arXiv subjects

Jürgen Gauss

Publications and source records attributed to Jürgen Gauss.

At least 19 recordsLinked to original sources

arXiv2026

Use of Cholesky decomposition in the CFOUR program package

An overview is given about our efforts to speed up high-level computations of molec- ular energies and properties using Cholesky decomposition (CD). We describe the cor- responding developments in the CFOUR quantum-chemical package with a focus on (a) the use of CD in complete-active space self-consistent-field (CASSCF) and coupled- cluster (CC) computations, (b) the implementation of analytic CC gradients using CD, (c) the efficient calculation of magnetic properties (NMR shieldings and magnetizabili- ties) using CD when carried out with explicit magnetic-field dependent basis functions, i.e., the so-called gauge-including atomic orbitals (GIAOs), (d) the efficient computa- tion of CASSCF response properties using CD, (e) the use of CD in relativistic two- and four-component computations, as well as (f) computations for molecules in finite magnetic fields using GIAOs together with CD. An outlook on future developments concerning the CFOUR package is given.

physics.chem-ph↗

arXiv2026

Markov State Model for the forced unfolding of a small peptide

In typical single-molecule force spectroscopy experiments the mechanical unfolding of molecular complexes or biomolecules is studied applying a force ramp to one end of the system while the other end is kept fixed in space. The computational counterpart of this type of experiments can routinely be performed using molecular dynamics simulations with atomistic resolution. However, due to the large difference in time scales often coarse graining procedures are applied in the simulations. Most of the applied techniques do not allow to follow the atomistic details of the relevant conformational transitions due to the structural simplifications used to speed up the simulations. Here, we apply an earlier developed dynamic coarse graining technique based on Markov state modeling to a model peptidic system that does not unfold in a simple two-state manner. Using the donor-acceptor distances of the helical hydrogen bonds as collective variables and performing a dimension reduction technique allows us to construct a Markov model of the unfolding process that correctly represents the microscopic behavior of the system. The chosen example shows that the method can be used to mimick the mechanical unfolding process of systems for which the end-to-end distance does not provide a sufficient order parameter and that do not unfold in a simple cooperative manner.

cond-mat.soft↗

arXiv2026

Experimental proof of strong $Π$-$Σ$ mixing in the Renner-Teller and Pseudo-Jahn-Teller affected CCH$^+$ ($^3Π$) ion

The ethynyl radical cation, CCH$^+$ ($^3Π$), offers a unique system for fundamental spectroscopic studies of non-adiabatic effects due to its open-shell linear structure and the presence of a low-lying $^3Σ^-$ state, which induces notable perturbations in the (ro-)vibrational spectrum. To probe these effects, we recorded the broadband vibrational spectrum of CCH$^+$ from 350-3450 cm$^{-1}$ using leak-out spectroscopy. The spectrum reveals a complex splitting pattern in the CCH bending mode, attributed to Renner-Teller and pseudo-Jahn-Teller coupling effects between the $^3 Π$ and $^3 Σ^-$ electronic states. A three-state diabatic model, validated here against high-resolution IR data of the CH stretching mode, facilitated assignments within the broadband infrared (IR) spectrum, including an additional $Π$ vibronic feature observed in the aforementioned high-resolution spectrum. Our results highlight a pronounced sensitivity of the splitting pattern to the $Π$-$Σ$ energy gap, with couplings so large that even the zero-point vibrational motion of the bending vibration is sufficient to disrupt the vibronic structure of this ion. This compact ion, with strong coupling effects and high-quality spectroscopic data, serves as an exemplary system for evaluating non-adiabatic models.

physics.chem-ph↗

arXiv2026

The Direct-Product Decomposition Approach for Symmetry Exploitation in Many-Body Methods in Case of Non-Abelian Point Groups

We demonstrate for the specific case of $C_{3v}$ how the direct-product decomposition scheme for the treatment of symmetry in coupled-cluster (CC) calculations can be extended to non-Abelian point groups. We show that for the two-electron integrals and CC amplitudes a block structure can be obtained by resolving the reducible products of two irreducible representations into their irreducible representations. To deal with the necessary resorts of the ordering of the two-electron integrals and amplitudes, spin-adaptation, and the O(M$^5$) contractions (with M as the number of basis functions) of a CC calculation, we suggest a strategy that uses both the reduced and non-reduced representation of the corresponding quantities and switches back and forth between them. While the reduced representations are the ones used in the O(M$^6$) contractions, the other steps are better carried out in the non-reduced representation. Our pilot implementation of the CC singles and doubles method confirms in test calculations for NH$_3$ and PH$_3$ using different basis sets that significant savings (of more than 20 compared to treatments without symmetry and about 5 compared to treatments using $C_s$ symmetry) are possible and suggest that the exploitation of non-Abelian symmetry would render CC computations on large highly symmetric molecules possible

physics.chem-ph↗

arXiv2025

A novel implementation of CCSD analytic gradients using Cholesky decomposition of the two-electron integrals and Abelian point-group symmetry

