arXiv subjects

Jürgen Gauss

Publications and source records attributed to Jürgen Gauss.

34 records · Page 2Linked to original sources

arXiv2021

Complex Ground-State and Excitation Energies in Coupled-Cluster Theory

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.

physics.chem-ph↗

arXiv2021

Mass-independent analysis of the stable isotopologues of gas-phase titanium monoxide -- TiO

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.

physics.chem-ph↗

arXiv2021

A Second-Order CASSCF Algorithm with the Cholesky Decomposition of the Two-Electron Integrals

In this contribution, we present the implementation of a second-order 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 of the wavefunction 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.

physics.chem-ph↗

arXiv2021

Incremental Treatments of the Full Configuration Interaction Problem

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.

physics.chem-ph↗

arXiv2021

Force probe simulations using an adaptive resolution scheme

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.

cond-mat.soft↗

arXiv2020

Ground and Excited State First-Order Properties in Many-Body Expanded Full Configuration Interaction Theory

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-$ζ$ 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.

physics.chem-ph↗

arXiv2020

The Ground State Electronic Energy of Benzene

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-$ζ$ 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.

physics.chem-ph↗

arXiv2020

Determination of accurate rest frequencies and hyperfine structure parameters of cyanobutadiyne, HC$_5$N

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.

astro-ph.IM↗

arXiv2019

Generalized Many-Body Expanded Full Configuration Interaction Theory

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.

physics.chem-ph↗

arXiv2019

Many-Body Expanded Full Configuration Interaction. II. Strongly Correlated Regime

In this second part of our series on the recently proposed many-body expanded full configuration interaction (MBE-FCI) method, we introduce the concept of multideterminantal expansion references. Through theoretical arguments and numerical validations, the use of this class of starting points is shown to result in a focussed compression of the MBE decomposition of the FCI energy, thus allowing chemical problems dominated by strong correlation to be addressed by the method. The general applicability and performance enhancements of MBE-FCI are verified for standard stress tests such as the bond dissociations in H$_2$O, N$_2$, C$_2$, and a linear H$_{10}$ chain. Furthermore, the benefits of employing a multideterminantal expansion reference in accelerating calculations of high accuracy are discussed, with an emphasis on calculations in extended basis sets. As an illustration of this latter quality of the MBE-FCI method, results for H$_2$O and C$_2$ in basis sets ranging from double- to pentuple-$ζ$ quality are presented, demonstrating near-ideal parallel scaling on up to almost $25000$ processing units.

physics.chem-ph↗

arXiv2018

Many-Body Expanded Full Configuration Interaction. I. Weakly Correlated Regime

Over the course of the past few decades, the field of computational chemistry has managed to manifest itself as a key complement to more traditional lab-oriented chemistry. This is particularly true in the wake of the recent renaissance of full configuration interaction (FCI)-level methodologies, albeit only if these can prove themselves sufficiently robust and versatile to be routinely applied to a variety of chemical problems of interest. In the present series of works, performance and feature enhancements of one such avenue towards FCI-level results for medium to large one-electron basis sets, the recently introduced many-body expanded full configuration interaction (MBE-FCI) formalism [J. Phys. Chem. Lett., 8, 4633 (2017)], will be presented. Specifically, in this opening part of the series, the capabilities of the MBE-FCI method in producing near-exact ground state energies for weakly correlated molecules of any spin multiplicity will be demonstrated.

physics.chem-ph↗

arXiv2017

Virtual orbital many-body expansions: A possible route towards the full configuration interaction limit

In the present letter, it is demonstrated how full configuration interaction (FCI) results in extended basis sets may be obtained to within sub-kJ/mol accuracy by decomposing the energy in terms of many-body expansions in the virtual orbitals of the molecular system at hand. This extension of the FCI application range lends itself to two unique features of the current approach, namely that the total energy calculation can be performed entirely within considerably reduced orbital subspaces and may be so by means of embarrassingly parallel programming. Facilitated by a rigorous and methodical screening protocol and further aided by expansion points different from the Hartree-Fock solution, all-electron numerical results are reported for H$_2$O in polarized core-valence basis sets ranging from double-$ζ$ (10 $e$, 28 $o$) to quadruple-$ζ$ (10 $e$, 144 $o$) quality.

physics.chem-ph↗

arXiv2016

Assessment of the accuracy of coupled cluster perturbation theory for open-shell systems. II. Quadruples expansions

