Required Citations
******************

When you publish results in the scientific literature that were
obtained with programs of the ADF package, you are required to include
references to the program package with the appropriate release number,
and a few key publications.

In addition to these general references, references to special
features are mandatory if you have used them.


General References
==================

For calculations with the molecular ADF program, version 2026.1:
   E.J. Baerends, N.F. Aguirre, N.D. Austin, J. Autschbach, F.M.
   Bickelhaupt, R. Bulo, C. Cappelli, A.C.T. van Duin, F. Egidi, C.
   Fonseca Guerra, A. Förster, M. Franchini, T.P.M. Goumans, T. Heine,
   M. Hellström, C.R. Jacob, L. Jensen, M.V. Krykunov, E. van Lenthe,
   A. Michalak, M. Mitoraj, J. Neugebauer, V.P. Nicu, P.H.T.
   Philipsen, H. Ramanantoanina, R. Rüger, G. Schreckenbach, M.
   Stener, M. Swart, J.M. Thijssen, T. Trnka, L. Visscher, A.L.
   Yakovlev, S.J.A. van Gisbergen, *The Amsterdam Modeling Suite*,
   Journal of Chemical Physics 162, 162501 (2025) ("bibtex")

   ADF 2026.1, SCM, Theoretical Chemistry, Vrije Universiteit,
   Amsterdam, The Netherlands, https://www.scm.com. Optionally, you
   may add the following list of authors and contributors: E.J.
   Baerends, T. Ziegler, A.J. Atkins, J. Autschbach, O. Baseggio, D.
   Bashford, A. Bérces, F.M. Bickelhaupt, C. Bo, P.M. Boerrigter, C.
   Cappelli, L. Cavallo, C. Daul, D.P. Chong, D.V. Chulhai, L. Deng,
   R.M. Dickson, J.M. Dieterich, F. Egidi, D.E. Ellis, M. van Faassen,
   L. Fan, T.H. Fischer, A. Förster, C. Fonseca Guerra, M. Franchini,
   A. Ghysels, A. Giammona, S.J.A. van Gisbergen, A. Goez, A.W. Götz,
   J.A. Groeneveld, O.V. Gritsenko, M. Grüning, S. Gusarov, F.E.
   Harris, P. van den Hoek, Z. Hu, C.R. Jacob, H. Jacobsen, L. Jensen,
   L. Joubert, J.W. Kaminski, G. van Kessel, C. König, F. Kootstra, A.
   Kovalenko, M.V. Krykunov, P. Lafiosca, E. van Lenthe, D.A.
   McCormack, M. Medves, A. Michalak, M. Mitoraj, S.M. Morton, J.
   Neugebauer, V.P. Nicu, L. Noodleman, V.P. Osinga, S. Patchkovskii,
   M. Pavanello, C.A. Peeples, P.H.T. Philipsen, D. Post, C.C. Pye, H.
   Ramanantoanina, P. Ramos, W. Ravenek, M. Reimann, J.I. Rodríguez,
   P. Ros, R. Rüger, P.R.T. Schipper, D. Schlüns, H. van Schoot, G.
   Schreckenbach, J.S. Seldenthuis, M. Seth, J.G. Snijders, M. Solà,
   M. Stener, M. Swart, D. Swerhone, V. Tognetti, G. te Velde, P.
   Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T.A.
   Wesolowski, E.M. van Wezenbeek, G. Wiesenekker, S.K. Wolff, T.K.
   Woo, A.L. Yakovlev

**Note:** if you have used a modified (by yourself, for instance)
version of the code, you should mention in the citation that a
modified version has been used.


Feature References
==================

When you have used special features, you should include one (or more,
as the case may be) lead reference(s) to the implementation.
Additional references to related publications are suggested.


Coordinates, basis sets, fragments
----------------------------------

Basis Sets
   E. van Lenthe and E.J. Baerends, *Optimized Slater-type basis sets
   for the elements 1-118*, Journal of Computational Chemistry 24,
   1142 (2003)

Correlation-consistent basis sets
   Arno Förster, Lucas Visscher, *GW100: A Slater-Type Orbital
   Perspective*, Journal of Chemical Theory and Computation 17 (8),
   5080–5097 (2021)

Spherical Gaussian nuclear charge distribution model
   J. Autschbach, *Magnitude of Finite-Nucleus-Size Effects in
   Relativistic Density Functional Computations of Indirect NMR
   Nuclear Spin-Spin Coupling Constants*, ChemPhysChem 10, 2274 (2009)


Geometry optimizations, transition states, and reaction paths
-------------------------------------------------------------

Transition State search
   L. Versluis and T. Ziegler, *The determination of Molecular
   Structure by Density Functional Theory*, Journal of Chemical
   Physics 88, 322 (1988)

   L. Fan and T. Ziegler, *Nonlocal density functional theory as a
   practical tool in calculations on transition states and activation
   energies*, Journal of the American Chemical Society 114, 10890
   (1992)

IRC
   L. Deng, T. Ziegler and L. Fan, *A combined density functional and
   intrinsic reaction coordinate study on the ground state energy
   surface of H2 CO*, Journal of Chemical Physics 99, 3823 (1993)

