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Despite their chemical simplicity, the spectroscopic investigation of light hydrides, such as hydrogen sulfide, is challenging due to strong hyperfine interactions and/or anomalous centrifugal-distortion effects. Several hydrides have already been detected in the interstellar medium, and the list includes H2S and some of its isotopologues. Astronomical observation of isotopic species and, in particular, those bearing deuterium is important to gain insights into the evolutionary stage of astronomical objects and to shed light on interstellar chemistry. These observations require a very accurate knowledge of the rotational spectrum, which is so far limited for mono-deuterated hydrogen sulfide, HDS. To fill this gap, high-level quantum-chemical calculations and sub-Doppler measurements have been combined for the investigation of the hyperfine structure of the rotational spectrum in the millimeter- and submillimeter-wave region. In addition to the determination of accurate hyperfine parameters, these new measurements together with the available literature data allowed us to extend the centrifugal analysis using a Watson-type Hamiltonian and a Hamiltonian-independent approach based on the Measured Active Ro-Vibrational Energy Levels (MARVEL) procedure. The present study thus permits to model the rotational spectrum of HDS from the microwave to far-infrared region with great accuracy, thereby accounting for the effect of the electric and magnetic interactions due to the deuterium and hydrogen nuclei.

In this contribution, we present the implementation of a second-order complete active space–self-consistent field (CASSCF) algorithm in conjunction with the Cholesky decomposition of the two-electron repulsion integrals. The algorithm, called norm-extended optimization, guarantees convergence of the optimization, but it involves the full Hessian and is therefore computationally expensive. Coupling the second-order procedure with the Cholesky decomposition leads to a significant reduction in the computational cost, reduced memory requirements, and an improved parallel performance. As a result, CASSCF calculations of larger molecular systems become possible as a routine task. The performance of the new implementation is illustrated by means of benchmark calculations on molecules of increasing size, with up to about 3000 basis functions and 14 active orbitals.

A rigorous analysis is carried out concerning the use of Cholesky decomposition (CD) of two-electron integrals in the case of quantum-chemical calculations with finite or perturbative magnetic fields and gauge-including atomic orbitals. We investigate in particular how permutational symmetry can be accounted for in such calculations and how this symmetry can be exploited to reduce the computational requirements. A modified CD procedure is suggested for the finite-field case that roughly halves the memory demands for the storage of the Cholesky vectors. The resulting symmetry of the Cholesky vectors also enables savings in the computational costs. For the derivative two-electron integrals in case of a perturbative magnetic field we derive CD expressions by means of a first-order Taylor expansion of the corresponding finite magnetic-field formulas with the field-free case as reference point. The perturbed Cholesky vectors are shown to be antisymmetric (as already proposed by Burger et al. (J. Chem. Phys., 155, 074105 (2021))) and the corresponding expressions enable significant savings in the required integral evaluations (by a factor of about four) as well as in the actual construction of the Cholesky vectors (by means of a two-step procedure similar to the one presented by Folkestad et al. (J. Chem. Phys., 150, 194112 (2019)) and Zhang et al. (J. Phys. Chem. A, 125, 4258-4265 (2021))). Numerical examples with cases involving several hundred basis functions verify our suggestions concerning CD in case of finite and perturbative magnetic fields.

The rotationally resolved infrared (IR) spectrum of the He-H

With a He-H

The rotationally resolved infrared (IR) spectrum of the He–[Formula: see text] complex has been measured in a cryogenic ion trap experiment at a nominal temperature of 4 K. Predissociation of the stored complex has been invoked by excitation of the degenerate ν2 mode of the [Formula: see text] sub-unit using a pulsed optical parametric oscillator system. An assignment of the experimental spectrum became possible through one-to-one correlations with bands of the spectrum theoretically predicted in Paper I [Harding et al., J. Chem. Phys. 156, 144307 (2022)]. 19 bands have been assigned and analyzed, and the energy term diagram of the lower states of this floppy molecular complex has been derived from combination differences (CDs) in the experimental spectrum. Ground state combination differences (GSCDs) reveal a large part of the energy term diagram for the He–[Formula: see text] complex in its vibrational ground state, v = 0. Experimental and theoretical term energies agree within experimental accuracy for the rotational fine structure associated with the total angular momentum quantum number J and the parity e/ f as well as for the coarse spacing of the lowest K states of the complex. This favorable comparison shows that the potential energy surface (PES) calculated in Paper I is accurate. The barriers between the three equivalent global minima in this PES are relatively low and the He–[Formula: see text] complex is extremely floppy, with nearly unhindered internal rotation of the [Formula: see text] sub-unit. The resulting Coriolis interactions couple the internal and end-over-end rotation of the complex and contribute significantly to the energy terms. They are observed both in experiment and theory and are, e.g., the origin of different rotational constants for states of e and f parity. Also in this respect, experiment and theory agree very well. Despite the assignment and analysis of many bands of the extremely rich IR spectrum of He–[Formula: see text], higher levels of excitation, including the complex stretching mode, need further attention.

