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Properly spin-adapted coupled-cluster theory for general open-shell configurations remains an active area of research in electronic structure theory. In this contribution we examine Lindgren's normal-ordered exponential ansatz to correlate specific spin states using spin-free excitation operators, with the aid of automatic equation generation software. We present an intermediately normalised and size-extensive reformulation of the unlinked working equations, and analyse the performance of the method with single and double excitations for simple molecular systems in terms of accuracy and size-consistency.

We extend the intrinsic atomic orbital (IAO) method for the localization of molecular orbitals to calculate well-localized generalized Wannier functions in crystals in the spirit of the Pipek-Mezey method. We furthermore present a one-shot diabatic Wannierization procedure that aligns the phases of the Bloch functions, providing immediate Wannier localization, which serves as an excellent initial guess for optimization. We test our Wannier localization implementation on a number of solid-state systems, highlighting the effectiveness of the diabatic preparation, especially for localizing core bands. Partial charges of Wannier functions generated using Bloch IAOs align well with chemical intuition, which we demonstrate through the example of the adsorption of CO on a MgO surface.

Computation of heats of reaction of large molecules is now feasible using the domain-based pair natural orbital (PNO)-coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] theory. However, to obtain agreement within 1 kcal/mol of experiment, it is necessary to eliminate basis set incompleteness error, which comprises both the AO basis set error and the PNO truncation error. Our investigation into the convergence to the canonical limit of PNO-CCSD(T) energies with the PNO truncation threshold T shows that errors follow the model E ( T ) = E + A T 1 / 2 . Therefore, PNO truncation errors can be eliminated using a simple two-point CPS extrapolation to the canonical limit so that subsequent CBS extrapolation is not limited by the residual PNO truncation error. Using the ISOL24 and MOBH35 data sets, we find that PNO truncation errors are larger for molecules with significant static correlation and that it is necessary to use very tight thresholds of T = 10 - 8 to ensure that errors do not exceed 1 kcal/mol. We present a lower-cost extrapolation scheme that uses information from small basis sets to estimate the PNO truncation errors for larger basis sets. In this way, the canonical limit of CCSD(T) calculations on sizable molecules with large basis sets can be reliably estimated in a practical way. Using this approach, we report near complete basis set (CBS)-CCSD(T) reaction energies for the full ISOL24 and MOBH35 data sets.

We report the development of a novel variant of cavity ringdown polarimetry using a continuous-wave laser operating at 532 nm for highly precise chiroptical activity and magnetometry measurements. The key methodology of the apparatus relies upon the external modulation of the laser frequency at the frequency splitting between non-degenerate left- and right-circularly polarized cavity modes. The method is demonstrated by the evaluation of the Verdet constants of crystalline CeF3 and fused silica, in addition to the observation of gas- and solution-phase optical rotations of selected chiral molecules. Specifically, optical rotations of (i) vapors of α-pinene and R-(+)-limonene, (ii) mutarotating D-glucose in water, and (iii) acidified L-histidine solutions are determined. The detection sensitivities for the gas- and solution-phase chiral activity measurements are ∼30 and ∼120μdeg over a 30 s detection period per cavity round trip pass, respectively. Furthermore, the measured optical rotations for R-(+)-limonene are compared with computations performed using the TURBOMOLE quantum chemistry package. The experimentally observed optically rotatory dispersion of this cyclic monoterpene was thus rationalized via a consideration of its room temperature conformer distribution as determined by the aforementioned single-point energy calculations., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order Møller-Plesset perturbation theory and Coupled Cluster Singles and Doubles within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for larger Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2.

First-quantized, grid-based methods for chemistry modeling are a natural and elegant fit for quantum computers. However, it is infeasible to use today's quantum prototypes to explore the power of this approach because it requires a substantial number of near-perfect qubits. Here, we use exactly emulated quantum computers with up to 36 qubits to execute deep yet resource-frugal algorithms that model 2D and 3D atoms with single and paired particles. A range of tasks is explored, from ground state preparation and energy estimation to the dynamics of scattering and ionization; we evaluate various methods within the split-operator QFT (SO-QFT) Hamiltonian simulation paradigm, including protocols previously described in theoretical papers and our own techniques. While we identify certain restrictions and caveats, generally, the grid-based method is found to perform very well; our results are consistent with the view that first-quantized paradigms will be dominant from the early fault-tolerant quantum computing era onward.