   L. Deng and T. Ziegler, *The determination of Intrinsic Reaction
   Coordinates by density functional theory*, International Journal of
   Quantum Chemistry 52, 731 (1994)

Nudged Elastic Band
   G. Henkelman, B.P. Uberuaga and H. Jónsson, *A climbing image
   nudged elastic band method for finding saddle points and minimum
   energy paths*, Journal of Chemical Physics 113, 9901 (2000)


Model Hamiltonians
------------------

Range Separated Functionals
   M. Seth and T. Ziegler, *Range-Separated Exchange Functionals with
   Slater-Type Functions*,  Journal of Chemical Theory and Computation
   8, 901 (2012)

MP2, double hybrids
   A. Förster, M. Franchini, E. van Lenthe, L. Visscher, *A Quadratic
   Pair Atomic Resolution of the Identity Based SOS-AO-MP2 Algorithm
   Using Slater Type Orbitals*, Journal of Chemical Theory and
   Computation 16, 875 (2020)

Double hybrids
   A. Förster, L. Visscher, *Double hybrid DFT calculations with
   Slater type orbitals*, Journal of Computational Chemistry 41,
   1660–1684 (2020)

RPA+SOSSX
   A. Förster, L. Visscher, *Exploring the statically screened G3W2
   correction to the GW self-energy: Charged excitations and total
   energies of finite systems*, Physical Review B 105, 125121 (2022)

RPA, RPA+SOSEX, RPA+SOSSX
   A. Förster, *Assessment of the Second-Order Statically Screened
   Exchange Correction to the Random Phase Approximation for
   Correlation Energies*, Journal of Chemical Theory and Computation
   18, 5948 (2022)

Sigma-functionals
   S.Fauser, A. Förster, L. Redeker, C. Neiss, J. Erhard, E. Trushin,
   A. Görling, *Basis Set Requirements of σ-Functionals for Gaussian-
   and Slater-Type Basis Functions and Comparison with Range-Separated
   Hybrid and Double Hybrid Functionals*, Journal of Chemical Theory
   and Computation 20 (6), 2404-2422 (2024)


Relativistic Effects
--------------------

ZORA
   E. van Lenthe, E.J. Baerends and J.G. Snijders,  *Relativistic
   regular two-component Hamiltonians*,  Journal of Chemical Physics
   99, 4597 (1993)

   E. van Lenthe, E.J. Baerends and J.G. Snijders,  *Relativistic
   total energy using regular approximations*,  Journal of Chemical
   Physics 101, 9783 (1994)

   E. van Lenthe, A.E. Ehlers and E.J. Baerends,  *Geometry
   optimization in the Zero Order Regular Approximation for
   relativistic effects*,  Journal of Chemical Physics 110, 8943
   (1999)

ZORA suggested
   E. van Lenthe, J.G. Snijders and E.J. Baerends,  *The zero-order
   regular approximation for relativistic effects: The effect of spin-
   orbit coupling in closed shell molecules*,  Journal of Chemical
   Physics 105, 6505 (1996)

   E. van Lenthe, R. van Leeuwen, E.J. Baerends and J.G. Snijders,
   *Relativistic regular two-component Hamiltonians*,  International
   Journal of Quantum Chemistry 57, 281 (1996)

Pauli
   J.G. Snijders, E.J. Baerends and P. Ros,  *A perturbation theory
   approach to relativistic calculations. II. Molecules*,  Molecular
   Physics 38, 1909 (1979)

   P.M. Boerrigter, E.J. Baerends and J.G. Snijders,  *A relativistic
   LCAO Hartree-Fock-Slater investigation of the electronic structure
   of the actinocenes M(COT)2 , M=Th, Pa, U, Np and Pu*,  Chemical
   Physics 122, 357 (1988)

   T. Ziegler, V. Tschinke, E.J. Baerends, J.G. Snijders and W.
   Ravenek,  *Calculation of bond energies in compounds of heavy
   elements by a quasi-relativistic approach*,  Journal of Physical
   Chemistry 93, 3050 (1989)


Solvents and other environments
-------------------------------

COSMO: Conductor-like Screening Model
   C.C. Pye and T. Ziegler,  *An implementation of the conductor-like
   screening model of solvation within the Amsterdam density
   functional package*, Theoretical Chemistry Accounts 101, 396 (1999)

SM12: Solvation Model 12
   C.A. Peeples and G. Schreckenbach, *Implementation of the SM12
   Solvation Model into ADF and Comparison with COSMO*, Journal of
   Chemical Theory and Computation 12, 4033 (2016)

QM/MM: Quantum Mechanical and Molecular Mechanics model
   T. K. Woo, L. Cavallo and T. Ziegler,  *Implementation of the IMOMM
   methodology for performing combined QM/MM molecular dynamics
   simulations and frequency calculations*, Theoretical Chemistry
   Accounts 100, 307 (1998)

QM/MM suggested
   T. K. Woo, S. Patchkovskii, and T. Ziegler, *Atomic Scale Modeling
   of Polymerization Catalysts*, Computing in Science & Engineering,
   2, 28-37 (2000)

