The Published Science Behind Every Number

Roothaan, C. C. J. (1951). New Developments in Molecular Orbital Theory. Rev. Mod. Phys. 23, 69-89.

Restricted Hartree-Fock (Roothaan equations)

Hall, G. G. (1951). The molecular orbital theory of chemical valency VIII. A method of calculating ionization potentials. Proc. R. Soc. Lond. A 205, 541-552.

Restricted Hartree-Fock (Hall equations)

Pople, J. A.; Nesbet, R. K. (1954). Self-Consistent Orbitals for Radicals. J. Chem. Phys. 22, 571-572.

Unrestricted Hartree-Fock

Pulay, P. (1980). Convergence acceleration of iterative sequences. The case of SCF iteration. Chem. Phys. Lett. 73, 393-398.

DIIS convergence acceleration

Pulay, P. (1982). Improved SCF convergence acceleration. J. Comput. Chem. 3, 556-560.

DIIS error vector for SCF

Saunders, V. R.; Hillier, I. H. (1973). A “Level-Shifting” method for converging closed shell Hartree-Fock wave functions. Int. J. Quantum Chem. 7, 699-705.

Level shifting for difficult SCF convergence

Almlöf, J.; Faegri, K.; Korsell, K. (1982). Principles for a direct SCF approach to LICAO-MO ab-initio calculations. J. Comput. Chem. 3, 385-399.

Direct SCF and incremental Fock builds

Häser, M.; Ahlrichs, R. (1989). Improvements on the direct SCF method. J. Comput. Chem. 10, 104-111.

Schwarz integral screening

Seeger, R.; Pople, J. A. (1977). Self-consistent molecular orbital methods. XVIII. Constraints and stability in Hartree-Fock theory. J. Chem. Phys. 66, 3045-3050.

Hartree-Fock stability analysis (RHF to UHF, real to complex)

Bauernschmitt, R.; Ahlrichs, R. (1996). Stability analysis for solutions of the closed shell Kohn-Sham equation. J. Chem. Phys. 104, 9047-9052.

Kohn-Sham stability analysis

Davidson, E. R. (1975). The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. J. Comput. Phys. 17, 87-94.

Davidson iterations for the lowest stability roots

Mulliken, R. S. (1955). Electronic Population Analysis on LCAO-MO Molecular Wave Functions. I. J. Chem. Phys. 23, 1833-1840.

Mulliken population analysis

Löwdin, P. (1950). On the Non-Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals. J. Chem. Phys. 18, 365-375.

Symmetric (Lowdin) orthogonalisation

Boys, S. F. (1950). Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system. Proc. R. Soc. Lond. A 200, 542-554.

Gaussian basis functions and the Boys function

McMurchie, L. E.; Davidson, E. R. (1978). One- and two-electron integrals over cartesian gaussian functions. J. Comput. Phys. 26, 218-231.

Integrals over Cartesian Gaussians, CPU and GPU

Obara, S.; Saika, A. (1986). Efficient recursive computation of molecular integrals over Cartesian Gaussian functions. J. Chem. Phys. 84, 3963-3974.

Recurrence relations for the reference integral code

Hehre, W. J.; Stewart, R. F.; Pople, J. A. (1969). Self-Consistent Molecular-Orbital Methods. I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals. J. Chem. Phys. 51, 2657-2664.

STO-3G, hydrogen to neon (Tables I and IX)

Hehre, W. J.; Ditchfield, R.; Stewart, R. F.; Pople, J. A. (1970). Self-Consistent Molecular Orbital Methods. IV. Use of Gaussian Expansions of Slater-Type Orbitals. Extension to Second-Row Molecules. J. Chem. Phys. 52, 2769-2773.

STO-3G, sodium to argon (Tables I and IX)

Ditchfield, R.; Hehre, W. J.; Pople, J. A. (1971). Self-Consistent Molecular-Orbital Methods. IX. An Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules. J. Chem. Phys. 54, 724-728.