With a He–[Formula: see text] interaction potential obtained from advanced electronic structure calculations, we computed the vibration-rotation-tunneling (VRT) states of this complex for total angular momenta J from 0 to 9, both for the vibrational ground state and for the twofold degenerate v2 = 1 excited state of [Formula: see text]. The potential has three equivalent global minima with depth D e = 455.3 cm−1 for He in the plane of [Formula: see text], three equatorial saddle points that separate these minima with barriers of 159.5 cm−1, and two axial saddle points with energies of 243.1 cm−1 above the minima. The dissociation energies calculated for the complexes of He with ortho-[Formula: see text] (o[Formula: see text]) and para-[Formula: see text] (p[Formula: see text]) are D0 = 234.5 and 236.3 cm−1, respectively. Wave function plots of the VRT states show that they may be characterized as weakly hindered internal rotor states, delocalized over the three minima in the potential and with considerable amplitude at the barriers. Most of them are dominated by the j k = 10 and 11 rotational ground states of o[Formula: see text] and p[Formula: see text], with the intermolecular stretching mode excited up to v = 4 inclusive. However, we also found excited internal rotor states: 33 in He–o[Formula: see text], and 22 and 21 in He–p[Formula: see text]. The VRT levels and wave functions were used to calculate the frequencies and line strengths of all allowed v2 = 0 → 1 rovibrational transitions in the complex. Theoretical spectra generated with these results are compared with the experimental spectra in Paper II [Salomon et al., J. Chem. Phys. 156, 144308 (2022)] and are extremely helpful in assigning these spectra. This comparison shows that the theoretical energy levels and spectra agree very well with the measured ones, which confirms the high accuracy of our ab initio He–[Formula: see text] interaction potential and of the ensuing calculations of the VRT states.

We present an interface of the wavefunction-based quantum chemical software CFOUR to the multiscale modeling framework MiMiC. Electrostatic embedding of the quantum mechanical (QM) part is achieved by analytic evaluation of one-electron integrals in CFOUR, while the rest of the QM/molecular mechanical (MM) operations are treated according to the previous MiMiC-based QM/MM implementation. Long-range electrostatic interactions are treated by a multipole expansion of the potential from the QM electron density to reduce the computational cost without loss of accuracy. Testing on model water/water systems, we verified that the CFOUR interface to MiMiC is robust, guaranteeing fast convergence of the self-consistent field cycles and optimal conservation of the energy during the integration of the equations of motion. Finally, we verified that the CFOUR interface to MiMiC is compatible with the use of a QM/QM multiple time-step algorithm, which effectively reduces the cost of ab initio MD (AIMD) or QM/MM-MD simulations using higher level wavefunction-based approaches compared to cheaper density functional theory-based ones. The new wavefunction-based AIMD and QM/MM-MD implementations were tested and validated for a large number of wavefunction approaches, including Hartree-Fock and post-Hartree-Fock methods like Møller-Plesset, coupled-cluster, and complete active space self-consistent field.

We report on a formulation and implementation of a scheme to compute NMR shieldings at second-order Moller-Plesset (MP2) perturbation theory using gauge-including atomic orbitals (GIAOs) to ensure gauge-origin independence and Cholesky decomposition (CD) to handle unperturbed as well as perturbed two-electron integrals. We investigate the accuracy of the CD for the derivatives of the two-electron integrals with respect to an external magnetic field as well as for the computed NMR shieldings, before we illustrate the applicability of our CD based GIAO-MP2 scheme in calculations involving up to about one hundred atoms and more than one thousand basis functions., 12 pages, 2 figures

The ν3 antisymmetric stretching mode of disilicon-carbide, Si2C, was studied using a narrow line width infrared quantum cascade laser spectrometer operating at 8.3 μm. The Si2C molecules were produ...

