence of an external magnetic field.

How accurate is density functional theory in predicting spin density? An insight from the prediction of hyperfine coupling constants

Electron paramagnetic resonance (EPR) spectroscopy has been proven to be an important technique for studying paramagnetic systems. Probably, the most accessible EPR parameter and the one that provides a significant amount of information about molecular structure and spin density is the hyperfine coupling constant (HFCC). Hence, accurate quantum-chemical modeling of HFCCs is frequently essential to the adequate interpretation of EPR spectra. It requires the precise spin density, which is the difference between the densities of α- and β-electrons, and thus, its quality is expected to reflect the quality of the total electron density. The question of which approximate exchange-correlation density functional yields sufficiently accurate HFCCs, and thus, the spin density remains open. To assess the performance of well-established density functionals for calculating HFCCs, we used a series of 26 small paramagnetic species and compared the obtained results to the CCSD reference values. The performance of DFT was also tested on EPR-studied o-semiquinone radical interacting with water molecules and Mg²⁺ cation. The HFCCs were additionally calculated by the DLPNO-CCSD method, and this wave function-based technique was found superior to all functionals we tested. Although some functionals were found, on average, to be fairly efficient, we found that the most accurate functional is system-dependent, and therefore, the DLPNO-CCSD method should be preferred for theoretical investigations of the HFCCs and spin density.

Equilibrium Structures of the Phosphorus Trihalides PF3 and PCl3, and the Phosphoranes PH3F2, PF5, PCl3F2, and PCl5

Among the title species, a reliable and accurate equilibrium geometry ( re structure) is available only for PF3, which has been determined experimentally more than 20 years ago. Here, we report accurate re structures for all title molecules, which were obtained using a composite computational approach based on explicitly correlated coupled-cluster theory (CCSD(T)-F12b) in conjunction with a large correlation-consistent basis set (cc-pCVQZ-F12) to take core-valence electron correlation into account. Additional terms were included to correct for the effects of iterative triple excitations (CCSDT), noniterative quadruple excitations (CCSDT(Q)), and scalar relativistic contributions (DKH2-CCSD(T)). The performance of this computational procedure was established through test calculations on selected small molecules (PH, PF, PCl, PH2, PF2, and PH3). For PF3, PCl3, PH3F2, and PF5 sufficiently accurate experimental ground-state rotational constants from the literature were used to determine semiexperimental re structures, which were found to be in excellent agreement with the corresponding best estimates from the current composite approach. The recommended equilibrium structural parameters are for PCl3, re(PCl) = 203.94 pm and θe(ClPCl) = 100.18°; for PH3F2, re(PHeq) = 138.38 pm and re(PFax) = 164.15 pm; for PF5, re(PFeq) = 153.10 pm and re(PFax) = 157.14 pm; for PCl3F2, re(PCleq) = 200.21 pm and re(PFax) = 159.37 pm; and for PCl5, re(PCleq) = 201.29 pm and re(PClax) = 211.83 pm. The associated uncertainties are estimated to be ±0.10 pm and ±0.10°, respectively.

Accurate Prediction of Hyperfine Coupling Tensors for Main Group Elements Using a Unitary Group Based Rigorously Spin-Adapted Coupled-Cluster Theory