6-31G hydrogen functions and scale factors (Tables I and IV)

Hehre, W. J.; Ditchfield, R.; Pople, J. A. (1972). Self-Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian-Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. J. Chem. Phys. 56, 2257-2261.

6-31G carbon to fluorine (Table II)

Weigend, F.; Ahlrichs, R. (2005). Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys. 7, 3297.

def2 basis sets, hydrogen to krypton (supplementary listings)

Weigend, F. (2006). Accurate Coulomb-fitting basis sets for H to Rn. Phys. Chem. Chem. Phys. 8, 1057.

def2-universal-J auxiliary basis for RI-J

Eichkorn, K.; Treutler, O.; Öhm, H.; Häser, M.; Ahlrichs, R. (1995). Auxiliary basis sets to approximate Coulomb potentials. Chem. Phys. Lett. 240, 283-290.

RI-J Coulomb fitting

Vahtras, O.; Almlöf, J.; Feyereisen, M. W. (1993). Integral approximations for LCAO-SCF calculations. Chem. Phys. Lett. 213, 514-518.

Origin of the density-fitting approximation

Kohn, W.; Sham, L. J. (1965). Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 140, A1133-A1138.

Kohn-Sham equations

Dirac, P. A. M. (1930). Note on Exchange Phenomena in the Thomas Atom. Math. Proc. Camb. Phil. Soc. 26, 376-385.

Local density exchange

Slater, J. C. (1951). A Simplification of the Hartree-Fock Method. Phys. Rev. 81, 385-390.

Slater exchange

Vosko, S. H.; Wilk, L.; Nusair, M. (1980). Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 58, 1200-1211.

VWN5 and VWN RPA correlation (parameters checked)

Becke, A. D. (1988). Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38, 3098-3100.

B88 exchange (parameter checked)

Lee, C.; Yang, W.; Parr, R. G. (1988). Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37, 785-789.

LYP correlation (constants checked, Eq. 3)

Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. (1989). Results obtained with the correlation energy density functionals of Becke and Lee, Yang and Parr. Chem. Phys. Lett. 157, 200-206.

LYP in the form without Laplacian terms

Perdew, J. P.; Wang, Y. (1992). Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 45, 13244-13249.

PW92 correlation (Table I checked)

Perdew, J. P.; Burke, K.; Ernzerhof, M. (1996). Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77, 3865-3868.

PBE exchange and correlation (constants checked)

Perdew, J. P.; Burke, K.; Ernzerhof, M. (1997). Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett. 78, 1396-1396.

PBE erratum

Johnson, B. G.; Gill, P. M. W.; Pople, J. A. (1993). The performance of a family of density functional methods. J. Chem. Phys. 98, 5612-5626.

Analytic Kohn-Sham gradients (Eqs. 9 to 11, Appendix B) This check found an erratum, J. Chem. Phys. 101, 9202 (1994), doi 10.1063/1.468507, not yet compared with our code (register item SI-104).

Grimme, S. (2006). Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787-1799.

DFT-D2 dispersion (Table 1, Eqs. 10 to 13)

Becke, A. D. (1988). A multicenter numerical integration scheme for polyatomic molecules. J. Chem. Phys. 88, 2547-2553.

Multicentre integration grid

Treutler, O.; Ahlrichs, R. (1995). Efficient molecular numerical integration schemes. J. Chem. Phys. 102, 346-354.

M4 radial grid and the 434-point angular rule (Tables I and II)

Slater, J. C. (1964). Atomic Radii in Crystals. J. Chem. Phys. 41, 3199-3204.

Bragg-Slater radii for grid partitioning (Table I)

Broyden, C. G. (1970). The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations. IMA J. Appl. Math. 6, 76-90.

BFGS Hessian update

Fletcher, R. (1970). A new approach to variable metric algorithms. Comput. J. 13, 317-322.