QM/MM AddRemove model
   M. Swart,  *AddRemove: A new link model for use in QM/MM studies*,
   International Journal of Quantum Chemistry 91, 177 (2003)

FDE: Frozen Density Embedding
   T.A. Wesolowski and A. Warshel,  *Frozen Density Functional
   Approach for ab-initio Calculations of Solvated Molecules*,
   Journal of Physical Chemistry 97, 8050 (1993)

   J. Neugebauer, C.R. Jacob, T.A. Wesolowski and E.J. Baerends,  *An
   Explicit Quantum Chemical Method for Modeling Large Solvation
   Shells Applied to Aminocoumarin C151*, Journal of Physical
   Chemistry A 109, 7805 (2005)

   C.R. Jacob, J. Neugebauer and L. Visscher,  *A flexible
   implementation of frozen-density embedding for use in multilevel
   simulations*,  Journal of Computational Chemistry 29, 1011 (2008)

DIM/QM: Discrete Interaction Model/Quantum Mechanics
   J.L. Payton, S.M. Morton, Justin E. Moore, and Lasse Jensen, *A
   discrete interaction model/quantum mechanical method for simulating
   surface-enhanced Raman spectroscopy*,  Journal of Chemical Physics
   136, 214103 (2012)

DRF: Discrete Solvent Reaction Field model
   L. Jensen, P.T. van Duijnen and J.G. Snijders,  *A discrete solvent
   reaction field model within density functional theory*  Journal of
   Chemical Physics 118, 514 (2003)

QM/FQ: Quantum Mechanics/Fluctuating Charges
   T. Giovannini, F. Egidi and C. Cappelli, *Molecular spectroscopy of
   aqueous solutions: a theoretical perspective*, Chemical Society
   Reviews, 49, 5664 (2020)

3D-RISM: Three-Dimensional Reference Interaction Site Model
   S. Gusarov, T. Ziegler, and A. Kovalenko,  *Self-Consistent
   Combination of the Three-Dimensional RISM Theory of Molecular
   Solvation with Analytical Gradients and the Amsterdam Density
   Functional Package*,  Journal of Physical Chemistry A 110, 6083
   (2006)

3D-RISM suggested
   A. Kovalenko and F. Hirata, *Self-consistent description of a
   metal-water interface by the Kohn-Sham density functional theory
   and the three-dimensional reference interaction site model*,
   Journal of Chemical Physics 110, 10095 (1999)

   A. Kovalenko, *Three-dimensional RISM theory for molecular liquids
   and solid-liquid interfaces*, In Molecular Theory of Solvation;
   Hirata, Fumio, Ed.; Understanding Chemical Reactivity (series);
   Mezey, Paul G., Series Ed.; Kluwer Academic Publishers: Dordrecht,
   The Netherlands, 2003; Vol. 24, pp 169-275.


Frequencies, IR Intensities, Raman, VCD
---------------------------------------

Numerical Differentiation of Gradients
   L. Fan and T. Ziegler,  *Application of density functional theory
   to infrared absorption intensity calculations on main group
   molecules*,  Journal of Chemical Physics 96, 9005 (1992)

   L. Fan and T. Ziegler,  *Application of density functional theory
   to infrared absorption intensity calculations on transition-metal
   carbonyls*,  Journal of Physical Chemistry 96, 6937 (1992)

Analytical Second Derivatives
   A. Bérces, R. M. Dickson, L. Fan, H. Jacobsen, D. Swerhone and T.
   Ziegler,  *An implementation of the coupled perturbed Kohn-Sham
   equations: perturbation due to nuclear displacements*,  Computer
   Physics Communications 100, 247 (1997)

   H. Jacobsen, A. Bérces, D. Swerhone and T. Ziegler,  *Analytic
   second derivatives of molecular energies: a density functional
   implementation*,  Computer Physics Communications 100, 263 (1997)

   S. K. Wolff,  *Analytical second derivatives in the Amsterdam
   density functional package*,  International Journal of Quantum
   Chemistry 104, 645 (2005)

Mobile Block Hessian (MBH)
   A. Ghysels, D. Van Neck, V. Van Speybroeck, T. Verstraelen and M.
   Waroquier, *Vibrational Modes in partially optimized molecular
   systems*  Journal of Chemical Physics 126, 224102 (2007)

MBH suggested
   A. Ghysels, D. Van Neck and M. Waroquier, *Cartesian formulation of
   the Mobile Block Hessian Approach to vibrational analysis in
   partially optimized systems*  Journal of Chemical Physics 127,
   164108 (2007)

Raman scattering
   S.J.A. van Gisbergen, J.G. Snijders and E.J. Baerends,
   *Application of time-dependent density functional response theory
   to Raman scattering*,  Chemical Physics Letters 259, 599 (1996)

   S.J.A. van Gisbergen, J.G. Snijders and E.J. Baerends,
   *Implementation of time-dependent density functional response
   equations*,  Computer Physics Communications 118, 119 (1999)

Resonance Raman: excited-state finite lifetime
   L. Jensen, L. Zhao, J. Autschbach and G.C. Schatz, *Theory and
   method for calculating resonance Raman scattering from resonance
   polarizability derivatives*,  Journal of Chemical Physics 123,
   174110 (2005)