Ab initio electronic excited state calculations are necessary for the quantitative study of photochemical reactions, but their accurate computation on classical computers is plagued by prohibitive resource scaling. The Variational Quantum Deflation (VQD) is an extension of the quantum-classical Variational Quantum Eigensolver (VQE) algorithm for calculating electronic excited state energies, and has the potential to address some of these scaling challenges using quantum computers. However, quantum computers available in the near term can only support a limited number of quantum circuit operations, so reducing the quantum computational cost in VQD methods is critical to their realisation. In this work, we investigate the use of adaptive quantum circuit growth (ADAPT-VQE) in excited state VQD calculations, a strategy that has been successful previously in reducing the resources required for ground state energy VQE calculations. We also invoke spin restrictions to separate the recovery of eigenstates with different spin symmetry to reduce the number of calculations and accumulation of errors in computing excited states. We created a quantum eigensolver emulation package - Quantum Eigensolver Building on Achievements of Both quantum computing and quantum chemistry (QEBAB) - for testing the proposed adaptive procedure against two existing VQD methods that use fixed-length quantum circuits: UCCGSD-VQD and k -UpCCGSD-VQD. For a lithium hydride test case we found that the spin-restricted adaptive growth variant of VQD uses the most compact circuits out of the tested methods by far, consistently recovers adequate electron correlation energy for different nuclear geometries and eigenstates while isolating the singlet and triplet manifold. This work is a further step towards developing techniques which improve the efficiency of hybrid quantum algorithms for excited state quantum chemistry, opening up the possibility of exploiting real quantum computers for electronic excited state calculations sooner than previously anticipated.

The rotational spectrum of the complex H 2 S⋯HI observed with a pulsed-jet, Fourier-transform microwave spectrometer shows that each rotational transition is split into a closely spaced doublet, a pattern similar to that observed earlier for the halogen-bonded complex H 2 S⋯F 2 . The origin of the doubling has been investigated by means of ab initio calculations conducted at the CCSD(T)(F12 * )/cc-pVDZ-F12 level. Two paths were examined by calculating the corresponding energy as a function of two angles. One path involved inversion of the configuration at S through a planar transition state of C 2v symmetry via changes in the angle ϕ between the C 2 axis of H 2 S and the line joining the H and I nuclei [the potential energy function V(ϕ)]. The other was a torsional oscillation θ about the local C 2 axis of H 2 S that also exchanges the equivalent H nuclei [the potential energy function V(θ)]. The inversion path is slightly lower in energy and much shorter in arc length and is therefore the favored tunneling pathway. In addition, calculation of V(ϕ) for the series of hydrogen- and halogen-bonded complexes H 2 S⋯HX (X = F, Cl, or Br) and H 2 S⋯XY (XY = Cl 2 , Br 2 , ClF, BrCl, or ICl) at the same level of theory revealed that doubling is unlikely to be resolved in these, in agreement with experimental observations. The barrier heights of the V(ϕ) of all ten complexes examined were found to be almost directly proportional to the dissociation energies D e.

We present the results of a benchmark study of the effect of Pair Natural Orbital (PNO) truncation errors on the performance of basis set extrapolation. We find that reliable conclusions from the application of Helgaker's extrapolation method are only obtained when using tight PNO thresholds of at least 10 -7 . The use of looser thresholds introduces a significant risk of observing a false basis set convergence and underestimating the residual basis set errors. We propose an alternative extrapolation approach based on the PNO truncation level that only requires a single basis set and show that it is a viable alternative to hierarchical basis set extrapolation methods.

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→C 2 H 4 +HOPO) at ca. 1000 K and subsequently trapped in an N 2 -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 (>10 4 for DOPO) and 16 O/ 18 O (1.19 for H 18 OPO and 1.06 for HOP 18 O) in N 2 -matrices., (© 2020 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

The rovibrational spectra of metaphosphorous acid, HOPO, and its deuterated isotopologue have been studied by vibrational configuration interaction calculations, relying on the internal coordinate path Hamiltonian and the Watson Hamiltonian. Tunneling effects for the overtones of the torsional mode, which gives rise to the cis-trans isomerization, and its rovibrational transitions have been investigated in detail. Due to strong matrix effects, comparison with experimental data is hindered, and thus, the calculations provide accurate estimates for the fundamental modes of these species.