We extend our assessment of the potential of perturbative coupled cluster (CC) expansions for a test set of open-shell atoms and organic radicals to the description of quadruple excitations. Namely, the second- through sixth-order models of the recently proposed CCSDT(Q-n) quadruples series [J. Chem. Phys. 140, 064108 (2014)] are compared to the prominent CCSDT(Q) and lambda-CCSDT(Q) models. From a comparison of the models in terms of their recovery of total CC singles, doubles, triples, and quadruples (CCSDTQ) energies, we find that the performance of the CCSDT(Q-n) models is independent of the reference used (unrestricted or restricted (open-shell) Hartree-Fock), in contrast to the CCSDT(Q) and lambda-CCSDT(Q) models, for which the accuracy is strongly dependent on the spin of the molecular ground state. By further comparing the ability of the models to recover relative CCSDTQ atomization energies, the discrepancy between them is found to be even more pronounced, stressing how a balanced description of both closed- and open-shell species - as found in the CCSDT(Q-n) models - is indeed of paramount importance if any perturbative CC model is to be of chemical relevance for high-accuracy applications. In particular, the third-order CCSDT(Q-3) model is found to offer an encouraging alternative to the existing choices of quadruples models used in modern computational thermochemistry, since the model is still only of moderate cost, albeit markedly more costly than, e.g., the CCSDT(Q) and lambda-CCSDT(Q) models.

physics.chem-ph↗

arXiv2016

Assessment of the accuracy of coupled cluster perturbation theory for open-shell systems. I. Triples expansions

The accuracy at which total energies of open-shell atoms and organic radicals may be calculated is assessed for selected coupled cluster perturbative triples expansions, all of which augment the coupled cluster singles and doubles (CCSD) energy by a non-iterative correction for the effect of triple excitations. Namely, the second- through sixth-order models of the recently proposed CCSD(T-n) triples series [J. Chem. Phys. 140, 064108 (2014)] are compared to the acclaimed CCSD(T) model for both unrestricted as well as restricted open-shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 modest-sized open-shell species with comparable RHF-based results, no behavioral differences are observed for the higher-order models of the CCSD(T-n) series in their correlated descriptions of closed- and open-shell species. In particular, we find that the convergence rate throughout the series towards the coupled cluster singles, doubles, and triples (CCSDT) solution is identical for the two cases. For the CCSD(T) model, on the other hand, not only its numerical consistency, but also its established, yet fortuitous cancellation of errors breaks down in the transition from closed- to open-shell systems. The higher-order CCSD(T-n) models (orders n>3) thus offer a consistent and significant improvement in accuracy relative to CCSDT over the CCSD(T) model, equally for RHF, UHF, and ROHF reference determinants, albeit at an increased computational cost.

physics.chem-ph↗

arXiv2015

Coupled-cluster theory for atoms and molecules in strong magnetic fields

An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles--doubles--perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the dependence of correlation and binding energies on the magnetic field.

physics.chem-ph↗

arXiv2009

Hyperfine structure in the J = 1-0 transitions of DCO+, DNC, and HN13C: astronomical observations and quantum-chemical calculations

We have observed the rotational ground-state (J = 1-0) transitions of DCO+, HN13C and DNC with the IRAM 30m telescope toward the dark cloud LDN 1512 which has exceptionally narrow lines permitting hyperfine splitting to be resolved in part. The measured splittings of 50-300 kHz are used to derive nuclear quadrupole and spin-rotation parameters for these species. The measurements are supplemented by high-level quantum-chemical calculations using coupled-cluster techniques and large atomic-orbital basis sets. We find eQq = +151.12 (400) kHz and C_I = -1.12 (43) kHz for DCO+, eQq = 272.5 (51) kHz for HN13C, and eQq(D) = 265.9 (83) kHz and eQq(N) = 288.2 (71) kHz for DNC. The numbers for DNC are consistent with previous laboratory data, while our constants for DCO+ are somewhat smaller than previous results based on astronomical data. For both DCO+ and DNC, our results are more accurate than previous determinations. Our results are in good agreement with the corresponding best theoretical estimates. We also derive updated rotational constants for HN13C: B = 43545.6000 (47) MHz and D = 93.7 (20) kHz. The hyperfine splittings of the DCO+, DNC and HN13C J = 1-0 lines range over 0.47-1.28 km/s, which is comparable to typical line widths in pre-stellar cores and to systematic gas motions on ~1000 AU scales in protostellar cores. We present tabular information to allow inclusion of the hyperfine splitting in astronomical data interpretation. The large differences in the 14N quadrupole parameters of DNC and HN13C have been traced to differences in the vibrational corrections caused by significant non-rigidity of these molecules, particularly along the bending coordinate.

astro-ph.GA↗