BFGS Hessian update

Goldfarb, D. (1970). A family of variable-metric methods derived by variational means. Math. Comp. 24, 23-26.

BFGS Hessian update

Shanno, D. F. (1970). Conditioning of quasi-Newton methods for function minimization. Math. Comp. 24, 647-656.

BFGS Hessian update

Liu, D. C.; Nocedal, J. (1989). On the limited memory BFGS method for large scale optimization. Math. Program. 45, 503-528.

L-BFGS minimisation

Pulay, P. (1969). Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. Mol. Phys. 17, 197-204.

Analytic gradients; force constants from gradient differences

Richardson, L. F. (1911). IX. The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam. Phil. Trans. R. Soc. Lond. A 210, 307-357.

Richardson extrapolation of frequencies

Miller, W. H.; Handy, N. C.; Adams, J. E. (1980). Reaction path Hamiltonian for polyatomic molecules. J. Chem. Phys. 72, 99-112.

Projecting translations and rotations out of the Hessian

Scott, A. P.; Radom, L. (1996). Harmonic Vibrational Frequencies: An Evaluation of Hartree-Fock, Møller-Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors. J. Phys. Chem. 100, 16502-16513.

Frequency scale factors, used as a check

Beruski, O.; Vidal, L. N. (2014). Algorithms for computer detection of symmetry elements in molecular systems. J. Comput. Chem. 35, 290-299.

Symmetry element search for point groups

Kabsch, W. (1976). A solution for the best rotation to relate two sets of vectors. Acta Cryst. A 32, 922-923.

Best rotation between two structures (RMSD)

Horn, B. K. P. (1987). Closed-form solution of absolute orientation using unit quaternions. J. Opt. Soc. Am. A 4, 629.

Quaternion best-fit alignment

Halgren, T. A. (1996). Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94. J. Comput. Chem. 17, 490-519.

MMFF94 form and parameters (Appendix B files checked)

Halgren, T. A. (1996). Merck molecular force field. II. MMFF94 van der Waals and electrostatic parameters for intermolecular interactions. J. Comput. Chem. 17, 520-552.

MMFF94 van der Waals and electrostatics

Halgren, T. A. (1996). Merck molecular force field. III. Molecular geometries and vibrational frequencies for MMFF94. J. Comput. Chem. 17, 553-586.

MMFF94 geometries and vibrational frequencies

Halgren, T. A.; Nachbar, R. B. (1996). Merck molecular force field. IV. Conformational energies and geometries for MMFF94. J. Comput. Chem. 17, 587-615.

MMFF94 conformational energies (Table II checked)

Halgren, T. A. (1996). Merck molecular force field. V. Extension of MMFF94 using experimental data, additional computational data, and empirical rules. J. Comput. Chem. 17, 616-641.

MMFF94 empirical rules (Tables VI and X checked)

Halgren, T. A. (1992). The representation of van der Waals (vdW) interactions in molecular mechanics force fields: potential form, combination rules, and vdW parameters. J. Am. Chem. Soc. 114, 7827-7843.

Buffered 14-7 van der Waals form

Blondel, A.; Karplus, M. (1996). New formulation for derivatives of torsion angles and improper torsion angles in molecular mechanics: Elimination of singularities. J. Comput. Chem. 17, 1132-1141.

Torsion angle derivatives

Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. (1992). UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc. 114, 10024-10035.

UFF force field: parameter table awaited, UFF runs refuse until it is checked

Gasteiger, J.; Marsili, M. (1980). Iterative partial equalization of orbital electronegativity, a rapid access to atomic charges. Tetrahedron 36, 3219-3228.

Gasteiger-Marsili charges: parameter table awaited

Halgren, T. A. (1998). MMFF94 Validation Suite (761 molecules with term energies). Computational Chemistry List archive.

Energy validation of every MMFF94 term

Weininger, D. (1988). SMILES, a chemical language and information system. 1. Introduction to methodology and encoding rules. J. Chem. Inf. Comput. Sci. 28, 31-36.

