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Copy file name to clipboardExpand all lines: content/about/accuracy.md
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@@ -12,10 +12,10 @@ There is also a [list of discussions](/Discussions/Discussion_topics.html) about
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In the broader context of atomistic simulation, the semiempirical quantum mechanics (SQM) models used by MOPAC are a middle ground in cost, accuracy, and transferability.
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Here, "transferability" generically refers to the ability of a model to retain its accuracy beyond its training data.
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First-principles (*ab initio*) quantum mechanics (QM) calculations are typically at least a thousand times more expensive than an equivalent SQM calculation,
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First-principles (i.e. *ab initio*) quantum mechanics (QM) calculations are typically at least a thousand times more expensive than an equivalent SQM calculation,
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but they are usually more accurate and more transferable. For example, density functional theory (DFT) calculations with a double-zeta or triple-zeta Gaussian basis set
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and the B3LYP density functional typically have errors that are two to five times smaller than any SQM model in MOPAC.
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Molecular mechanics (MM) models based on a force field (interatomic potential) are typically at least a thousand times less expensive than an equivalent SQM calculation.
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Molecular mechanics (MM) models based on a force field (i.e. interatomic potential) are typically at least a thousand times less expensive than an equivalent SQM calculation.
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However, the transferability of force fields is usually quite low. They can be more accurate than an SQM calculation, but that accuracy can rapidly degrade
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if a force field is used for systems that are not well represented by its training data. For the application of force fields to long molecular dynamics trajectories,
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it can be challenging to monitor or estimate the overall accuracy of a force field.
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for more efficient MM simulations or fit a custom force field for your application.
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Note that recent developments in machine learning (ML) research have greatly improved the tools for fitting new force fields for MM-based applications.
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ML research has also generated very extensive sets of atomistic training data that are being used to improve the transferability of big-data force fields.
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ML research has also generated very extensive sets of atomistic training data such as [OMol25](https://arxiv.org/abs/2505.08762)
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that are being used to improve the transferability of big-data force fields.
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In principle, SQM model development can also benefit from the data and fitting tools being generated by ML research.
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However, there has been far less research activity in SQM than MM for many decades now, so the progress of SQM in this direction has been much slower.
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These exact mappings are computationally intractable just like the exact force field, but they can be approximated by SQM models and practical DFT functionals.
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An important distinction between SQM models and DFT functionals is that DFT is used to approximate electron correlation effects beyond a mean-field calculation
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in a large basis set while SQM models are additionally used to approximate the complete basis set limit beyond a minimal-basis calculation.
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More is required of an SQM model, but they also tend to have more free parameters than DFT functionals.
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in a large basis set while SQM models use a small basis set and also rely on the model to approximate the complete basis set limit.
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SQM models are thus used to correct for more sources of error than DFT functionals, but they also tend to have more free parameters.
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Although available SQM models are not as accurate as popular DFT functionals, that is more a reflection of relative development effort and not a fundamental limit.
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DFT functional development has been an extremely popular research activity in chemistry, condensed-matter physics, and materials science for several decades,
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while SQM model development has been kept alive by only a handful of people and research groups since its popularity among method developers faded in the 1970s.
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An important additional limitation of MNDO-family models is that they do not directly use diatomic model parameters.
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Most parameters are specific to individual chemical elements and describe their average behavior in all chemical environments.
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Interatomic matrix elements between pair of elements come either from a Slater-type orbital approximation of their valence atomic orbitals,
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Interatomic matrix elements between pairs of elements come either from a Slater-type orbital approximation of their valence atomic orbitals,
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or a Klopman-Ohno approximation of their atomic charge distributions. In either case, a single fixed number---a Slater exponent or a charge radius---is
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used to characterize the average electronic "size" of each atom. The NDDO approximation also neglects electronic charges from pairs of atomic orbitals on different atoms.
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used to characterize the average electronic "size" of each atom. The NDDO approximation also neglects electronic charges from overlapping pairs of atomic orbitals on different atoms.
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Some of the later MNDO-family models like PM6 and PM7 added a limited set of diatomic interatomic repulsion terms to fix error outliers
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and also include diatomic parameters indirectly through their use of dispersion models such as Grimme's [D3 model](https://doi.org/10.1063/1.3382344).
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and also included diatomic parameters indirectly through their use of dispersion models such as Grimme's [D3 model](https://doi.org/10.1063/1.3382344).