We present an implementation of coupled-perturbed complete active space self-consistent field (CP-CASSCF) theory for the computation of nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals and Cholesky decomposed two-electron integrals. The CP-CASSCF equations are solved using a direct algorithm where the magnetic Hessian matrix–vector product is expressed in terms of one-index transformed quantities. Numerical tests on systems with up to about 1300 basis functions provide information regarding both the computational efficiency and limitations of our implementation.

Since in coupled-cluster (CC) theory ground-state and excitation energies are eigenvalues of a non-Hermitian matrix, these energies can in principle take on complex values. In this paper we discuss the appearance of complex energy values in CC calculations from a mathematical perspective. We analyze the behaviour of the eigenvalues of Hermitian matrices that are perturbed (in a non-Hermitian manner) by a real parameter. Based on these results we show that for CC calculations with real-valued Hamiltonian matrices the ground-state energy generally takes a real value. Furthermore, we show that in the case of real-valued Hamiltonian matrices complex excitation energies only occur in the context of conical intersections. In such a case, unphysical consequences are encountered such as a wrong dimension of the intersection seam, large numerical deviations from full configuration-interaction (FCI) results, and the square-root-like behaviour of the potential surfaces near the conical intersection. In the case of CC calculations with complex-valued Hamiltonian matrix elements, it turns out that complex energy values are to be expected for ground and excited states when no symmetry is present. We confirm the occurrence of complex energies by sample calculations using a six-state model and by CC calculations for the H2O molecule in a strong magnetic field. We furthermore show that symmetry can prevent the occurrence of complex energy values. Lastly, we demonstrate that in most cases the real part of the complex energy values provides a very good approximation to the FCI energy., 19 pages, 8 figures

Molecular simulations of the forced unfolding and refolding of biomolecules or molecular complexes allow to gain important kinetic, structural and thermodynamic information about the folding process and the underlying energy landscape. In force probe molecular dynamics (FPMD) simulations, one pulls one end of the molecule with a constant velocity in order to induce the relevant conformational transitions. Since the extended configuration of the system has to fit into the simulation box together with the solvent such simulations are very time consuming. Here, we apply a hybrid scheme in which the solute is treated with atomistic resolution and the solvent molecules far away from the solute are described in a coarse-grained manner. We use the adaptive resolution scheme (AdResS) that has very successfully been applied to various examples of equilibrium simulations. We perform FPMD simulations using AdResS on a well studied system, a dimer formed from mechanically interlocked calixarene capsules. The results of the multiscale simulations are compared to all-atom simulations of the identical system and we observe that the size of the region in which atomistic resolution is required depends on the pulling velocity, i.e. the particular non-equilibrium situation. For large pulling velocities a larger all atom region is required. Our results show that multiscale simulations can be applied also in the strong non-equilibrium situations that the system experiences in FPMD simulations., 22 pages, 12 figures

We present the implementation of a quadratically convergent self-consistent field (QCSCF) algorithm based on an adaptive trust-radius optimisation scheme for restricted open-shell Hartree���Fock (ROHF), restricted Hartree���Fock (RHF), and unrestricted Hartree���Fock (UHF) references. The algorithm can exploit Cholesky decomposition (CD) of the two-electron integrals to allow calculations on larger systems. The most important feature of the QCSCF code lies in its black-box nature ��� probably the most important quality desired by a generic user. As shown for pilot applications, it does not require one to tune the self-consistent field (SCF) parameters (damping, Pulay's DIIS, and other similar techniques) in difficult-to-converge molecules. Also, it can be used to obtain a very tight convergence with extended basis sets ��� a situation often needed when computing high-order molecular properties ��� where the standard SCF algorithm starts to oscillate. Nevertheless, trouble may appear even with a QCSCF solver. In this respect, we discuss what can go wrong, focusing on the multiple UHF solutions of ortho-benzyne.