SMILES reading and writing

Weininger, D.; Weininger, A.; Weininger, J. L. (1989). SMILES. 2. Algorithm for generation of unique SMILES notation. J. Chem. Inf. Comput. Sci. 29, 97-101.

Canonical SMILES (CANON and GENES)

McKay, B. D.; Piperno, A. (2014). Practical graph isomorphism, II. J. Symb. Comput. 60, 94-112.

Canonical labelling by individualisation and refinement

Schneider, N.; Sayle, R. A.; Landrum, G. A. (2015). Get Your Atoms in Order: An Open-Source Implementation of a Novel and Robust Molecular Canonicalization Algorithm. J. Chem. Inf. Model. 55, 2111-2120.

Stereo-aware canonical ranking

Hückel, E. (1931). Quantentheoretische Beiträge zum Benzolproblem. Z. Phys. 70, 204-286.

Aromaticity by the 4n+2 rule In German.

Rogers, D.; Hahn, M. (2010). Extended-Connectivity Fingerprints. J. Chem. Inf. Model. 50, 742-754.

ECFP4 circular fingerprints

Willett, P.; Barnard, J. M.; Downs, G. M. (1998). Chemical Similarity Searching. J. Chem. Inf. Comput. Sci. 38, 983-996.

Tanimoto similarity

Cordella, L. P.; Foggia, P.; Sansone, C.; Vento, M. (2004). A (sub)graph isomorphism algorithm for matching large graphs. IEEE Trans. Pattern Anal. Mach. Intell. 26, 1367-1372.

Substructure search

Butina, D. (1999). Unsupervised Data Base Clustering Based on Daylight's Fingerprint and Tanimoto Similarity: A Fast and Automated Way To Cluster Small and Large Data Sets. J. Chem. Inf. Comput. Sci. 39, 747-750.

Butina clustering

Kamada, T.; Kawai, S. (1989). An algorithm for drawing general undirected graphs. Inf. Process. Lett. 31, 7-15.

2D layout for drawings

Havel, T. F.; Kuntz, I. D.; Crippen, G. M. (1983). The theory and practice of distance geometry. Bull. Math. Biol. 45, 665-720.

3D structures by distance geometry

Wildman, S. A.; Crippen, G. M. (1999). Prediction of Physicochemical Parameters by Atomic Contributions. J. Chem. Inf. Comput. Sci. 39, 868-873.

Crippen logP: atom table not yet checked against Table 1, results say Unverified

Ertl, P.; Rohde, B.; Selzer, P. (2000). Fast Calculation of Molecular Polar Surface Area as a Sum of Fragment-Based Contributions and Its Application to the Prediction of Drug Transport Properties. J. Med. Chem. 43, 3714-3717.

TPSA: fragment table not yet checked against the paper, results say Unverified

Lipinski, C. A.; Lombardo, F.; Dominy, B. W.; Feeney, P. J. (1997). Experimental and computational approaches to estimate solubility and permeability in drug discovery and development settings. Adv. Drug Deliv. Rev. 23, 3-25.

Rule of five, hydrogen-bond donors and acceptors

Veber, D. F.; Johnson, S. R.; Cheng, H.; Smith, B. R.; Ward, K. W.; Kopple, K. D. (2002). Molecular Properties That Influence the Oral Bioavailability of Drug Candidates. J. Med. Chem. 45, 2615-2623.

Rotatable bonds

Pyykkö, P.; Atsumi, M. (2009). Molecular Single-Bond Covalent Radii for Elements 1-118. Chem. Eur. J. 15, 186-197.

Single-bond covalent radii for 3D bounds

Pyykkö, P.; Atsumi, M. (2009). Molecular Double-Bond Covalent Radii for Elements Li-E112. Chem. Eur. J. 15, 12770-12779.

Double-bond covalent radii for 3D bounds

Pyykkö, P.; Riedel, S.; Patzschke, M. (2005). Triple-Bond Covalent Radii. Chem. Eur. J. 11, 3511-3520.