Accurate theoretical methods are needed to correctly describe adsorption on solid surfaces or in porous materials. The random phase approximation (RPA) with singles corrections scheme and the second order Møller-Plesset perturbation theory (MP2) are two schemes, which offer high accuracy at affordable computational cost. However, there is little knowledge about their applicability and reliability for different adsorbates and surfaces. Here, we calculate adsorption energies of seven different molecules in zeolite chabazite to show that RPA with singles corrections is superior to MP2, not only in terms of accuracy but also in terms of computer time. Therefore, RPA with singles is a suitable scheme for obtaining highly accurate adsorption energies in porous materials and similar systems.

The computational efficiency of local correlation methods is strongly dependent on the size of the domain of functions used to expand local correlating orbitals such as orbital specific or pair natural orbitals. Here, we define a principal domain of order m as the subset of m one-particle functions that provides the best support for a given n -electron wave function by maximizing the partial trace of the one-body reduced density matrix. Principal domains maximize the overlap between the wave function and its approximant for two-electron systems and are the domain selection equivalent of Löwdin's natural orbitals. We present an efficient linear scaling greedy algorithm for obtaining principal domains of projected atomic orbitals and demonstrate its utility in the context of the pair natural orbital local correlation theory. We numerically determine thresholds such that the projected atomic orbital domain error is an order of magnitude smaller than the pair natural orbital truncation error.

Analytic second nuclear derivatives for excited electronic state energies have been implemented for the resolution-of-the-identity accelerated CC2, CIS(D ∞ ) and ADC(2) models. Our efficient implementation with O(N 2 ) memory demands enables the treatment of medium sized molecules with large basis sets and high numerical precision and thereby paves the way for semi-numerical evaluation of the higher-order derivatives required for anharmonic corrections to excited state vibrational frequencies. We compare CC2 harmonic and anharmonic excited state frequencies with experimental values for para-difluorobenzene, toluene and catechol. Basis set problems occur for out-of-plane bending vibrations due to intramolecular basis set superposition error. For non-planar molecules and in plane modes of planar molecules, the agreement between theory and experiment is better than 30 cm -1 on average and we reassign a number of experimental bands on the basis of the ab initio predictions.

Ammonia and amines are emitted into the troposphere by various natural and anthropogenic sources, where they have a significant role in aerosol formation. Here, we explore the significance of their removal by reaction with Criegee intermediates, which are produced in the troposphere by ozonolysis of alkenes. Rate coefficients for the reactions of two representative Criegee intermediates, formaldehyde oxide (CH2OO) and acetone oxide ((CH3)2COO) with NH3 and CH3NH2 were measured using cavity ring-down spectroscopy. Temperature-dependent rate coefficients, k(CH2OO + NH3) = (3.1 ± 0.5) × 10-20T2 exp(1011 ± 48/T) cm3 s-1 and k(CH2OO + CH3NH2) = (5 ± 2) × 10-19T2 exp(1384 ± 96/T) cm3 s-1 were obtained in the 240 to 320 K range. Both the reactions of CH2OO were found to be independent of pressure in the 10 to 100 Torr (N2) range, and average rate coefficients k(CH2OO + NH3) = (8.4 ± 1.2) × 10-14 cm3 s-1 and k(CH2OO + CH3NH2) = (5.6 ± 0.4) × 10-12 cm3 s-1 were deduced at 293 K. An upper limit of ≤2.7 × 10-15 cm3 s-1 was estimated for the rate coefficient of the (CH3)2COO + NH3 reaction. Complementary measurements were performed with mass spectrometry using synchrotron radiation photoionization giving k(CH2OO + CH3NH2) = (4.3 ± 0.5) × 10-12 cm3 s-1 at 298 K and 4 Torr (He). Photoionization mass spectra indicated production of NH2CH2OOH and CH3N(H)CH2OOH functionalized organic hydroperoxide adducts from CH2OO + NH3 and CH2OO + CH3NH2 reactions, respectively. Ab initio calculations performed at the CCSD(T)(F12*)/cc-pVQZ-F12//CCSD(T)(F12*)/cc-pVDZ-F12 level of theory predicted pre-reactive complex formation, consistent with previous studies. Master equation simulations of the experimental data using the ab initio computed structures identified submerged barrier heights of -2.1 ± 0.1 kJ mol-1 and -22.4 ± 0.2 kJ mol-1 for the CH2OO + NH3 and CH2OO + CH3NH2 reactions, respectively. The reactions of NH3 and CH3NH2 with CH2OO are not expected to compete with its removal by reaction with (H2O)2 in the troposphere. Similarly, losses of NH3 and CH3NH2 by reaction with Criegee intermediates will be insignificant compared with reactions with OH radicals.