The recent many-body expanded full configuration interaction (MBE-FCI) method is reviewed by critically assessing its advantages and drawbacks in the context of contemporary near-exact electronic structure theory. Besides providing a succinct summary of the history of MBE-FCI to date within a generalized and unified theoretical setting, its finer algorithmic details are discussed alongside our optimized computational implementation of the theory. A selected few of the most recent applications of MBE-FCI are revisited, before we close by outlining its future research directions as well as its place among modern near-exact wave function-based methods., 18+8 pages, 5 figures. Invited review to WIREs Comput Mol Sci

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$\zeta$ quality. As a broad international endeavour, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around $-863$ m$E_{\text{H}}$. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 m$E_{\text{H}}$), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward., Comment: 29 pages, 1 figure, 2 tables. SI as an ancillary file

Experiments within a cryogenic 22-pole ion trap have revealed an interesting reaction dynamic phenomenon, where rovibrational excitation of an ionic molecule slows down a reaction with a neutral partner. This is demonstrated for the low-temperature hydrogen abstraction reaction $\mathrm{c}\text{\ensuremath{-}}{\mathrm{C}}_{3}{{\mathrm{H}}_{2}}^{+}+{\mathrm{H}}_{2}$, where excitation of the ion into the ${\ensuremath{\nu}}_{7}$ antisymmetric C-H stretching mode decreased the reaction rate coefficient toward the products $\mathrm{c}\text{\ensuremath{-}}{\mathrm{C}}_{3}{{\mathrm{H}}_{3}}^{+}+\mathrm{H}$. Supported by high-level quantum-chemical calculations, this observation is explained by the reaction proceeding through a $\mathrm{c}\text{\ensuremath{-}}{\mathrm{C}}_{3}{{\mathrm{H}}_{2}}^{+}\ensuremath{-}{\mathrm{H}}_{2}$ collision complex in the entrance channel, in which the hydrogen molecule is loosely bound to the hydrogen atom of the $\mathrm{c}\text{\ensuremath{-}}{\mathrm{C}}_{3}{{\mathrm{H}}_{2}}^{+}$ ion. This discovery enables high-resolution vibrational action spectroscopy for $\mathrm{c}\text{\ensuremath{-}}{\mathrm{C}}_{3}{{\mathrm{H}}_{2}}^{+}$ and other molecular ions with similar reaction pathways. Moreover, a detailed kinetic model relating the extent of the observed product depletion signal to the rate coefficients of inelastic collisions reveals that rotational relaxation of the vibrationally excited ions is significantly faster than the rovibrational relaxation, allowing for a large fraction of the ions to be vibrationally excited. This result provides fundamental insight into the mechanism for an important class of chemical reactions, and is capable of probing the inelastic collisional dynamics of molecular ions.

More than 130 pure rotational transitions of $^{46}$TiO, $^{47}$TiO, $^{48}$TiO, $^{49}$TiO, $^{50}$TiO, and $^{48}$Ti$^{18}$O are recorded using a high-resolution mm-wave supersonic jet spectrometer in combination with a laser ablation source. For the first time a mass-independent Dunham-like analysis is performed encompassing rare titanium monoxide isotopologues, and are compared to results from high-accuracy quantum-chemical calculations. The obtained parametrization reveals for titanium monoxide effects due to deviations from the Born-Oppenheimer approximation. Additionally, the dominant titanium properties enable an insight into the electronic structure of TiO by analyzing its hyperfine interactions. Further, based on the mass-independent analysis, the frequency positions of the pure rotational transitions of the short lived rare isotopologue $^{44}$TiO are predicted with high accuracy, i.e., on a sub-MHz uncertainty level. This allows for dedicated radio-astronomical searches of this species in core-collapse environments of supernovae., Comment: 29 pages, 3 figures

The different importance of scalar-relativistic two-electron contributions in second-order direct perturbation theory (DPT2) and the spin-free one-electron variant of exact two-component theory (SF...

Pure rotational transitions of 27Al16O, 27Al18O, 27Al32S, and 27Al34S are recorded in the vibrational ground state and singly excited vibrational state using a mm-wavelength supersonic jet spectrometer in combination with a laser ablation source. In total 275 rotational transitions have been assigned. For the first time, mass-independent expanded Dunham analyses are performed using isotopologues of aluminum monoxide and aluminum monosulfide. The breakdown of the Born-Oppenheimer approximation is observed. Based on these mass-independent analyses, frequency positions of pure rotational transitions of the rare radioactive isotopologues 26AlO and 26AlS are predicted with uncertainties at the sub-MHz level. These data will allow to search for 26Al-species in astrophysical environments using submm-observation facilities.