We present the development of a perturbative triples correction scheme for the previously reported unitary group based spin-adapted combinatoric open-shell coupled-cluster (CC) singles and doubles (COS-CCSD) approach and report on the applications of the newly developed method, termed "COS-CCSD(T)", to the calculation of hyperfine coupling (HFC) tensors for radicals consisting of hydrogen, second- and third-row elements. The COS-CCSD(T) method involves a single noniterative step with [Formula: see text] scaling of the computational cost for the calculation of triples corrections to the energy. The key feature of this development is the use of spatial semicanonical orbitals generated from standard restricted open-shell Hartree-Fock (ROHF) orbitals, which allows the unperturbed Hamiltonian operator to be defined in terms of a diagonal spin-free Fock operator. The HFC tensors are computed as a first-order property via implementation of an analytic derivative scheme. The required one-particle spin density matrix is computed by using one- and two-particle spin-free density matrices that are obtained from the analytic derivative implementation, in this way avoiding the use of any spin-dependent operator and maintaining spin adaptation of the CC wavefunction. Benchmark calculations of HFC tensors for a set of 21 radicals indicate reasonably good agreement of the COS-CCSD(T) results with experiment and a consistent improvement over the COS-CCSD method. We demonstrate that the accuracies of the isotropic hyperfine coupling constants obtained in unrestricted HF (UHF) reference based spin-orbital CCSD(T) calculations deteriorate when spin contamination in the UHF wavefunction is large, and the results may even become qualitatively incorrect when spin polarization is the driving mechanism. Within a similar noniterative perturbative treatment of triple excitations, the spin-adapted COS-CCSD(T) approach produces accurate results, thus ensuring cost-effectiveness together with reliability.

Accurate spin-densities based on the domain-based local pair-natural orbital coupled-cluster theory

Exploiting locality in the electron correlation reduces the computational cost for solving the Coupled-Cluster (CC) equations. This is important for making CC theory applicable to routine computational chemistry applications where it promises to deliver results of "gold-standard" quality. Recently, we have proposed a series of CC formulations in the domain-based local pair-natural orbital framework [DLPNO-coupled-cluster with singles and doubles (CCSD) and DLPNO-coupled-cluster singles and doubles with perturbative triples] which are designed to reproduce approximately 99.9% of the canonical correlation energy. In our previous work, the DLPNO-CCSD method has been extended to the high-spin open-shell reference and shown to possess comparable accuracy to the closed-shell counterpart [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)]. The so-called Λ-equations have been formulated in the DLPNO framework for the closed-shell species as an exact derivative of the DLPNO-CCSD Lagrangian with respect to the PNO-based cluster amplitudes [D. Datta et al., J. Chem. Phys. 145, 114101 (2016)]. In this paper, we extend the DLPNO-based Lagrangian scheme to the high-spin open-shell reference cases, thus enabling the accurate computation of the electron- and spin-densities for large open-shell species. We apply this newly developed approach to various first-order electronic and magnetic properties such as isotropic and anisotropic components in the hyperfine coupling interactions and the electric field gradient. We demonstrate that the DLPNO-CCSD results converge toward the respective canonical CC density and also that the DLPNO-CCSD-based properties are more accurate than the conventional density functional theory (DFT) results in real-life applications. The additional computational cost is not more than one energy evaluation in the DLPNO-CCSD framework.

Selected-Nuclei Method for the Computation of Hyperfine Coupling Constants within Second-Order Møller-Plesset Perturbation Theory

We introduce a new ansatz to compute hyperfine coupling constants of selected nuclei at the level of second-order Møller-Plesset perturbation (MP2) and double-hybrid density functional theory with reduced computational effort, opening the route to the analyis of hyperfine coupling constants of large molecular structures. Our approach is based on a reformulation of the canonical MP2 term in atomic orbitals, thus exploiting the locality of electron correlation. We show that a perturbation-including integral screening reduces the scaling behavior of the number of significant two-electron integrals to sublinear. This selected-nuclei approach allows for an efficient computation within scaled-opposite spin (SOS) RI-MP2 on massively parallelized architectures such as graphical processor units (GPUs), thus enabling studies on the influence of the environment on hyperfine coupling constants.

Laboratory measurements and astronomical search for the HSO radical

CONTEXT

Despite the fact that many sulfur-bearing molecules, ranging from simple diatomic species up to astronomical complex molecules, have been detected in the interstellar medium, the sulfur chemistry in space is largely unknown and a depletion in the abundance of S-containing species has been observed in the cold, dense interstellar medium (ISM). The chemical form of the missing sulfur has yet to be identified.

AIMS

For these reasons, in view of the fact that there is a large abundance of triatomic species harbouring sulfur, oxygen, and hydrogen, we decided to investigate the HSO radical in the laboratory to try its astronomical detection.