Resonance Raman: excited-state gradient
   J. Neugebauer, E.J. Baerends, E. Efremov, F. Ariese and C. Gooijer,
   *Combined Theoretical and Experimental Deep-UV Resonance Raman
   Studies of Substituted Pyrenes*,  Journal of Physical Chemistry A
   109, 2100 (2005)

VROA: (Resonance) vibrational Raman optical activity
   L. Jensen, J. Autschbach, M. Krykunov, and G.C. Schatz, *Resonance
   vibrational Raman optical activity: A time-dependent density
   functional theory approach*,  Journal of Chemical Physics 127,
   134101 (2007)

Vibrational Circular Dichroism (VCD)
   V.P. Nicu J. Neugebauer S.K. Wolff and E.J. Baerends,  *A
   vibrational circular dichroism implementation within a Slater-type-
   orbital based density functional framework and its application to
   hexa- and hepta-helicenes*, Theoretical Chemical Accounts 119, 245
   (2008)

VCD analysis: VCDtools
   V.P. Nicu, J. Neugebauer and E.J. Baerends, *Effects of Complex
   Formation on Vibrational Circular Dichroism Spectra*, Journal of
   Physical Chemistry A 112, 6978 (2008)

   M.A.J. Koenis, O. Visser, L. Visscher, W.J. Buma, V.P. Nicu, *GUI
   Implementation of VCDtools, A Program to Analyze Computed
   Vibrational Circular Dichroism Spectra*, J. Chem. Inf. Model 60,
   259 (2020)

   V.P. Nicu, *Revisiting an old concept: the coupled oscillator model
   for VCD. Part 1: the generalised coupled oscillator mechanism and
   its intrinsic connection to the strength of VCD signals*, Physical
   Chemistry Chemical Physics 18, 21202 (2016).

Franck-Condon factors
   J.S. Seldenthuis, H.S.J. van der Zant, M.A. Ratner and J.M.
   Thijssen, *Vibrational Excitations in Weakly Coupled Single-
   Molecule Junctions: A Computational Analysis*,  ACS Nano 2, 1445
   (2008)


Time-Dependent DFT
------------------

For all Time-Dependent DFT features (Excitation Energies, (Hyper)
Polarizabilities, Dispersion Coefficients, Raman Scattering, include:
   S.J.A. van Gisbergen, J.G. Snijders and E.J. Baerends,
   *Implementation of time-dependent density functional response
   equations*,  Computer Physics Communications 118, 119 (1999)


Excitation Energies and Oscillator Strengths
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Lead reference
   S.J.A. van Gisbergen, J.G. Snijders and E.J. Baerends,
   *Implementation of time-dependent density functional response
   equations*,  Computer Physics Communications 118, 119 (1999)

Suggested (when ZORA relativistic results are used)
   A. Rosa, E.J. Baerends, S.J.A. van Gisbergen, E. van Lenthe, J.A.
   Groeneveld and J. G. Snijders, *Article Electronic Spectra of
   M(CO)6 (M = Cr, Mo, W) Revisited by a Relativistic TDDFT Approach*,
   Journal of the American Chemical Society 121, 10356 (1999)

Open Shell ground state
   F. Wang and T. Ziegler, Mol. Phys.102, 2585 (2004)

Spin-flip transitions
   F. Wang and T. Ziegler,  *Time-dependent density functional theory
   based on a noncollinear formulation of the exchange-correlation
   potential*,  Journal of Chemical Physics 121, 12191 (2004)

   F. Wang and T. Ziegler,  *The performance of time-dependent density
   functional theory based on a noncollinear exchange-correlation
   potential in the calculations of excitation energies*,  Journal of
   Chemical Physics 122, 74109 (2005)

Core excitations
   M. Stener, G. Fronzoni and M. de Simone,  *Time dependent density
   functional theory of core electrons excitations*,  Chemical Physics
   Letters 373, 115 (2003)

Quadrupole intensities
   S. Bernadotte, A.J. Atkins, Ch.R. Jacob, *Origin-independent
   calculation of quadrupole intensities in X-ray spectroscopy*,
   Journal of Chemical Physics 137, 204106 (2012)

XES: X-ray emission spectroscopy
   A.J. Atkins, M. Bauer, and Ch.R. Jacob, *The chemical sensitivity
   of X-ray spectroscopy: high energy resolution XANES versus X-ray
   emission spectroscopy of substituted ferrocenes*, Physical
   Chemistry Chemical Physics 15, 8095 (2013)

Excitations including spin-orbit coupling
   F. Wang, T. Ziegler, E. van Lenthe, S.J.A. vand Gisbergen and E.J.
   Baerends, *The calculation of excitation energies based on the
   relativistic two-component zeroth-order regular approximation and
   time-dependent density-functional with full use of symmetry*,
   Journal of Chemical Physics 122, 204103 (2005)

Perturbative approach to include spin-orbit coupling
   F. Wang and T. Ziegler, *A simplified relativistic time-dependent
   density-functional theory formalism for the calculations of
   excitation energies including spin-orbit coupling effect*,  Journal
   of Chemical Physics 123, 154102 (2005)

