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The Python Simulations of Chemistry Framework: 10 years of an open-source quantum chemistry project
Authors:
Qiming Sun,
Matthew R Hermes,
Xiaojie Wu,
Huanchen Zhai,
Xing Zhang,
Abdelrahman M. Ahmed,
Juan José Aucar,
Oliver J. Backhouse,
Samragni Banerjee,
Peng Bao,
Nikolay A. Bogdanov,
Kyle Bystrom,
Frédéric Chapoton,
Ning-Yuan Chen,
Ivan Yu. Chernyshov,
Helen S. Clifford,
Sander Cohen-Janes,
Zhi-Hao Cui,
Yann D. Damour,
Nike Dattani,
Linus Bjarne Dittmer,
Sebastian Ehlert,
Janus Juul Eriksen,
Francesco A. Evangelista,
Simon A. Ewing
, et al. (78 additional authors not shown)
Abstract:
Over the past decade, the Python-based Simulations of Chemistry Framework (PySCF) has developed into a widely used open-source platform for electronic structure theory and quantum chemical method development. This article reviews the major advances since the previous overview in 2020, covering new modules and methodology, infrastructure changes, and performance benchmarks.
Over the past decade, the Python-based Simulations of Chemistry Framework (PySCF) has developed into a widely used open-source platform for electronic structure theory and quantum chemical method development. This article reviews the major advances since the previous overview in 2020, covering new modules and methodology, infrastructure changes, and performance benchmarks.
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Submitted 7 April, 2026; v1 submitted 14 March, 2026;
originally announced March 2026.
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Solvation Lies Within: Simulating Condensed-Phase Properties from Local Electronic Structures
Authors:
Kasper F. Schaltz,
Jonas Greiner,
Filippo Lipparini,
Janus J. Eriksen
Abstract:
In transitions between different environmental settings, a molecular system inevitably undergoes a range of detectable changes, and the ability to accurately simulate such responses, e.g., in the form of shifts to molecular energies, remains an important challenge across physical chemistry. Based on an exact decomposition of total energies from Kohn--Sham density functional theory in a basis of sp…
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In transitions between different environmental settings, a molecular system inevitably undergoes a range of detectable changes, and the ability to accurately simulate such responses, e.g., in the form of shifts to molecular energies, remains an important challenge across physical chemistry. Based on an exact decomposition of total energies from Kohn--Sham density functional theory in a basis of spatially localized molecular orbitals, the present work outlines a robust protocol for sampling the effect of solvation within homogeneous condensed phases by focusing on perturbations to local electronic structures only. We report chemically intuitive results for binding energies of water, ethanol, and acetonitrile that all display fast convergence with respect to the bulk size. Results stay largely invariant with respect to the choice of basis set while reflecting differences in density functional approximations, and our protocol thus allows for a physically sound and efficient estimation of general effects related to bulk solvation.
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Submitted 13 January, 2026;
originally announced January 2026.
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A Reusable Library for Second-Order Orbital Optimization Using the Trust Region Method
Authors:
Jonas Greiner,
Ida-Marie Høyvik,
Susi Lehtola,
Janus J. Eriksen
Abstract:
We present a reusable, open-source software implementation of the second-order trust region algorithm in the new OpenTrustRegion library. We apply the implementation to the general-purpose optimization of molecular orbitals in various contexts within electronic-structure theory. Our permissibly licensed implementation can be included in any software package, be it free and open-source, academicall…
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We present a reusable, open-source software implementation of the second-order trust region algorithm in the new OpenTrustRegion library. We apply the implementation to the general-purpose optimization of molecular orbitals in various contexts within electronic-structure theory. Our permissibly licensed implementation can be included in any software package, be it free and open-source, academically licensed closed-source, or commercial. Detailing the implementation in OpenTrustRegion, we present a review of the theory behind trust region-based methods alongside various extensions. We demonstrate the robustness and efficiency of our optimization library with extensive benchmarks for self-consistent field calculations, orbital localization, as well as orbital symmetrization tasks, featuring challenging and pathological systems.