METHODS

High-resolution measurements of the rotational spectrum of the HSO radical were carried out within a frequency range well up into the THz region. Subsequently, a rigorous search for HSO in the two most studied high-mass star-forming regions, Orion KL and Sagittarius (Sgr) B2, and in the cold dark cloud Barnard 1 (B1-b) was performed.

RESULTS

The frequency coverage and the spectral resolution of our measurements allowed us to improve and extend the existing dataset of spectroscopic parameters, thus enabling accurate frequency predictions up to the THz range. These were used to derive the synthetic spectrum of HSO, by means of the MADEX code, according to the physical parameters of the astronomical source under consideration. For all sources investigated, the lack of HSO lines above the confusion limit of the data is evident.

CONCLUSIONS

The derived upper limit to the abundance of HSO clearly indicates that this molecule does not achieve significant abundances in either the gas phase or in the ice mantles of dust grains.

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.

Rotational spectroscopy meets theory

Rotational spectroscopy is known to be a technique that is widely used to infer information on molecular structure and dynamics. In the last few decades, its role in the field of atmospheric and astrophysical investigations has rapidly grown. However, several are the challenging aspects in rotational spectroscopy, since the detection and analysis of spectra as well as interpretation of obtained results are not at all straightforward. Quantum chemistry has reached such an accuracy that can be used to disentangle these challenging situations by guiding the experimental investigation, assisting in the determination of the spectroscopic parameters, and extracting information of chemical interest. This perspective provides an overview of the theoretical background and computational requirements needed for the accurate evaluation of the spectroscopic parameters of relevance to rotational spectroscopy. The role of theory in guiding and supporting experiment is detailed through a few examples, and the interplay of experiment and theory is discussed in terms of the information of physical and chemical interest that can be derived.

Franck-Condon simulation, including anharmonicity, of the photodetachment spectrum of P2H(-): restricted-spin coupled-cluster single-double plus perturbative triple and unrestricted-spin coupled-cluster single-double plus perturbative triple -F12x potential energy functions of P2H and P2H(-)

Geometry optimization and harmonic vibrational frequency calculations have been carried out on the X̃(2)A(') state of P(2)H and the X̃(1)A(') state of P(2)H(-) using the restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] and explicitly correlated unrestricted-spin coupled-cluster single-double plus perturbative triple excitation [UCCSD(T)-F12x] methods. For RCCSD(T) calculations, basis sets of up to the augmented correlation-consistent polarized valence quintuple-zeta (aug-cc-pV5Z) quality were employed, and contributions from extrapolation to the complete basis set limit and from core correlation of the P 2s(2)2p(6) electrons were also included. For UCCSD(T)-F12x calculations, different atomic orbital basis sets of triple-zeta quality with different associated complementary auxiliary basis sets and different geminal Slater exponents were used. When the P 2s(2)2p(6) core electrons were correlated in these F12x calculations, appropriate core-valence basis sets were employed. In addition, potential energy functions (PEFs) of the X̃(2)A(') state of P(2)H and the X̃(1)A(') state of P(2)H(-) were computed at different RCCSD(T) and UCCSD(T)-F12x levels, and were used in variational calculations of anharmonic vibrational wavefunctions, which were then utilized to calculate Franck-Condon factors (FCFs) between these two states, employing a method which includes allowance for anharmonicity and Duschinsky rotation. The photodetachment spectrum of P(2)H(-) was then simulated using the computed FCFs. Simulated spectra obtained using the RCCSD(T)/aug-cc-pV5Z and UCCSD(T)-F12x(x = a or b)/aug-cc-pCVTZ PEFs are compared and found to be essentially identical. Based on the computed FCFs, a more detailed assignment of the observed vibrational structure than previously reported, which includes "hot bands," has been proposed. Comparison between simulated and available experimental spectra has been made, and the currently most reliable sets of equilibrium geometrical parameters for P(2)H and its anion have been derived. The photodetachment spectrum of P(2)D, yet to be recorded, has also been simulated.