CV(n)-DFT: Constricted Variational DFT
   J. Cullen, M. Krykunov, and T. Ziegler, *The formulation of a self-
   consistent constricted variational density functional theory for
   the description of excited states*, Chemical Physics 391, 11 (2011)

   M. Krykunov and T. Ziegler, *Self-consistent Formulation of
   Constricted Variational Density Functional Theory with Orbital
   Relaxation. Implementation and Applications*, Journal of Chemical
   Theory and Computation 9, 2761 (2013)

CV(n)-DFT: triplet states
   Y.C. Park, F. Senn, M. Krykunov, and T. Ziegler, *Self-Consistent
   Constricted Variational Theory RSCF-CV(* \infty *)-DFT and Its
   Restrictions To Obtain a Numerically Stable* \Delta *SCF-DFT-like
   Method: Theory and Calculations for Triplet States*, Journal of
   Chemical Theory and Computation 12, 5438 (2016)

TD-DFT+TB: Tight-Binding approximations to time-dependent Density
Functional Theory
   R. Rüger, E. van Lenthe, T. Heine, L. Visscher, *Tight-Binding
   Approximations to Time-Dependent Density Functional Theory - a fast
   approach for the calculation of electronically excited states*,
   Journal of Chemical Physics 144, 184103 (2016)

GW-BSE: GW-Bethe-Salpeter Equation
   Arno Förster, Lucas Visscher, *Quasiparticle Self-Consistent GW-
   Bethe-Salpeter equation calculations for large chromophoric
   systems*, Journal of Chemical Theory and Computation 18 (11)
   6779–6793 (2022)


Excited state gradients
~~~~~~~~~~~~~~~~~~~~~~~

General
   M. Seth, G. Mazur, and T. Ziegler, *Time-dependent density
   functional theory gradients in the Amsterdam density functional
   package: geometry optimizations of spin-flip excitations*,
   Theoretical Chemistry Accounts 129, 331 (2011)

TD-DFT+TB excited state gradients
   S. Havenridge, R. Rüger, C.M. Aikens, *Analytical excited state
   gradients for time-dependent density functional theory plus tight
   binding (TDDFT + TB)* The Journal of Chemical Physics 158, 224103
   (2023).


Polarizabilities
~~~~~~~~~~~~~~~~

General
   S.J.A. van Gisbergen, J.G. Snijders and E.J. Baerends,  *A Density
   Functional Theory study of frequency-dependent polarizabilities and
   van der Waals dispersion coefficients for polyatomic molecules*,
   Journal of Chemical Physics 103, 9347 (1995)

Suggested
   V.P. Osinga, S.J.A. van Gisbergen, J.G. Snijders and E.J. Baerends,
   *Density functional results for isotropic and anisotropic multipole
   polarizabilities and C6 , C7 , and C8  Van der Waals dispersion
   coefficients for molecules*,  Journal of Chemical Physics 106, 5091
   (1997)

Polarizabilities including spin-orbit coupling
   A. Devarajan, A. Gaenko, and J. Autschbach, *Two-component
   relativistic density functional method for computing nonsingular
   complex linear response of molecules based on the zeroth order
   regular approximation*,  Journal of Chemical Physics 130, 194102
   (2009)

PolTDDFT: Damped complex polarizabilities
   O. Baseggio, G. Fronzoni, and M. Stener, *A new time dependent
   density functional algorithm for large systems and plasmons in
   metal clusters*, Journal of Chemical Physics 143, 024106 (2015)