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Submitted 10 November, 2025; v1 submitted 17 September, 2025;
originally announced September 2025.
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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
Authors:
Jonas Greiner,
Jürgen Gauss,
Janus J. Eriksen
Abstract:
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 wh…
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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.
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Submitted 31 July, 2024;
originally announced July 2024.
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Error Control and Automatic Detection of Reference Active Spaces in Many-Body Expanded Full Configuration Interaction
Authors:
Jonas Greiner,
Jürgen Gauss,
Janus J. Eriksen
Abstract:
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 clu…
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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.
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Submitted 17 June, 2024;
originally announced June 2024.
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Functionality Optimization for Singlet Fission Rate Screening in the Full-Dimensional Molecular and Intermolecular Coordinate Space
Authors:
Johannes Greiner,
Anurag Singh,
Merle I. S. Röhr
Abstract:
In computational chemistry, accurately predicting molecular configurations that exhibit specific properties remains a critical challenge. Its intricacies become especially evident in the study of molecular aggregates, where the light-induced functionality is tied to highly structure-dependent electronic couplings between molecules. Here, we present an efficient strategy for the targeted screening…
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In computational chemistry, accurately predicting molecular configurations that exhibit specific properties remains a critical challenge. Its intricacies become especially evident in the study of molecular aggregates, where the light-induced functionality is tied to highly structure-dependent electronic couplings between molecules. Here, we present an efficient strategy for the targeted screening of the structural space employing a "functionality optimization" technique, in which a chosen descriptor, constrained by the ground state energy expression, is optimized. The chosen algorithmic differentiation (AD) framework allows to automatically obtain gradients without its tedious implementation. We demonstrate the effectiveness of the approach by identifying Perylene Bisiimide (PBI) dimer motifs with enhanced SF rate. Our findings reveal that certain structural modifications of the PBI monomer, such as helical twisting and bending, as well as slipped-rotated packing arrangements, can significantly increase the SF rate.
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Submitted 3 April, 2024;
originally announced April 2024.
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MBE-CASSCF Approach for the Accurate Treatment of Large Active Spaces
Authors:
Jonas Greiner,
Ivan Gianni,
Tommaso Nottoli,
Filippo Lipparini,
Janus J. Eriksen,
Jürgen Gauss
Abstract:
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 molecula…
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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.
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Submitted 18 June, 2024; v1 submitted 26 March, 2024;
originally announced March 2024.
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Symmetrization of Localized Molecular Orbitals
Authors:
Jonas Greiner,
Janus J. Eriksen
Abstract:
We present a novel algorithm for (i) detecting approximate symmetries inherently present among spatially localized molecular orbitals and (ii) enforcing these in numerically exact manners by means of unitary optimization techniques. The vast potential of our algorithm to compress a full set of molecular orbitals into only a minimal set of symmetry-unique orbitals is demonstrated, starting from loc…
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We present a novel algorithm for (i) detecting approximate symmetries inherently present among spatially localized molecular orbitals and (ii) enforcing these in numerically exact manners by means of unitary optimization techniques. The vast potential of our algorithm to compress a full set of molecular orbitals into only a minimal set of symmetry-unique orbitals is demonstrated, starting from localized bases of either Pipek-Mezey or Foster-Boys orbitals. Comparisons of results based on either of these two localization procedures indicate that Foster-Boys molecular orbitals can be spanned by a smaller number of symmetry-unique orbitals on average, making these outstanding candidates for the exploitation of general, (non-)Abelian point-group symmetries in a range of local correlation methods. As an illustration of said compressibility, our algorithm is capable of identifying a mere 14 symmetry-unique orbitals for the buckminsterfullerene in the highly symmetric $I_h$ molecular point group, corresponding to only $1.7\%$ of its total 840 molecular orbitals in a standard double-$ζ$ basis set. The present work thus marks an important advancement in the exploitation of point-group symmetry within local correlation methods, for which the appropriate adaption of symmetry uniqueness among orbitals has the potential to yield unprecedented speed-ups.