Benchmark scalar-relativistic coupled-cluster calculations for dissociation energies of the 20 diatomic molecules containing 3d transition metals in the 3dMLBE20 database ( J. Chem. Theory Comput. 2015 , 11 , 2036 ) are reported. Electron correlation and basis set effects are systematically studied. The agreement between theory and experiment is in general satisfactory. For a subset of 16 molecules, the standard deviation between computational and experimental values is 9 kJ/mol with the maximum deviation being 15 kJ/mol. The discrepancies between theory and experiment remain substantial (more than 20 kJ/mol) for VH, CrH, CoH, and FeH. To explore the source of the latter discrepancies, the analysis used to determine the experimental dissociation energies for VH and CrH is revisited. It is shown that, if improved values are used for the heterolytic C-H dissociation energies of di- and trimethylamine involved in the experimental determination, the experimental values for the dissociation energies of VH and CrH are increased by 18 kJ/mol, such that D

An up-to-date overview of the CFOUR program system is given. After providing a brief outline of the evolution of the program since its inception in 1989, a comprehensive presentation is given of its well-known capabilities for high-level coupled-cluster theory and its application to molecular properties. Subsequent to this generally well-known background information, much of the remaining content focuses on lesser-known capabilities of CFOUR, most of which have become available to the public only recently or will become available in the near future. Each of these new features is illustrated by a representative example, with additional discussion targeted to educating users as to classes of applications that are now enabled by these capabilities. Finally, some speculation about future directions is given, and the mode of distribution and support for CFOUR are outlined. ispartof: JOURNAL OF CHEMICAL PHYSICS vol:152 issue:21 ispartof: location:United States status: published

The recently proposed many-body expanded full configuration interaction (MBE-FCI) method is extended to excited states and static first-order properties different from total, ground state correlation energies. Results are presented for excitation energies and (transition) dipole moments of two prototypical, heteronuclear diatomics---LiH and MgO---in augmented correlation consistent basis sets of up to quadruple-$\zeta$ quality. Given that MBE-FCI properties are evaluated without recourse to a sampled wave function and the storage of corresponding reduced density matrices, the memory overhead associated with the calculation of general first-order properties only scales with the dimension of the desired property. In combination with the demonstrated performance, the present developments are bound to admit a wide range of future applications by means of many-body expanded treatments of electron correlation., Comment: 22 pages, 2 figures, 2 tables. SI added as ancillary file

More than 100 years since its discovery, the mechanism of the Grignard reaction remains unresolved. Ambiguities arise from the concomitant presence of multiple organomagnesium species and the competing mechanisms involving either nucleophilic addition or the formation of radical intermediates. To shed light on this topic, quantum-chemical calculations and ab initio molecular dynamics simulations are used to study the reaction of CH3MgCl in tetrahydrofuran with acetaldehyde and fluorenone as prototypical reagents. All organomagnesium species coexisting in solution due to the Schlenk equilibrium are found to be competent reagents for the nucleophilic pathway. The range of activation energies displayed by all of these compounds is relatively small. The most reactive species are a dinuclear Mg complex in which the substrate and the nucleophile initially bind to different Mg centers and the mononuclear dimethyl magnesium. The radical reaction, which requires the homolytic cleavage of the Mg-CH3 bond, cannot occur unless a substrate with a low-lying π*(CO) orbital coordinates the Mg center. This rationalizes why a radical mechanism is detected only in the presence of substrates with a low reduction potential. This feature, in turn, does not necessarily favor the nucleophilic addition, as shown for the reaction with fluorenone. The solvent needs to be considered as a reactant for both the nucleophilic and the radical reactions, and its dynamics is essential for representing the energy profile. The similar reactivity of several species in fast equilibrium implies that the reaction does not occur via a single process but by an ensemble of parallel reactions.