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While the lack of diatomic parameters limits the accuracy and transferability of MNDO-family models,
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it was an essential limitation that kept the number of model parameters low enough to be fit to the scarce experimental data that was available in the 1980's.
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A nuance of MNDO-family models that complicates their use is that they were designed to approximate heats of formation rather than ground-state total energies.
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A Hartree-Fock calculation is performed on the MNDO-family many-electron Hamiltonian, and the ground-state total energy of that calculation is assigned to be
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the heat of formation at standard temperature and pressure.
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The simple reason for this design decision was that experiments directly measured heats of formation and not total energies.
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A Hartree-Fock calculation is performed on a MNDO-family many-electron Hamiltonian, and the ground-state total energy of that calculation is assigned to be
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the heat of formation at a standard temperature (25°C) and pressure.
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The simple reason for this design decision was that experiments directly measure heats of formation and not total energies.
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If the model output was a total energy, then additional corrections for atomic vibrations would be needed to approximate the heat of formation.
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The direct modeling of heat is formally awkward because it is a statistical property that only relates to a specific atomic configuration if
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However, the direct modeling of heat is formally awkward because it is a statistical property that only relates to a specific atomic configuration if
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the thermal distribution over atomic configuration is tightly peaked around a single equilibrium configuration.
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The heat of formation for a non-equilibrium atomic configuration doesn't make formal sense without introducing constraints that cause it to be an
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equilibrium configuration (e.g. in an external potential).
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The interactions between a solvent and solute can primarily be categorized as electrostatic and statistical. For solute molecules that have a net charge,
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dipole moment, or highly non-uniform charge distribution, the largest solvation effects are electrostatic in nature.
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The solvent polarizes in response to the solute's charge distribution, and this response is approximated by the COSMO model as an ideal conductor located
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at a solvent accessible surface (SAS) of the solute molecule. The electrostatic energy between the SAS conductor and solute is then modified to approximate
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on a solvent accessible surface (SAS) of the solute molecule. The electrostatic energy between the SAS conductor and solute is then modified to approximate
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the energy associated with a finite dielectric constant. The SAS is formally defined by a union of atom-centered spheres with radii proportional to each atom's
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Van der Waals radius, but the SAS is approximated by tessellation to a triangular mesh for numerical work. The tesselation can be adjusted by keywords in the
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MOPAC input file to test numerical sensitivity.
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Users should be careful when evaluating finite-difference-based derivatives of numerical outputs from MOPAC. The atomic forces evaluated by MOPAC are only
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partially analytical derivatives and do typically contain terms that are evaluated by finite differences. MOPAC evaluates all second derivatives
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(vibrational matrix elements) as finite-difference derivatives of the atomic forces. While MOPAC has keywords that can be used to adjust many numerical details,
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the finite-difference step size cannot be adjusted without altering the source code. The default convergence tolerances of the self-consistent field (SCF) cycle
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the finite-difference step sizes cannot be adjusted without altering the source code. The default convergence tolerances of the self-consistent field (SCF) cycle
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were chosen to achieve reasonable overall accuracy in finite-difference derivatives, but that source of error can be further reduced by setting tighter SCF tolerances
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using keyword in the MOPAC input file.
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using keywords in the MOPAC input file.
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Calculations of periodic systems have additional sources of error. MOPAC does not use Brillouin zone sampling, so the only way to reduce finite-size effects in
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periodic calculations is to expand the unit cell into supercells of increasing size. MOPAC also does not have a proper periodic electrostatics solver (e.g.
Copy file name to clipboardExpand all lines: content/about/history/index.md
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@@ -47,14 +47,14 @@ in 1992, which included d orbitals. MNDO/d was then incorporated into MOPAC in t
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## Austin era
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The development of MOPAC began in 1981 after [James "Jimmy" Stewart](stewart_bio/) joined the Dewar group as a visiting scholar.
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The development of MOPAC began in 1981 after [James "Jimmy" Stewart](../stewart_bio) joined the Dewar group as a visiting scholar.
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Stewart was a professor at the University of Strathclyde in Scotland with a lot of prior software development experience in quantum chemistry.