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Submitted 25 April, 2023; v1 submitted 27 February, 2023;
originally announced February 2023.
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Unbiased All-Optical Random-Number Generator
Authors:
Tobias Steinle,
Johannes N. Greiner,
Jörg Wrachtrup,
Harald Giessen,
Ilja Gerhardt
Abstract:
The generation of random bits is of enormous importance in modern information science. Cryptographic security is based on random numbers which require a physical process for their generation. This is commonly performed by hardware random number generators. These exhibit often a number of problems, namely experimental bias, memory in the system, and other technical subtleties, which reduce the reli…
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The generation of random bits is of enormous importance in modern information science. Cryptographic security is based on random numbers which require a physical process for their generation. This is commonly performed by hardware random number generators. These exhibit often a number of problems, namely experimental bias, memory in the system, and other technical subtleties, which reduce the reliability in the entropy estimation. Further, the generated outcome has to be post-processed to "iron out" such spurious effects. Here, we present a purely optical randomness generator, based on the bi-stable output of an optical parametric oscillator. Detector noise plays no role and no further post-processing is required. Upon entering the bi-stable regime, initially the resulting output phase depends on vacuum fluctuations. Later, the phase is rigidly locked and can be well determined versus a pulse train, which is derived from the pump laser. This delivers an ambiguity-free output, which is reliably detected and associated with a binary outcome. The resulting random bit stream resembles a perfect coin toss and passes all relevant randomness measures. The random nature of the generated binary outcome is furthermore confirmed by an analysis of resulting conditional entropies.
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Submitted 6 December, 2017;
originally announced December 2017.
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Purification of an unpolarized spin ensemble into entangled singlet pairs
Authors:
Johannes N. Greiner,
D. D. Bhaktavatsala Rao,
Jörg Wrachtrup
Abstract:
Dynamical polarization of nuclear spin ensembles is of central importance for magnetic resonance studies, precision sensing and for applications in quantum information theory. Here we propose a scheme to generate long-lived singlet pairs in an unpolarized nuclear spin ensemble which is dipolar coupled to the electron spins of a Nitrogen Vacancy center in diamond. The quantum mechanical back-action…
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Dynamical polarization of nuclear spin ensembles is of central importance for magnetic resonance studies, precision sensing and for applications in quantum information theory. Here we propose a scheme to generate long-lived singlet pairs in an unpolarized nuclear spin ensemble which is dipolar coupled to the electron spins of a Nitrogen Vacancy center in diamond. The quantum mechanical back-action induced by frequent spin-selective readout of the NV centers allows the nuclear spins to pair up into maximally entangled singlet pairs. Counterintuitively, the robustness of the pair formation to dephasing noise improves with increasing size of the spin ensemble. We also show how the paired nuclear spin state allows for enhanced sensing capabilities of NV centers in diamond.
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Submitted 5 April, 2017; v1 submitted 27 October, 2016;
originally announced October 2016.
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Indirect quantum sensors: Improving the sensitivity in characterizing very weakly coupled spins
Authors:
Johannes N. Greiner,
D. D. Bhaktavatsala Rao,
Philipp Neumann,
Jörg Wrachtrup
Abstract:
We propose a scheme to increase the sensitivity and thus the detection volume of nanoscale single molecule magnetic resonance imaging. The proposal aims to surpass the T1 limited detection of the sensor by taking advantage of a long-lived ancilla nuclear spin to which the sensor is coupled. We show how this nuclear spin takes over the role of the sensor spin, keeping the characteristic time-scales…
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We propose a scheme to increase the sensitivity and thus the detection volume of nanoscale single molecule magnetic resonance imaging. The proposal aims to surpass the T1 limited detection of the sensor by taking advantage of a long-lived ancilla nuclear spin to which the sensor is coupled. We show how this nuclear spin takes over the role of the sensor spin, keeping the characteristic time-scales of detection on the same order but with a longer life-time allowing it to detect a larger volume of the sample which is not possible by the sensor alone.
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Submitted 20 July, 2015;
originally announced July 2015.