Methodologies for creating reactive potential energy surfaces from molecular mechanics force-fields are becoming increasingly popular. To date, molecular mechanics force-fields in biochemistry and small molecule organic chemistry tend to use harmonic expressions to treat bonding stretches, which is a poor approximation in reactive and nonequilibirum molecular dynamics simulations since bonds are often displaced significantly from their equilibrium positions. For such applications there is need for a better treatment of anharmonicity. In this contribution, Morse bonding potentials have been extensively parametrized for the atom types in the MM3 force field of Allinger and co-workers using high level CCSD(T)(F12*) energies. To our knowledge this is among the first instances of a comprehensive parametrization of Morse potentials in a popular organic chemistry force field. In the context of molecular dynamics simulations, these data will: (1) facilitate the fitting of reactive potential energy surfaces using empirical valence bond approaches and (2) enable more accurate treatments of energy transfer.

The role of valence and semicore correlation in differentially stabilizing the intermediate spin state of Fe(II)-porphyrins is analyzed. For CASSCF treatments of valence correlation, a (32,34) active space containing metal 3 d, d' orbitals and the entire π system of the porphyrin is necessary to stabilize the intermediate spin state. Semicore correlation provides a minor (-1.6 kcal/mol) but quantitatively significant correction. Accounting for valence, semicore, and correlation beyond the active space enlarges the ( 3 E g - 5 A 1 g ) spin gap to -5.7 kcal/mol.

A combination of orbital-optimized methods with explicit correlation is discussed for the example of the orbital-optimized distinguishable cluster approach. It is shown that the perturbative approach is applicable even in strongly correlated situations, and it is important in these cases to use Lagrange multipliers together with the amplitudes. The partial amplitude relaxation can be applied to relax the amplitudes and makes absolute energies closer to complete basis set results.

Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into the calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but it is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but it requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.

We present a comprehensive theoretical study of the physical phenomena that determine the relative energies of three of the lowest electronic states of each of the square-planar copper complexes [CuCl 4 ] 2- , [Cu(NH 3 ) 4 ] 2+ , and [Cu(H 2 O) 4 ] 2+ and present a detailed analysis of the extent to which truncated configuration interaction (CI) and coupled cluster (CC) theories succeed in predicing the excitation energies. We find that ligand-metal charge transfer (CT) single excitations play a crucial role in the correct determination of the properties of these systems, even though the first impact of these CT on the energetics of these systems appears at fourth-order in perturbation theory. We provide a minimal selected CI space for describing these systems with multireference theories and use a high-order perturbation theory analysis within this space to derive a simple and general physical picture for the LMCT process. We find that coupled cluster singles and doubles (CCSD) energy differences agree very well with near full CI values even though the D 1 diagnostics are large, which casts doubt on the usefulness of single-amplitude-based multireference diagnostics. Configuration interaction singles and doubles (CISD) severely underestimates the excitation energies, and the failure is a direct consequence of the size-inconsisency errors in CISD. Finally, we present reference values for the energy differences computed using explicitly correlated CCSD(T) and BCCD(T) theory.

We present a Lagrangian correction for the energy change upon releasing constraints imposed on coupled cluster amplitudes. We demonstrate that our correction (i) eliminates the systematic basis set error of the posthoc F12 treatment in orbital optimized methods and (ii) can be used to relax the F12 amplitudes and significantly reduce the sensitivity of the core-valence correlation energies to the exponent of the correlation factor, while retaining the low cost of the fixed amplitude approach.

While the title question is a clear "yes" from purely theoretical arguments, the case is less clear for practical calculations with finite (one-particle) basis sets. To shed further light on this issue, the convergence to the basis set limit of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) has been investigated in detail for the W4-17 thermochemical benchmark. Near the CBS ([1-particle] complete basis set) limit, CCSD and CCSD(F12 * ) agree to within their respective uncertainties (about ±0.04 kcal/mol) due to residual basis set incompleteness error, but a nontrivial difference remains between CCSD-F12b and CCSD(F12 * ), which is roughly proportional to the degree of static correlation. The observed basis set convergence behavior results from the superposition of a rapidly converging, attractive, CCSD[F12]-CCSD-F12b difference (consisting mostly of third-order terms) and a more slowly converging, repulsive, fourth-order difference between CCSD(F12 * ) and CCSD[F12]. For accurate thermochemistry, we recommend CCSD(F12 * ) over CCSD-F12b if at all possible. There are some indications that the nZaPa family of basis sets exhibits somewhat smoother convergence than the correlation consistent family.