Hyperpolarizabilities
~~~~~~~~~~~~~~~~~~~~~

Hyperpolarizabilities with RESPONSE
   S.J.A. van Gisbergen, J.G. Snijders and E.J. Baerends,
   *Calculating frequency-dependent hyperpolarizabilities using time-
   dependent density functional theory*,  Journal of Chemical Physics
   109, 10644 (1998)

Suggested:
   S.J.A. van Gisbergen, J.G. Snijders, and E.J. Baerends,  *Time-
   dependent Density Functional Results for the Dynamic
   Hyperpolarizability of C60*,  Physical Review Letters 78, 3097
   (1997)

First hyperpolarizabilities with AORESPONSE
   Z. Hu, J. Autschbach, and L. Jensen, *Simulation of resonance
   hyper-Rayleigh scattering of molecules and metal clusters using a
   time-dependent density functional theory approach*, Journal of
   Chemical Physics 141, 124305 (2014)

Second hyperpolarizabilities with AORESPONSE
   Z. Hu, J. Autschbach, and L. Jensen, *Simulating Third-Order
   Nonlinear Optical Properties Using Damped Cubic Response Theory
   within Time-Dependent Density Functional Theory*, Journal of
   Chemical Theory and Computation 12, 1294 (2016)


CD, ORD, magnetizability, MCD, Verdet constants
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Circular Dichroism (CD)
   J. Autschbach and T. Ziegler,  *Calculating molecular electric and
   magnetic properties from time-dependent density functional response
   theory*,  Journal of Chemical Physics 116, 891 (2002)

   J. Autschbach, T. Ziegler, S.J.A. van Gisbergen and  E.J. Baerends,
   *Chiroptical properties from time-dependent density functional
   theory. I. Circular dichroism spectra of organic molecules*,
   Journal of Chemical Physics 116, 6930 (2002)

Optical Rotation (OR), Optical Rotation Dispersion (ORD)
   J. Autschbach and T. Ziegler, *Calculating molecular electric and
   magnetic properties from time-dependent density functional response
   theory*,  Journal of Chemical Physics 116, 891 (2002)

   J. Autschbach, S. Patchkovskii, T. Ziegler, S.J.A. van Gisbergen
   and  E.J. Baerends,  *Chiroptical properties from time-dependent
   density functional theory. II. Optical rotations of small to medium
   sized organic molecules*,  Journal of Chemical Physics 117, 581
   (2002)

Magnetizability
   M. Krykunov and J. Autschbach, *Calculation of static and dynamic
   linear magnetic response in approximate time-dependent density
   functional theory*,  Journal of Chemical Physics 126, 24101 (2007)

Magnetic Circular Dichroism (MCD)
   M. Seth, M. Krykunov, T. Ziegler, J. Autschbach and A. Banerjee,
   *Application of magnetically perturbed time-dependent density
   functional theory to magnetic circular dichroism: Calculation of B
   terms*,  Journal of Chemical Physics 128, 144105 (2008)

   M. Seth, M. Krykunov, T. Ziegler and J. Autschbach, *Application of
   magnetically perturbed time-dependent density functional theory to
   magnetic circular dichroism. II. Calculation of A terms*,  Journal
   of Chemical Physics 128, 234102 (2008)

   M. Seth, T. Ziegler and J. Autschbach, *Application of magnetically
   perturbed time-dependent density functional theory to magnetic
   circular dichroism. III. Temperature-dependent magnetic circular
   dichroism induced by spin-orbit coupling*,  Journal of Chemical
   Physics 129, 104105 (2008)

Verdet constant and Faraday term
   M. Krykunov, A. Banerjee, T. Ziegler and J. Autschbach,
   *Calculation of Verdet constants with time-dependent density
   functional theory. Implementation and results for small molecules*,
   Journal of Chemical Physics 122, 074105 (2005)

   M. Krykunov, M. Seth, T. Ziegler and J. Autschbach, *Calculation of
   the magnetic circular dichroism B term from the imaginary part of
   the Verdet constant using damped time-dependent density functional
   theory*,  Journal of Chemical Physics 127, 244102 (2007)


Dispersion Coefficients
~~~~~~~~~~~~~~~~~~~~~~~

Lead reference
   V.P. Osinga, S.J.A. van Gisbergen, J.G. Snijders and E.J. Baerends,
   *Density functional results for isotropic and anisotropic multipole
   polarizabilities and C6 , C7 , and C8  Van der Waals dispersion
   coefficients for molecules*,  Journal of Chemical Physics 106, 5091
   (1997)

Suggested
   S.J.A. van Gisbergen, J.G. Snijders and E.J. Baerends, *A Density
   Functional Theory study of frequency-dependent polarizabilities and
   van der Waals dispersion coefficients for polyatomic molecules*,
   Journal of Chemical Physics 103, 9347 (1995)


LFDFT
-----

Lead reference
   M. Atanasov, C.A. Daul, C. Rauzy, *A DFT Based Ligand Field
   Theory*, Structure & Bonding 106, 97 (2004)

LFDFT for two-open-shell configuration
   H. Ramanantoanina, W. Urland, F. Cimpoesu, and C. Daul, *Ligand
   field density functional theory calculation of the* 4f^2 → 4f^1
   5d^1 *transitions in the quantum cutter* Cs_2 KYF_6 Pr^3+, Physical
   Chemistry Chemical Physics 15, 13902 (2013).


NMR
---


NMR Chemical Shifts
~~~~~~~~~~~~~~~~~~~

Lead reference
   G. Schreckenbach and T. Ziegler,  *The calculation of NMR shielding
   tensors using GIAO's and modern density functional theory*,
   Journal of Physical Chemistry 99, 606 (1995)

NMR chemical shifts with hybrid functionals
   M. Krykunov, T. Ziegler and E. van Lenthe, *Hybrid density
   functional calculations of nuclear magnetic shieldings using
   Slater-type orbitals and the zeroth-order regular approximation*,
   International Journal of Quantum Chemistry 109, 1676 (2009)

NMR chemical shifts with NBO analysis
   J. Autschbach and S. Zheng, *Analyzing Pt chemical shifts
   calculated from relativistic density functional theory using
   localized orbitals: The role of Pt 5d lone pairs*,  Magnetic
   Resonance in Chemistry 46, S45 (2008)

   J. Autschbach, *Analyzing NMR shielding tensors calculated with
   two-component relativistic methods using spin-free localized
   molecular orbitals*,  Journal of Chemical Physics 128, 164112
   (2008)

Paramagnetic NMR chemical shifts
   J. Autschbach, S. Patchkovskii, and B. Pritchard, *Calculation of
   Hyperfine Tensors and Paramagnetic NMR Shifts Using the
   Relativistic Zeroth-Order Regular Approximation and Density
   Functional Theory*,  Journal of Chemical Theory and Computation 7,
   2175 (2011)

Suggested
   G. Schreckenbach and T. Ziegler,  *The calculation of NMR shielding
   tensors based on density functional theory and the frozen-core
   approximation*,  International Journal of Quantum Chemistry 60, 753
   (1996)

   G. Schreckenbach and T. Ziegler,  *Calculation of NMR shielding
   tensors based on density functional theory and a scalar
   relativistic Pauli-type Hamiltonian. The application to transition
   metal complexes*,  International Journal of Quantum Chemistry 61,
   899 (1997)

   S.K. Wolff and T. Ziegler,  *Calculation of DFT-GIAO NMR shifts
   with inclusion of spin-orbit coupling*,  Journal of Chemical
   Physics 109, 895 (1998)

   S.K. Wolff, T. Ziegler, E. van Lenthe and E.J. Baerends,  *Density
   functional calculations of nuclear magnetic shieldings using the
   zeroth-order regular approximation (ZORA) for relativistic effects:
   ZORA nuclear magnetic resonance*,  Journal of Chemical Physics 110,
   7689 (1999)


NMR spin-spin coupling
~~~~~~~~~~~~~~~~~~~~~~