In the context of radio-astronomical observations, laboratory experiments constitute a cornerstone in the interpretation of rich line surveys due to the concomitant presence of numerous emitting molecules. Here, we report the investigation of three different rotational transitions of mono-deuterated ammonia (NH2D), a species of astrophysical interest, for which the contribution of the deuterium nuclear spin to the rotational spectrum has been resolved for the first time in the millimeter- and submillimeter-wave domain. The effect of hyperfine interactions on the rotational spectrum has been unveiled by a combined theoretical and experimental approach. Quantum-chemical calculations based on coupled-cluster theory have been employed to evaluate the hyperfine parameters of nitrogen, hydrogen, and deuterium in NH2D. Subsequently, the Lamb-dip technique has been used to investigate the rotational spectrum of NH2D at high-resolution. In detail, three low-J transitions have been recorded at 86, 110, and 333 GHz with a frequency-modulation millimeter-/submillimeter-wave spectrometer. From the line profile analysis of the recorded spectra, the main terms responsible for the rotational hyperfine structure have been determined with good accuracy. Our work allows a comprehensive analysis of the rotational features of NH2D in radioastronomical spectra and a more accurate evaluation of its column density, especially in non-turbulent regions showing narrow linewidths.

The shape and size of self‐assembled structures upon local organization of their molecular building blocks are hard to predict in the presence of long‐range interactions. Combining small‐angle X‐ray/neutron scattering data, theoretical modelling, and computer simulations, sodium dodecyl sulfate (SDS), over a broad range of concentrations and ionic strengths, was investigated. Computer simulations indicate that micellar shape changes are associated with different binding of the counterions. By employing a toy model based on point charges on a surface, and comparing it to experiments and simulations, it is demonstrated that the observed morphological changes are caused by symmetry breaking of the irreducible building blocks, with the formation of transient surfactant dimers mediated by the counterions that promote the stabilization of cylindrical instead of spherical micelles. The present model is of general applicability and can be extended to all systems controlled by the presence of mobile charges., Micellar shape changes of sodium dodecyl sulfate are associated with different binding modes of the counterions. Morphological changes are caused by symmetry breaking of the irreducible building blocks, with the formation of transient surfactant dimers mediated by the counterions that promote the stabilization of cylindrical instead of spherical micelles.

Facilitated by a rigorous partitioning of a molecular system's orbital basis into two fundamental subspaces - a reference and an expansion space, both with orbitals of unspecified occupancy - we generalize our recently introduced many-body expanded full configuration interaction (MBE-FCI) method to allow for electron-rich model and molecular systems dominated by both weak and strong correlation to be addressed. By employing minimal or even empty reference spaces, we show through calculations on the one-dimensional Hubbard model with up to 46 lattice sites, the chromium dimer, and the benzene molecule how near-exact results may be obtained in a entirely unbiased manner for chemical and physical problems of not only academic, but also applied chemical interest. Given the massive parallelism and overall accuracy of the resulting method, we argue that generalized MBE-FCI theory possesses an immense potential to yield near-exact correlation energies for molecular systems of unprecedented size, composition, and complexity in the years to come., 19 pages, 1 TOC figure, 4 main figures, 1 SI attached as an ancillary file. UPDATE-v2 (Dec. 19): Discussion of Hubbard results now focussed on comparison again DMRG reference numbers

Using atomistic molecular dynamics simulations, we study the temperature dependence of the mechanical unfolding of a model supramolecular complex, a dimer of interlocked calixarene capsules. This system shows reversible transitions between two conformations that are stabilized by different networks of hydrogen bonds. We study the forced dissociation and formation of these networks as a function of temperature and find a strong impact of the nonequilibrium conditions imposed by pulling the system mechanically. The kinetics of the transition between the two conformations is ideally suited to investigate the range of validity of the stochastic models employed in the analysis of force dependent kinetic rates obtained from experimental or simulation data. These models usually assume activated dynamics for the relevant transitions, and therefore, the analytical expressions for the kinetic rates are of an Arrhenius form. A study of the temperature- and force-dependent kinetics by simulation allows an analysis of the transition rates without any model assumption. We find that the temperature dependence of the rates is well described by an Arrhenius law for each value of the force. This enables us to determine the activation free energy and the bare kinetic rate as a function of force independent of each other. In accord with the common model assumptions, we find that the activation free energy decreases with increasing force. The force dependence of the bare rates is compatible with the results of model calculations in the low force regime, and deviations are observed at high forces.