Advances in control techniques for vibrational quantum states in molecules present new challenges for modelling such systems, which could be amenable to quantum simulation methods. Here, by exploiting a natural mapping between vibrations in molecules and photons in waveguides, we demonstrate a reprogrammable photonic chip as a versatile simulation platform for a range of quantum dynamic behaviour in different molecules. We begin by simulating the time evolution of vibrational excitations in the harmonic approximation for several four-atom molecules, including H 2 CS, SO 3 , HNCO, HFHF, N 4 and P 4 . We then simulate coherent and dephased energy transport in the simplest model of the peptide bond in proteins-N-methylacetamide-and simulate thermal relaxation and the effect of anharmonicities in H 2 O. Finally, we use multi-photon statistics with a feedback control algorithm to iteratively identify quantum states that increase a particular dissociation pathway of NH 3 . These methods point to powerful new simulation tools for molecular quantum dynamics and the field of femtochemistry.

The requirement that the linear density fitting error in the integral exactly vanishes introduces unphysical long range contributions to the approximate density when the auxiliary basis is incomplete. A quasi-robust density fitting formulation is presented where spatial locality is recovered at the expense of permitting a linear error that is made small by the fitting procedure, which involves optimising the Coulomb potential of the approximate charge density. The method is shown to be stable and almost as accurate as standard robust density fitting without local approximations in practical calculations using standard density fitting basis sets.

The rotational spectra of H 3 N⋯AgI and H 2 O⋯AgI have been recorded between 6.5 and 18.5 GHz by chirped-pulse Fourier-transform microwave spectroscopy. The complexes were generated through laser vaporisation of a solid target of silver or silver iodide in the presence of an argon gas pulse containing a low concentration of the Lewis base. The gaseous sample subsequently undergoes supersonic expansion which results in cooling of rotational and vibrational motions such that weakly bound complexes can form within the expanding gas jet. Spectroscopic parameters have been determined for eight isotopologues of H 3 N⋯AgI and six isotopologues of H 2 O⋯AgI. Rotational constants, B 0 ; centrifugal distortion constants, D J , D JK or Δ J , Δ JK ; and the nuclear quadrupole coupling constants, χ aa (I) and χ bb (I) - χ cc (I) are reported. H 3 N⋯AgI is shown to adopt a geometry that has C 3v symmetry. The geometry of H 2 O⋯AgI is C s at equilibrium but with a low barrier to inversion such that the vibrational wavefunction for the v = 0 state has C 2v symmetry. Trends in the nuclear quadrupole coupling constant of the iodine nucleus, χ aa (I), of L⋯AgI complexes are examined, where L is varied across the series (L = Ar, H 3 N, H 2 O, H 2 S, H 3 P, or CO). The results of experiments are reported alongside those of ab initio calculations at the CCSD(T)(F12*)/AVXZ level (X = T, Q).

The shapes of macromolecules and their complexes with small molecules are often determined by extended networks of hydrogen bonds. Here, for the first time, we provide a detailed description of a cooperative pair of hydrogen bonds to an individual molecule of urea. The structure and properties of a gas phase complex formed between urea and isocyanic acid are characterised through microwave spectroscopy and ab initio calculations at the CCSD(T)(F12*)/aug-cc-pVTZ level.

The facile synthesis of a stable and isolable compound with a fluoroalkynyl group, M-C≡CF, is reported. Reaction of [Ru(C≡CH)(η 5 -C 5 Me 5 )(dppe)] with an electrophilic fluorinating agent (NFSI) results in the formation of the fluorovinylidene complex [Ru(=C=CHF)(η 5 -C 5 Me 5 )(dppe)][N(SO 2 Ph) 2 ]. Subsequent deprotonation with LiN(SiMe 3 ) 2 affords the fluoroalkynyl complex [Ru(C≡CF)(η 5 -C 5 Me 5 )(dppe)]. In marked contrast to the rare and highly reactive examples of fluoroalkynes that have been reported previously, this compound can be readily isolated and structurally characterized. This has allowed the structure and bonding in the CCF motif to be explored. Further electrophilic fluorination of this species yields the difluorovinylidene complex [Ru(C=CF 2 )(η 5 -C 5 Me 5 )(dppe)][N(SO 2 Ph) 2 ]., (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Extensive density functional theory (DFT) calculations using the B3LYP functional were used to explore the sextet and quartet energy potential energy surfaces (PESs) of the title reaction, and as a basis to fit global analytical reactive PESs. Surface-hopping dynamics on these PESs reproduce the experimentally observed reactivity and confirm that hydrogen activation rather than spin-state change is rate-limiting at low reaction energy, where the main products are Fe + and H 2 O. A change in spin state is inefficient in the product region so that excited-state 4 Fe + is the dominant product. At higher energies, spin-allowed hydrogen atom abstraction to form FeOH + predominates. At intermediate energy, a previously unexpected rebound mechanism contributes significantly to the reactivity., (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, nonfault tolerant, quantum devices. Here we report experimental results demonstrating that this intuition need not be true. We implement a recently proposed adaptive Bayesian approach to quantum phase estimation and use it to simulate molecular energies on a silicon quantum photonic device. The approach is verified to be well suited for prethreshold quantum processors by investigating its superior robustness to noise and decoherence compared to the iterative phase estimation algorithm. This shows a promising route to unlock the power of quantum phase estimation much sooner than previously believed.