Triple-bond covalent radii for 3D bounds

Bondi, A. (1964). van der Waals Volumes and Radii. J. Phys. Chem. 68, 441-451.

Van der Waals radii for distance bounds

Cordero, B.; Gómez, V.; Platero-Prats, A. E.; Revés, M.; Echeverría, J.; Cremades, E.; et al. (2008). Covalent radii revisited. Dalton Trans., 2832.

Covalent radii for structure checks (Table 2)

Colbert, D. T.; Miller, W. H. (1992). A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method. J. Chem. Phys. 96, 1982-1991.

Sinc discrete variable representation grids

Fornberg, B. (1988). Generation of finite difference formulas on arbitrarily spaced grids. Math. Comp. 51, 699-706.

Finite-difference Laplacians

Morse, P. M. (1929). Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels. Phys. Rev. 34, 57-64.

Morse oscillator, exact levels for tests

Eckart, C. (1930). The Penetration of a Potential Barrier by Electrons. Phys. Rev. 35, 1303-1309.

Eckart barrier and its transmission

Johnston, H. S.; Heicklen, J. (1962). Tunnelling corrections for unsymmetrical Eckart potential energy barriers. J. Phys. Chem. 66, 532-533.

Tunnelling corrections for unsymmetrical Eckart barriers

Wigner, E. (1932). Über das Überschreiten von Potentialschwellen bei chemischen Reaktionen. Z. Phys. Chem. B 19B, 203-216.

Wigner tunnelling correction In German.

Feit, M. D.; Fleck, J. A.; Steiger, A. (1982). Solution of the Schrödinger equation by a spectral method. J. Comput. Phys. 47, 412-433.

Split-operator wavepacket propagation

Lanczos, C. (1950). An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Natl. Bur. Stand. 45, 255.

Lanczos iteration for 2D and 3D grids

Cooley, J. W.; Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19, 297-301.

Fast Fourier transform (radix 2)

Bluestein, L. (1970). A linear filtering approach to the computation of discrete Fourier transform. IEEE Trans. Audio Electroacoust. 18, 451-455.

Fourier transform of any length (chirp z)

Stockham, T. G. (1966). High-speed convolution and correlation. AFIPS '66 Spring Joint Computer Conference, 229.

Self-sorting FFT on the GPU

Govindaraju, N. K.; Lloyd, B.; Dotsenko, Y.; Smith, B.; Manferdelli, J. (2008). High performance discrete Fourier transforms on graphics processors. SC08, International Conference for High Performance Computing, 1-12.

FFT on graphics processors

Householder, A. S. (1958). Unitary Triangularization of a Nonsymmetric Matrix. J. ACM 5, 339-342.

Householder reduction

Martin, R. S.; Reinsch, C.; Wilkinson, J. H. (1968). Householder's tridiagonalization of a symmetric matrix. Numer. Math. 11, 181-195.

Householder tridiagonalisation

Bowdler, H.; Martin, R. S.; Reinsch, C.; Wilkinson, J. H. (1968). The QR and QL algorithms for symmetric matrices. Numer. Math. 11, 293-306.

QL iterations for symmetric eigenproblems

Jacobi, C. G. J. (1846). Über ein leichtes Verfahren die in der Theorie der Säcularstörungen vorkommenden Gleichungen numerisch aufzulösen. J. Reine Angew. Math. 1846, 51-94.

Jacobi eigenvalue method (fallback) In German.

Matsumoto, M.; Nishimura, T. (1998). Mersenne twister. ACM Trans. Model. Comput. Simul. 8, 3-30.

Random numbers for conformer search and tests

Tiesinga, E.; Mohr, P. J.; Newell, D. B.; Taylor, B. N. (2021). CODATA recommended values of the fundamental physical constants: 2018. Rev. Mod. Phys. 93.