We present a novel and efficient implementation of coupled-cluster with singles and doubles (CCSD) analytic gradients that combines the Cholesky decomposition (CD) of electron-repulsion integrals with the exploitation of Abelian point-group symmetry. This approach is particularly effective for medium-sized and large symmetric molecular systems. The CD of two-electron integrals is performed using a symmetry-adapted two-step algorithm, while the derivatives of the Cholesky vectors are computed with respect to symmetry-adapted nuclear displacements and contracted on-the-fly with the CCSD density matrices. Geometry optimizations of symmetric systems with several hundreds of basis functions have been carried out to assess the efficiency of our implementation and to quantify the computational gain provided by the exploitation of point-group symmetry.

physics.chem-ph↗

arXiv2024

Cholesky Decomposition and the Second-Derivative Two-Electron Integrals Required for the Computation of Magnetizabilities using Gauge-Including Atomic Orbitals

The computation of magnetizability tensors using gauge-including atomic orbitals is discussed in the context of Cholesky decomposition for the two-electron repulsion integrals with a focus on the involved doubly differentiated integrals. Three schemes for their handling are suggested: the first exploits the DF aspect of Cholesky decomposition, the second uses expressions obtained by differentiating the CD expression for the unperturbed two electron integrals, while the third addresses the issue that the first two schemes are not able to represent the doubly differentiated integrals with arbitrary accuracy. This scheme uses a separate Cholesky decomposition for the cross terms in the doubly differentiated two-electron integrals. Test calculations reveal that all three schemes are able to represent the integrals with similar accuracy and yield indistinguishable results for the values of the computed magnetizability tensor elements. Thus, we recommend our first scheme which has the lowest computational cost for routine computations. The applicability of our CD schemes is further shown in large-scale Hartree-Fock calculations of the magnetizability tensor of coronene (C24H12) with a doubly polarized triple-zeta basis consisting of 684 basis functions.

physics.chem-ph↗

arXiv2024

Exploiting Non-Abelian Point-Group Symmetry to Estimate the Exact Ground-State Correlation Energy of Benzene in a Polarized Split-Valence Triple-Zeta Basis Set

Local electronic-structure methods in quantum chemistry operate on the ability to compress electron correlations more efficiently in a basis of spatially localized molecular orbitals than in a parent set of canonical orbitals. However, many typical choices of localized orbitals tend to be related by selected, near-exact symmetry operations whenever a molecule belongs to a point group, a feature which remains largely unexploited in most local correlation methods. The present Letter demonstrates how to leverage a recent unitary protocol for enforcing symmetry properties among localized orbitals to yield a high-accuracy estimate of the exact ground-state correlation energy of benzene ($D_{6h}$) in correlation-consistent polarized basis sets of both double- and triple-$ζ$ quality. Through an initial application to many-body expanded full configuration interaction (MBE-FCI) theory, we show how molecular point-group symmetry can lead to computational savings that are inversely proportional to the order of the point group in a manner generally applicable to the acceleration of modern local correlation methods.

physics.chem-ph↗

arXiv2024

Adaptive Resolution Force Probe Simulations: Coarse Graining in the Ideal Gas Approximation

The unfolding of molecular complexes or biomolecules under the influence of external mechanical forces can routinely be simulated with atomistic resolution. To obtain a match of the characteristic time scales with those of experimental force spectroscopy, often coarse graining procedures are employed. Here, building on a previous study, we apply the adaptice resolution scheme (AdResS) to force probe molecular dynamics (FPMD) simulations using two model systems as examples. One system is the previously investigated calix[4]arene dimer that shows reversible one-step unfolding and the other example is provided by a small peptide, a $β$-alanine octamer in methanol solvent. The mechanical unfolding of this peptide proceeds via a metastable intermediate and therefore represents a first step towards a complex unfolding pathway. In addition to increasing the complexity of the relevant conformational changes we study the impact of the methodology used for coarse graining. Apart from a standard technique, the iterative Boltzmann inversion method, we apply an ideal gas approximation and therefore we replace the solvent by a non-interacting system of spherical particles. In all cases we find excellent agreement between the results of FPMD simulations performed fully atomistically and the AdResS simulations also in the case of fast pulling. This holds for all details of the unfolding pathways like the distributions of the characteristic forces and also the sequence of hydrogen-bond opening in case of the $β$-alanine octamer. Therefore, the methodology is very well suited to simulate the mechanical unfolding of systems of experimental relevance also in the presence of protic solvents.