A global analytic potential energy surface for the ro-vibrational dynamics of cis- and trans-formic acid is presented, constructed using LASSO-based regression to reproduce CCSD(T)(F12*)/cc-pVTZ-F12 energies. The fit is accurate to 0.25% has an RMS deviation from the ab initio data of 9 cm -1 for the energy range 0-15000 cm -1 . Converged J = 0 vibrational eigenstates are reported, computed using vibrational configuration interaction with an internal coordinate path Hamiltonian for the torsional motion connecting the cis and trans rotamers. Methodological choices concerning the appropriate definitions of the curvilinear and diabatic bath coordinates are discussed. The zero point of the cis rotamer is 1412 cm -1 above that of the trans, which lies at 7354 cm -1 . The computed fundamentals match the bands recorded from gas-phase IR spectroscopy with an RMSD of only 3 cm -1 . A fresh assignment of the overtone spectra of both the cis and trans rotamers is presented for the energy range 0-4720 cm -1 , where 14 out of the 51 bands are reassigned on the basis of the VCI calculations.

Complexes formed between H 2 S and each of CuI, AgI, and AuI have been isolated and structurally characterised in the gas phase. The H 2 S⋯MI complexes (where M is the metal atom) are generated through laser vaporisation of a metal rod in the presence of a low concentration of H 2 S and CF 3 I in a buffer gas of argon undergoing supersonic expansion. The microwave spectra of six isotopologues of each of H 2 S⋯CuI, H 2 S⋯AgI and three isotopologues of H 2 S⋯AuI have been measured by chirped-pulse Fourier transform microwave spectroscopy. The spectra are interpreted to determine geometries for the complexes and to establish the values of structural parameters. The complexes have C s symmetry at equilibrium and have a pyramidal configuration about the sulfur atom. The local C 2 axis of the hydrogen sulfide molecule intersects the linear axis defined by the three heavy atoms at an angle, ϕ = 75.00(47)° for M = Cu, ϕ = 78.43(76)° for M = Ag, and ϕ = 71.587(13)° for M = Au. The trend in the molecular geometries is consistent with significant relativistic effects in the gold-containing complex. The force constant describing the interaction between the H 2 S and MI sub-units is determined from the measured centrifugal distortion constant, Δ J , of each complex. Nuclear quadrupole coupling constants, χ aa (M) and χ aa (I) (where M denotes the metal atom), are determined for H 2 S⋯CuI and H 2 S⋯AuI for the first time.

Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations.

Brueckner orbitals are the optimal orbitals for use in F12 explicitly correlated coupled-cluster (CC) treatments. A novel approach, Brueckner coupled-cluster doubles with perturbative triples BCCD(T)(F12*) is presented that avoids the expensive re-evaluation of F12 integrals throughout the orbital optimisation and includes a newly derived basis set correction to the Brueckner reference energy. The generalisation of F12 theory to arbitrary non-Hartree-Fock references and to Fock operators that include scalar relativistic effects is also presented. The performance of the new Brueckner F12 method is assessed for a test set of 50 open- and closed-shell reactions and for the ionisation potentials and electron affinities (EAs) of the first-row transition metal atoms. Benchmark basis set limit coupled-cluster singles, doubles and perturbative triples (CCSD(T)) and BCCD(T) values are reported for all energies in the test sets. BCCD(T)(F12*) performs systematically better than CCSD(T)(F12*) for electron affinities where orbital relaxation effects are significant.