CODATA 2018 constants (extracted from the NIST file)

Prohaska, T.; Irrgeher, J.; Benefield, J.; Böhlke, J. K.; Chesson, L. A.; Coplen, T. B.; et al. (2022). Standard atomic weights of the elements 2021 (IUPAC Technical Report). Pure Appl. Chem. 94, 573-600.

Standard atomic weights

IUPAC CIAAW (2025). Standard atomic weights of three technology critical elements revised. Chem. Int. 47, 20-20.

2024 revision of gadolinium, lutetium and zirconium

Meija, J.; Coplen, T. B.; Berglund, M.; Brand, W. A.; De Bièvre, P.; Gröning, M.; et al. (2016). Isotopic compositions of the elements 2013 (IUPAC Technical Report). Pure Appl. Chem. 88, 293-306.

Isotopic compositions

Wang, M.; Huang, W. J.; Kondev, F. G.; Audi, G.; Naimi, S. (2021). The AME 2020 atomic mass evaluation (II). Tables, graphs and references. Chinese Phys. C 45, 030003.

AME2020 atomic and nuclide masses

Kim, S.; Chen, J.; Cheng, T.; Gindulyte, A.; He, J.; He, S.; et al. (2023). PubChem 2023 update. Nucleic Acids Res. 51, D1373-D1380.

Weights, TPSA and rotatable bonds, used as a check

Huber, K. P.; Herzberg, G. (1979). Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules. Van Nostrand Reinhold; values as served by the NIST Chemistry WebBook.

Hydrogen spectroscopic constants for Model Systems tests

NIST. Computational Chemistry Comparison and Benchmark Database (CCCBDB). National Institute of Standards and Technology.

Point group reference set, 27 of 27 molecules

OpenSMILES. OpenSMILES Specification, Version 1.0. opensmiles.org.

Stereo marks, isotopes and valence rules in SMILES

BIOVIA (2020). CTfile Formats. Dassault Systemes BIOVIA.

MOL and SDF files, V2000 and V3000

wwPDB. Atomic Coordinate Entry Format Description, Version 3.30. Worldwide Protein Data Bank.

PDB files

Bray, T. (ed.) (2017). The JavaScript Object Notation (JSON) Data Interchange Format. IETF RFC 8259.

Engine input and result files

NIST (2015). Secure Hash Standard (SHS), FIPS PUB 180-4. National Institute of Standards and Technology.

Checksums on every data file and cache key

Szabo, A.; Ostlund, N. S. (1996). Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Dover.

Hartree-Fock theory; hydrogen molecule value in tests

Helgaker, T.; Jorgensen, P.; Olsen, J. (2000). Molecular Electronic-Structure Theory. Wiley.

Integral recurrences and the Boys function

Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. (1986). Ab Initio Molecular Orbital Theory. Wiley.

Hartree-Fock methods and basis sets

Wilson, E. B.; Decius, J. C.; Cross, P. C. (1980). Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra. Dover reprint.

Normal-mode analysis

Cotton, F. A. (1990). Chemical Applications of Group Theory, 3rd ed.. Wiley.

Point group flow chart (chapter 3)

Golub, G. H.; Van Loan, C. F. (2013). Matrix Computations, 4th ed.. Johns Hopkins University Press.

Cholesky, Lanczos and matrix exponential

Nocedal, J.; Wright, S. J. (2006). Numerical Optimization, 2nd ed.. Springer.

Line search and L-BFGS details

Crippen, G. M.; Havel, T. F. (1988). Distance Geometry and Molecular Conformation. Research Studies Press and Wiley.

3D embedding

Allen, M. P.; Tildesley, D. J. (2017). Computer Simulation of Liquids, 2nd ed.. Oxford University Press.

Force-field topology (bonds, angles, 1-4 pairs)

Rall, L. B. (1981). Automatic Differentiation: Techniques and Applications (Lecture Notes in Computer Science 120). Springer.

Exact derivatives by dual numbers