Lead reference
   J. Autschbach and T. Ziegler,  *Nuclear spin-spin coupling
   constants from regular approximate density functional calculations.
   I. Formalism and scalar relativistic results for heavy metal
   compounds*,  Journal of Chemical Physics 113, 936 (2000)

   J. Autschbach and T. Ziegler,  *Nuclear spin-spin coupling
   constants from regular approximate relativistic density functional
   calculations. II. Spin-orbit coupling effects and anisotropies*,
   Journal of Chemical Physics 113, 9410 (2000)

NMR spin-spin couplings with PBE0
   J. Autschbach, *Two-component relativistic hybrid density
   functional computations of nuclear spin-spin coupling tensors using
   Slater-type basis sets and density-fitting techniques*,  Journal of
   Chemical Physics 129, 094105 (2008), Erratum:  Journal of Chemical
   Physics 130, 209901 (2009)

NMR spin-spin couplings with NBO analysis
   J. Autschbach, *Analyzing molecular properties calculated with two-
   component relativistic methods using spin-free Natural Bond
   Orbitals: NMR spin-spin coupling constants*  Journal of Chemical
   Physics 127, 124106 (2007)

Suggested
   R.M. Dickson and T. Ziegler,  *NMR Spin-Spin Coupling Constants
   from Density Functional Theory with Slater-Type Basis Functions*,
   Journal of Physical Chemistry 100, 5286 (1996)

   J. Khandogin and T. Ziegler,  *A density functional study of
   nuclear magnetic resonance spin-spin coupling constants in
   transition-metal systems*,  Spectrochimica Acta 55, 607 (1999)

   J. Autschbach and T. Ziegler,  *Solvent Effects on Heavy Atom
   Nuclear Spin-Spin Coupling Constants:  A Theoretical Study of Hg.C
   and Pt.P Couplings*,  Journal of the American Chemical Society 123,
   3341 (2001)

   J. Autschbach and T. Ziegler,  *A Theoretical Investigation of the
   Remarkable Nuclear Spin-Spin Coupling Pattern in [(NC)5 Pt-
   Tl(CN)]-*,  Journal of the American Chemical Society 123, 5320
   (2001)

Suggested book reference
   J. Autschbach, T. Ziegler, in *Encyclopedia of Nuclear Magnetic
   Resonance*, Eds. D.M. Grant, R. K. Harris, John Wiley and Sons,
   Chichester, 2002, Vol. 9 *Advances in NMR*.


ESR/EPR
-------


G-tensor: Zeeman interaction
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

G-tensor: self-consistent spin-orbit coupling
   E. van Lenthe, A. van der Avoird and P.E.S. Wormer,  *Density
   functional calculations of molecular g-tensors in the zero order
   regular approximation for relativistic effects*,  Journal of
   Chemical Physics 107, 2488 (1997)

G-tensor: perturbative inclusion spin-orbit coupling
   J. Autschbach and B. Pritchard, *Calculation of molecular g-tensors
   using the zeroth-order regular approximation and density functional
   theory: expectation value versus linear response approaches*,
   Theoretical Chemistry Accounts 129, 453 (2011)

G-tensor: perturbative inclusion spin-orbit coupling with EPR/NMR
program
   G. Schreckenbach and T. Ziegler,  *Calculation of the G-tensor of
   electron paramagnetic resonance spectroscopy using Gauge-Including
   Atomic Orbitals and Density Functional Theory*,  Journal of
   Physical Chemistry A 101, 3388 (1997) (for ESR/EPR g-tensor)

   S. Patchkovskii and T. Ziegler,  *Calculation of the EPR g-Tensors
   of High-Spin Radicals with Density Functional Theory*,  Journal of
   Physical Chemistry A 105, 5490 (2001) (for high-spin ESR/EPR
   g-tensor)


A-tensor: Nuclear magnetic dipole hyperfine interaction
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A-tensor
   E. van Lenthe, A. van der Avoird and P.E.S. Wormer,  *Density
   functional calculations of molecular hyperfine interactions in the
   zero order regular approximation for relativistic effects*,
   Journal of Chemical Physics 108, 4783 (1998)