The new compound H3PAgI has been synthesized in the gas phase by means of the reaction of laser-ablated silver metal with a pulse of gas consisting of a dilute mixture of ICF3 and PH3 in argon. Ground-state rotational spectra were detected and assigned for the two isotopologues H3P(107)AgI and H3P(109)AgI in their natural abundance by means of a chirped-pulse, Fourier-transform, microwave spectrometer. Both isotopologues exhibit rotational spectra of the symmetric-top type, analysis of which led to accurate values of the rotational constant B0, the quartic centrifugal distortion constants DJ and DJK, and the iodine nuclear quadrupole coupling constant χaa(I) = eQqaa. Ab initio calculations at the explicitly-correlated level of theory CCSD(T)(F12*)/aug-cc-pVDZ confirmed that the atoms PAg-I lie on the C3 axis in that order. The experimental rotational constants were interpreted to give the bond lengths r0(PAg) = 2.3488(20) Å and r0(Ag-I) = 2.5483(1) Å, in good agreement with the equilibrium lengths of 2.3387 Å and 2.5537 Å, respectively, obtained in the ab initio calculations. Measures of the strength of the interaction of PH3 and AgI (the dissociation energy De for the process H3PAgI = H3P + AgI and the intermolecular stretching force constant FPAg) are presented and are interpreted to show that the order of binding strength is H3PHI < H3PICl < H3PAgI for these metal-bonded molecules and their halogen-bonded and hydrogen-bonded analogues.

Complexes of H3NCuF and H3NCuI have been synthesised in the gas phase and characterized by microwave spectroscopy. The rotational spectra of 4 isotopologues of H3NCuF and 5 isotopologues of H3NCuI have been measured in the 6.5-18.5 GHz frequency range using a chirped-pulse Fourier transform microwave spectrometer. Each complex is generated from a gas sample containing NH3 and a halogen-containing precursor diluted in Ar. Copper is introduced by laser ablation of a solid target prior to supersonic expansion of the sample into the vacuum chamber of the microwave spectrometer. The spectrum of each complex is characteristic of a symmetric rotor and a C3v geometry in which the N, Cu and X atoms (where X is F or I) lie on the C axis. The rotational constant (B0), centrifugal distortion constants (DJ and DJK), nuclear spin-rotation (Cbb(Cu) = Ccc(Cu)) constant (for H3NCuF only) and nuclear quadrupole coupling constants (χaa(X) where (X = N, Cu, I)) are fitted to the observed transition frequencies. Structural parameters are determined from the measured rotational constants and also calculated ab initio at the CCSD(T)(F12*)/AVQZ level of theory. Force constants describing the interaction between ammonia and each metal halide are determined from DJ for each complex. Trends in the interaction strengths and geometries of BCuX (B = NH3, CO) (X = F, Cl, Br, I) are discussed.

An isolated, gas-phase dimer of imidazole is generated through laser vaporisation of a solid rod containing a 1:1 mixture of imidazole and copper in the presence of an argon buffer gas undergoing supersonic expansion. The complex is characterised through broadband rotational spectroscopy and is shown to have a twisted, hydrogen-bonded geometry. Calculations at the CCSD(T)(F12*)/cc-pVDZ-F12 level of theory confirm this to be the lowest-energy conformer of the imidazole dimer. The distance between the respective centres of mass of the imidazole monomer subunits is determined to be 5.2751(1) Å, and the twist angle γ describing rotation of one monomer with respect to the other about a line connecting the centres of mass of the monomers is determined to be 87.9(4)°. Four out of six intermolecular parameters in the model geometry are precisely determined from the experimental rotational constants and are consistent with results calculated ab initio., (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Carbenes of platinum and palladium, PtC3 and PdC3 , were generated in the gas phase through laser vaporization of a metal target in the presence of a low concentration of a hydrocarbon precursor undergoing supersonic expansion. Rotational spectroscopy and ab initio calculations confirm that both molecules are linear. The geometry of PtC3 was accurately determined by fitting to the experimental moments of inertia of twenty-six isotopologues. The results are consistent with the proposal of an autogenic isolobal relationship between O, Au(+) , and Pt atoms., (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Carbenes of platinum and palladium, PtC 3 and PdC 3 , were generated in the gas phase through laser vaporization of a metal target in the presence of a low concentration of a hydrocarbon precursor undergoing supersonic expansion. Rotational spectroscopy and ab initio calculations confirm that both molecules are linear. The geometry of PtC 3 was accurately determined by fitting to the experimental moments of inertia of twenty-six isotopologues. The results are consistent with the proposal of an autogenic isolobal relationship between O, Au + , and Pt atoms.