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He was tasked by Dewar to refactor the research software that his group had produced during the development of the MINDO/3 and MNDO models into
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a unified, user-friendly computer program. The first release of MOPAC was in 1983 as software available by mail order from the [Quantum Chemistry Program
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Exchange](https://en.wikipedia.org/wiki/Quantum_Chemistry_Program_Exchange) (QCPE). After GAUSSIAN became commercial software and was removed
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from the QCPE catalog, MOPAC became the most popular software on the QCPE.
The Dewar group also simultaneously developed the Austin Model 1 (AM1) semiempirical model alongside MOPAC, which included the development of
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new model parameterization software. Stewart also contributed to the development of AM1 and its parameterization software, which he would eventually release as the PARAM
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As part of a broader investment in atomistic simulation software, Fujitsu hired Stewart as a consultant and acquired the distribution rights to future versions of MOPAC.
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The first Fujitsu commercial release of MOPAC was MOPAC 93 in 1993. Fujitsu later acquired the CAChe software from Oxford Molecular Group in 2000 around the time of that
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company's bankruptcy and liquidation, and MOPAC and CAChe formed the foundation for Fujitsu's SCIGRESS software. MOPAC was adapted into the MO-G simulation engine of
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SCIGRESS and its development continued at FQS Poland subsidiary of Fujitsu. Some Fujitsu-exclusive semiempirical quantum chemistry features include the PM5 model and the
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SCIGRESS, and its development continued at FQS Poland subsidiary of Fujitsu. Some Fujitsu-exclusive semiempirical quantum chemistry features include the PM5 model and the
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[LocalSCF](https://doi.org/10.1063/1.1764496) fast solver algorithm, which is technically distinct from MOPAC's
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[MOZYME](https://doi.org/10.1002/(SICI)1097-461X(1996)58:2%3C133::AID-QUA2%3E3.0.CO;2-Z) fast solver algorithm.
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Stewart stopped working for Fujitsu in 2004 and distributed subsequent versions of MOPAC through Stewart Computational Chemistry
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in partnership with third-party commercial resellers.
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Versions of MOPAC from this era were free for academic use, but it required a commercial license for government and industrial use. MOPAC's model coverage of the periodic table was
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greatly expanded to include the first 83 elements of the periodic table (with the lanthanides being modeled only in the +3 valence as classical "sparkles") in the
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[PM6](https://doi.org/10.1007/s00894-007-0233-4) and [PM7](https://doi.org/10.1007/s00894-012-1667-x) models. MOPAC's support for biomolecular simulation, particularly of protein
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structures from the [Protein Data Bank](https://www.rcsb.org) (PDB), was also improved.
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greatly expanded to include the first 83 elements of the periodic table in the [PM6](https://doi.org/10.1007/s00894-007-0233-4) and [PM7](https://doi.org/10.1007/s00894-012-1667-x)
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models (with the lanthanides being modeled only in the +3 valence as classical "sparkles"). MOPAC's support for biomolecular simulation was also improved, particularly of protein
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structures from the [Protein Data Bank](https://www.rcsb.org) (PDB).
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In 2019, Stewart began a partnership with the Molecular Science Software Institute (MolSSI) to migrate MOPAC into an open-source software project.
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On the technical side, this process involved improving the portability of MOPAC's code base, reorganizing its to be easier to understand and contribute to,
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On the technical side, this process involved improving the portability of MOPAC's code base, reorganizing it to be easier to understand and contribute to,
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adapting its building, testing, and distribution to the modern open-source ecosystem, fixing some performance issues, and adding new interfaces to improve accessibility.
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On the social side, this involved contacting and coordinating with various stakeholders and collecting essential institutional knowledge.
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This process concluded in 2022 with a legal transfer of MOPAC's intellectual property to Virginia Tech and its first open-source release.
This popular GUI software has gone through multiple names and owners (most recently Chem3D Ultra from PerkinElmer), and it is now developed and sold by Revvity Signals Software.
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Note that MOPAC executables not distributed with MDI support enabled. To use MOPAC as an MDI engine, you must build it yourself with the CMake command-line option
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`-DMDI=ON`.
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### [Mopactools](/mopactools/)
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### [mopactools](/mopactools/)
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A Python wrapper for MOPAC, for both command-line usage and its native API.
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### [Pymopac](https://pymopac.readthedocs.io)
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### [pymopac](https://pymopac.readthedocs.io)
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Another Python wrapper for MOPAC, for both command-line usage and its native API.
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