cond-mat.soft↗

arXiv2024

Cholesky decomposition in spin-free Dirac-Coulomb coupled-cluster calculations

We present an implementation for the use of Cholesky decomposition (CD) of two-electron integrals within the spin-free Dirac-Coulomb (SFDC) scheme that enables to perform high-accuracy coupled-cluster (CC) calculations at costs almost comparable to those of their non-relativistic counterparts. While for non-relativistic CC calculations atomic-orbital (AO) based algorithms, due to their significantly reduced disk-space requirements, are the key to efficient large-scale computations, such algorithms are less advantageous in the SFDC case due to their increased computational cost on that case. Here, molecular-orbital (MO) based algorithms exploiting the CD of the two-electron integrals allow to reduce disk-space requirements, and lead to computational cost in the CC step that are more or less the same as in the non-relativistic case. The only remaining overhead in a CD-SFDC-CC calculation are due to the need to compute additional two-electron integrals, the somewhat higher cost of the Hartree-Fock calculation in the SFDC case, and additional cost in the transformation of the Cholesky vectors from the AO to the MO representation. However, these additional costs typically amount to less than 5-15 % of the total wall time and are thus acceptable. We illustrate the efficiency of our CD scheme for SFDC-CC calculations on a series of illustrative calculations for the X(CO)$_4$ molecules with X = Ni, Pd, Pt.

physics.chem-ph↗

arXiv2024

MBE-CASSCF Approach for the Accurate Treatment of Large Active Spaces

We present a novel implementation of the complete active space self-consistent field (CASSCF) method that makes use of the many-body expanded full configuration interaction (MBE-FCI) method to incrementally approximate electronic structures within large active spaces. On the basis of a hybrid first-order algorithm employing both Super-CI and quasi-Newton strategies for the optimization of molecular orbitals, we demonstrate both computational efficacy and high accuracy of the resulting MBE-CASSCF method. We assess the performance of our implementation on a set of established numerical tests before applying MBE-CASSCF in the investigation of the triplet-quintet spin gap of iron(II) porphyrin with active spaces as large as 50 electrons in 50 orbitals.

physics.chem-ph↗

arXiv2024

Error Control and Automatic Detection of Reference Active Spaces in Many-Body Expanded Full Configuration Interaction

We present a wide-reaching revamp of the generalized many-body expanded full configuration interaction (MBE-FCI) method. First, we outline how to automatize the selection of reference active spaces whereby the inherent bias introduced through a manual identification is reduced, also within the context of traditional complete active space methods. Second, we allow for the use of compact orbital clusters as expansion objects, which works to circumvent the unfavorable scaling with the number of orbitals included in the space complementary to the reference orbitals. Finally, we present a new algorithm for ensuring that many-body expansions can be efficiently terminated while conservatively accounting for resulting errors. These developments are all tested on a variety of molecular systems and different orbital representations to illustrate the abilities of our algorithm to produce correlation energies within predetermined error bounds, significantly broadening the overall applicability of the MBE-FCI method.

physics.chem-ph↗

arXiv2023

A novel coupled-cluster singles and doubles implementation that combines the exploitation of point-group symmetry and Cholesky decomposition of the two-electron integrals

A novel implementation of the coupled-cluster singles and doubles (CCSD) approach is presented that is specifically tailored for the treatment of large, symmetric systems. It fully exploits Abelian point-group symmetry and the use of the Cholesky decomposition of the two-electron repulsion integrals. In accordance with modern CCSD algorithms, we propose two alternative strategies for the computation of the so-called particle-particle ladder term. The code is driven towards the optimal choice depending on the available hardware resources. As a large-scale application, we computed the frozen-core correlation energy of buckminsterfullerene (C$_{60}$) with a polarized valence triple-zeta basis set (240 correlated electrons in 1740 orbitals).

physics.chem-ph↗

arXiv2023

A Cholesky decomposition-based implementation of relativistic two-component coupled-cluster methods for medium-sized molecules

A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules have been performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of $10^{-4}$ is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF$_6$, with up to quadruple-zeta basis sets, and the lowest excitation energy in solvated uranyl ion [UO$_2^{2+}$(H$_2$O)$_{12}$].

physics.chem-ph↗

arXiv2022

Computation of NMR shieldings at the CASSCF level using gauge-including atomic orbitals and Cholesky decomposition

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.

physics.chem-ph↗

arXiv2022

Cholesky decomposition of two-electron integrals in quantum-chemical calculations with perturbative or finite magnetic fields using gauge-including atomic 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.

physics.chem-ph↗

arXiv2021

Wavefunction-based electrostatic-embedding QM/MM using CFOUR through MiMiC

We present an interface of the wavefunction-based quantum-chemical software CFOUR to the multiscale modeling framework MiMiC. Electrostatic embedding of the quantummechanical (QM) part is achieved by analytic evaluation of one-electron integrals in CFOUR, while the rest of the QM/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 SCF 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 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 implementation was tested and validated for a large number of wavefunction approaches, including Hartree-Fock and post-Hartree-Fock methods like Moller-Plesset, coupled cluster, and complete active space self-consistent field.

physics.chem-ph↗

arXiv2021

A black-box, general purpose quadratic self-consistent field code with and without Cholesky Decomposition of the two-electron integrals

We present the implementation of a quadratically convergent Self-consistent field (QCSCF) algorithm based on an adaptive trust-radius optimization 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 thigh convergence with extended basis set - 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

physics.chem-ph↗

arXiv2021

NMR Chemical Shift Computations at Second-Order Møller-Plesset Perturbation Theory Using Gauge-Including Atomic Orbitals and Cholesky-Decomposed Two-Electron Integrals

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.

physics.chem-ph↗