The incremental scheme makes it possible to compute CCSD(T) correlation energies to high accuracy for large systems. We present the first extension of this fully automated black-box approach to open-shell systems using an Unrestricted Hartree-Fock (UHF) wave function, extending the efficient domain-specific basis set approach to handle open-shell references. We test our approach on a set of organic and metal organic structures and molecular clusters and demonstrate standard deviations from canonical CCSD(T) values of only 1.35 kJ/mol using a triple ζ basis set. We find that the incremental scheme is significantly more cost-effective than the canonical implementation even for relatively small systems and that the ease of parallelization makes it possible to perform high-level calculations on large systems in a few hours on inexpensive computers. We show that the approximations that make our approach widely applicable are significantly smaller than both the basis set incompleteness error and the intrinsic error of the CCSD(T) method, and we further demonstrate that incremental energies can be reliably used in extrapolation schemes to obtain near complete basis set limit CCSD(T) reaction energies for large systems.

Strongly bound complexes (CH2)3⋯MCl (M = Cu or Ag), formed by non-covalent interaction of cyclopropane and either cuprous chloride or argentous chloride, have been generated in the gas phase by means of the laser ablation of either copper or silver metal in the presence of supersonically expanded pulses of a gas mixture containing small amounts of cyclopropane and carbon tetrachloride in a large excess of argon. The rotational spectra of the complexes so formed were detected with a chirped-pulse, Fourier transform microwave spectrometer and analysed to give rotational constants and Cu and Cl nuclear quadrupole coupling constants for eight isotopologues of each of (CH2)3⋯CuCl and (CH2)3⋯AgCl. The geometry of each of these complexes was established unambiguously to have C(2v) symmetry, with the three C atoms coplanar, and with the MCl molecule lying along a median of the cyclopropane C3 triangle. This median coincides with the principal inertia axis a in each of the two complexes (CH2)3⋯MCl. The M atom interacts with the pseudo-π bond linking the pair of equivalent carbon atoms (F)C (F = front) nearest to it, so that M forms a non-covalent bond to one C-C edge of the cyclopropane molecule. The (CH2)3⋯MCl complexes have similar angular geometries to those of the hydrogen- and halogen-bonded analogues (CH2)3⋯HCl and (CH2)3⋯ClF, respectively. Quantitative details of the geometries were determined by interpretation of the observed rotational constants and gave results in good agreement with those from ab initio calculations carried out at the CCSD(T)(F12*)/aug-cc-pVTZ-F12 level of theory. Interesting geometrical features are the lengthening of the (F)C-(F)C bond and the shrinkage of the two equivalent (B)C-(F)C (B = back) bonds relative to the C-C bond in cyclopropane itself. The expansions of the (F)C-(F)C bond are 0.1024(9) Å and 0.0727(17) Å in (CH2)3⋯CuCl and (CH2)3⋯AgCl, respectively, according to the determined r0 geometries. The C-C bond lengthening is in each case about four times that observed by similar methods in the corresponding complexes of MCl with ethyne and ethene, even though the cyclopropane complexes are more weakly bound than their ethyne and ethene analogues. Reasons for the larger increase in r(CC) in the pseudo-π complexes are discussed.

A molecular complex of C2H2 and AuI has been generated and isolated in the gas phase through laser ablation of a gold surface in the presence of an expanding sample containing small percentages of C2H2 and CF3I in a buffer gas of argon. Rotational, B0, centrifugal distortion, ΔJ and ΔJK, and nuclear quadrupole coupling constants, χaa(Au), χbb(Au) - χcc(Au), χaa(I), and χbb(I) - χcc(I), are measured for three isotopologues of C2H2···AuI through broadband rotational spectroscopy. The complex is C2v and T-shaped with C2H2 coordinating to the gold atom via donation of electrons from the π-orbitals of ethyne. On formation of the complex, the C≡C bond of ethyne extends by 0.032(4) Å relative to r(C≡C) in isolated ethyne when the respective r0 geometries are compared. The geometry of ethyne distorts such that ∠(*-C-H) (where * indicates the midpoint of the C≡C bond) is 194.7(12)° in the r0 geometry of C2H2···AuI. Ab initio calculations at the CCSD(T)(F12*)/AVTZ level are consistent with the experimentally determined geometry and further allow calculation of the dissociation energy (De) as 136 kJ mol(-1). The χaa(Au) and χaa(I) nuclear quadrupole coupling constants of AuI and also the Au-I bond length change significantly on formation of the complex consistent with the strong interaction calculated to occur between C2H2 and AuI.