We present a general formulation of analytic nuclear gradients for the coupled-cluster with single and double substitution (CCSD) and equation-of-motion (EOM) CCSD energies computed using Cholesky decomposition (CD) representations of the electron repulsion integrals. By rewriting the correlated energy and response equations such that the storage of the largest four-index intermediates is eliminated, CD leads to a significant reduction in disk storage requirements, reduced I/O penalties, and an improved parallel performance. CD thus extends the scope of the systems that can be treated by (EOM-)CCSD methods, although analytic gradients in the framework of CD are needed to extend the applicability of (EOM-)CCSD methods in the context of geometry optimizations. This paper presents a formulation of analytic (EOM-)CCSD gradient within the CD framework and reports on the salient details of the corresponding implementation. The accuracy and the capabilities of analytic CD-based (EOM-)CCSD gradients are illustrated by benchmark calculations and several illustrative examples.

We present a scheme for the calculation of energies and analytic energy gradients within spin-free exact two-component (SFX2C) theory in its mean-field variant, which we refer to as SFX2C-mf. In the presented scheme, the Foldy-Wouthuysen transformation is carried out after the spin-free four-component Hartree-Fock treatment such that in electron-correlated calculations only the non-mean-field part of the two-electron interactions is handled in an untransformed manner. The formulation of analytic gradients requires some adjustments in comparison with the nonrelativistic case, i.e., the additional solution of the spin-free Dirac Coulomb coupled-perturbed Hartee-Fock equations together with a simplified treatment of orbital relaxation at the SFX2C-mf level. The improved accuracy of SFX2C-mf in comparison with SFX2C-1e is demonstrated in the calculation of energies, dipole moments, and electric-field gradients for the hydrogen halides HX, X = F-At. It is shown that the main contribution to the improvement stems from the elimination of the error at the Hartree-Fock (HF) level; however, the corresponding correlation contribution is also improved such that SFX2C-mf can be considered a suitable scheme for the treatment of heavy-element compounds for which the error of SFX2C-1e is rather substantial.

The ν

We present a derivation and efficient implementation of the formally complete analytic second derivatives for the domain-based local pair natural orbital second order Møller–Plesset perturbation theory (MP2) method, applicable to electric or magnetic field-response properties but not yet to harmonic frequencies. We also discuss the occurrence and avoidance of numerical instability issues related to singular linear equation systems and near linear dependences in the projected atomic orbital domains. A series of benchmark calculations on medium-sized systems is performed to assess the effect of the local approximation on calculated nuclear magnetic resonance shieldings and the static dipole polarizabilities. Relative deviations from the resolution of the identity-based MP2 (RI-MP2) reference for both properties are below 0.5% with the default truncation thresholds. For large systems, our implementation achieves quadratic effective scaling, is more efficient than RI-MP2 starting at 280 correlated electrons, and is never more than 5–20 times slower than the equivalent Hartree–Fock property calculation. The largest calculation performed here was on the vancomycin molecule with 176 atoms, 542 correlated electrons, and 4700 basis functions and took 3.3 days on 12 central processing unit cores.

High-resolution infrared studies of laser ablation products from carbon-selenium targets have revealed a new vibrational band at 2057 cm−1 that is identified as the ν 3 vibrational fundamental of the SeC3Se cluster. Because of the rich isotopic composition of selenium and the heavy nuclear masses involved, the vibrational band shows a relatively compact and complex structure despite the simple linear geometric arrangement. Overall, rotational-vibrational lines of six isotopologues could be assigned and fitted permitting the derivation of an accurate selenium-carbon bond length. Spectroscopic analysis has been greatly supported by high-level quantum-chemical calculations of the molecular structure and the harmonic and anharmonic force fields performed at the CCSD(T) level of theory. Scalar-relativistic effects on the molecular structure were also considered but found of little importance.

Quantifying molecular abundances of astrochemical species is a key step towards the understanding of the chemistry occurring in the interstellar medium. This process requires a profound knowledge of the molecular energy levels, including their structure resulting from weak interactions between nuclear spins and the molecular rotation. With the aim of increasing the quality of spectral line catalogs for the singly- and doubly-deuterated ammonia (NH2D and ND2H), we have revised their rotational spectra by observing many hyperfine-resolved lines and more accurate high-frequency transitions. The measurements have been performed in the submillimeter-wave region (265–1565 GHz) using a frequency modulation submillimeter spectrometer and in the far-infrared domain (45–220 cm−1) with a synchrotron-based Fourier-transform interferometer. The analysis of the new data, with the interpretation of the hyperfine structure supported by state-of-the-art quantum-chemical calculations, led to an overall improvement of all spectroscopic parameters. Moreover, the effect of the inclusion of deuterium splittings in the analysis of astrophysical NH2D emissions at millimeter wavelengths has been tested using recent observations of the starless core L1544, an ideal astrophysical laboratory for the study of deuterated species. Our results show that accounting for hyperfine interactions leads to a small but significant change in the physical parameters used to model NH2D line emissions.

We present the first analytical implementation of CC3 second derivatives using the spin-unrestricted approach. This allows, for the first time, the calculation of nuclear spin–spin coupling constants (SSCC) relevant to NMR spectroscopy at the CC3 level of theory in a fully analytical manner. CC3 results for the SSCCs of a number of small molecules and their fluorine substituted derivatives are compared with the corresponding coupled cluster singles and doubles (CCSD) results obtained using specialized basis sets. For one-bond couplings the change when going from CCSD to CC3 is typically 1–3%, but much higher corrections were found for 1JCN in FCN, 15.7%, and 1JOF in OF2, 6.4%. The changes vary significantly in the case of multibond couplings, with differences of up to 10%, and even 13.6% for 3JFH in fluoroacetylene. Calculations at the coupled cluster singles, doubles, and triples (CCSDT) level indicate that the most important contributions arising from connected triple excitations in the coupled cluster ...

The ν 7 antisymmetric C–H stretching fundamental of c- C 3 H 2 + has been characterized in a cryogenic 22-pole ion trap by a novel type of action spectroscopy, in which the rovibrational excitation of c- C 3 H 2 + is detected as a slowing down of the low-temperature reaction c- C 3 H 2 + + H2 → C 3 H 3 + + H. Ninety-one rovibrational transitions with partly resolved fine structure doublets were measured in high resolution. Supported by high-level quantum chemical calculations, spectroscopic parameters were determined by fitting the observed lines with an effective Hamiltonian for an asymmetric rotor in a doublet electronic ground state, X ˜ A 1 2 , yielding a band origin at 3113.6400(3) cm−1. Based on these spectroscopic parameters, the rotational spectrum of this astronomically important molecule is predicted.

Very accurate transition frequencies of HC$_5$N were determined between 5.3 and 21.4 GHz with a Fourier transform microwave spectrometer. The molecules were generated by passing a mixture of HC$_3$N and C$_2$H$_2$ highly diluted in neon through a discharge valve followed by supersonic expansion into the Fabry-Perot cavity of the spectrometer. The accuracies of the data permitted us to improve the experimental $^{14}$N nuclear quadrupole coupling parameter considerably and the first experimental determination of the $^{14}$N nuclear spin-rotation parameter. The transition frequencies are also well suited to determine in astronomical observations the local speed of rest velocities in molecular clouds with high fidelity. The same setup was used to study HC$_7$N, albeit with modest improvement of the experimental $^{14}$N nuclear quadrupole coupling parameter. Quantum chemical calculations were carried out to determine $^{14}$N nuclear quadrupole and spin-rotation coupling parameters of HC$_5$N, HC$_7$N, and related molecules. These calculations included evaluation of vibrational and relativistic corrections to the non-relativistic equilibrium quadrupole coupling parameters; their considerations improved the agreement between calculated and experimental values substantially., Comment: 9 pages; J. Mol. Spectrosc., accepted

We report the first gas-phase vibrational spectra of the hydrocarbon ions C3H+ and C3H2+. The ions were produced by electron impact ionization of allene. Vibrational spectra of the mass-selected ions tagged with Ne were recorded using infrared predissociation spectroscopy in a cryogenic ion trap instrument using the intense and widely tunable radiation of a free electron laser. Comparison of high-level quantum chemical calculations and resonant depletion measurements revealed that the C3H+ ion is exclusively formed in its most stable linear isomeric form, whereas two isomers were observed for C3H2+. Bands of the energetically favored cyclic c-C3H2+ are in excellent agreement with calculated anharmonic frequencies, whereas for the linear open-shell HCCCH+ (2Πg) a detailed theoretical description of the spectrum remains challenging because of Renner-Teller and spin-orbit interactions. Good agreement between theory and experiment, however, is observed for the frequencies of the stretching modes for which an anharmonic treatment was possible. In the case of linear l-C3H+, small but non-negligible effects of the attached Ne on the ion fundamental band positions and the overall spectrum were found.