A-tensor: perturbative inclusion spin-orbit coupling
   J. Autschbach, S. Patchkovskii, and B. Pritchard, *Calculation of
   Hyperfine Tensors and Paramagnetic NMR Shifts Using the
   Relativistic Zeroth-Order Regular Approximation and Density
   Functional Theory*,  Journal of Chemical Theory and Computation 7,
   2175 (2011)


Nuclear Quadrupole Interaction (EFG)
------------------------------------

EFG, NQCC (in ESR, called Q-tensor: Nuclear electric quadrupole
hyperfine interaction)
   E. van Lenthe and E.J. Baerends,  *Density functional calculations
   of nuclear quadrupole coupling constants in the zero-order regular
   approximation for relativistic effects*,  Journal of Chemical
   Physics 112, 8279 (2000)

EFG with NBO analysis
   A.J. Rossini, R.W. Mills, G.A. Briscoe, E.L. Norton, S.J. Geier, I.
   Hung, S. Zheng, J. Autschbach, and R.W. Schurko, *Solid-State
   Chlorine NMR of Group IV Transition Metal Organometallic
   Complexes*,  Journal of the American Chemical Society 131, 3317
   (2009)

   J. Autschbach, S. Zheng, and R.W. Schurko, *Analysis of Electric
   Field Gradient Tensors at Quadrupolar Nuclei in Common Structural
   Motifs*,  Concepts in Magnetic Resonance Part A 36A, 84 (2010)


GW
--

Lead reference
   Arno Förster, Lucas Visscher, *Low-order scaling G0W0 by pair
   atomic density fitting*, Journal of Chemical Theory and Computation
   16 (12), 7381–7399 (2020)

Suggested
   Arno Förster, Lucas Visscher, *GW100: A Slater-Type Orbital
   Perspective*, Journal of Chemical Theory and Computation 17 (8),
   5080–5097 (2021)

Quasiparticle self-consistent GW
   Arno Förster, Lucas Visscher, *Low-Order Scaling Quasiparticle
   Self-Consistent GW for Molecules*, Frontiers in Chemistry 9, 736591
   (2021)

Vertex-corrected GW
   Arno Förster, Lucas Visscher, *Exploring the statically screened
   G3W2 correction to the GW self-energy: Charged excitations and
   total energies of finite systems*, Physical Review B 105, 125121
   (2022)

   F.Bruneval, A. Förster, *Fully Dynamic G3W2 Self-Energy for Finite
   Systems: Formulas and Benchmark*, Journal of Chemical Theory and
   Computation 20 (8), 3218-3230 (2024)

   A. Förster, F.Bruneval,  *Why Does the GW Approximation Give
   Accurate Quasiparticle Energies? The Cancellation of Vertex
   Corrections Quantified*, The Journal of Physical Chemistry Letters
   15, 12526-12534 (2024)

   A. Förster, *Beyond quasi-particle self-consistent GW for molecules
   with vertex corrections*, arXiv:2412.01581 (2024)


Transport properties: Non-self-consistent Green's function
----------------------------------------------------------

Lead reference
   Chapter 2 and appendix C of J.S. Seldenthuis, Electrical and
   mechanical effects in single-molecule junctions, PhD thesis, Delft
   University of Technology, 2011

Wide-band limit
   C.J.O. Verzijl, J.S. Seldenthuis, and J.M. Thijssen, *Applicability
   of the wide-band limit in DFT-based molecular transport
   calculations*,  Journal of Chemical Physics 138, 094102 (2013)


Analysis
--------

Bond Energy Analysis
   T. Ziegler and A. Rauk,  *A theoretical study of the ethylene-metal
   bond in complexes between* Cu^+ , Ag^+ , Au^+ , Pt^0  or Pt^2+
   *and ethylene, based on the Hartree-Fock-Slater transition-state
   method*,  Inorganic Chemistry 18, 1558 (1979)

   T. Ziegler and A. Rauk,  *Carbon monoxide, carbon monosulfide,
   molecular nitrogen, phosphorus trifluoride, and methyl isocyanide
   as sigma donors and pi acceptors. A theoretical study by the
   Hartree-Fock-Slater transition-state method*,  Inorganic Chemistry
   18, 1755 (1979)

   F.M. Bickelhaupt and E.J. Baerends, In: Rev. Comput. Chem.; K.B.
   Lipkowitz and D.B. Boyd, Eds.; Wiley, New York, 2000, Vol. 15, p.
   1-86

ETS-NOCV
   M. Mitoraj, A. Michalak and T. Ziegler, *A Combined Charge and
   Energy Decomposition Scheme for Bond Analysis*,  Journal of
   Chemical Theory and Computation 5, 962 (2009)

QTAIM, Bader analysis, grid-based algorithm
   J.I. Rodríguez, R.F.W. Bader, P.W. Ayers, C. Michel, A.W. Götz and
   C. Bo, *A high performance grid-based algorithm for computing QTAIM
   properties*,  Chemical Physics Letters 472, 149 (2009)

   J.I. Rodríguez, *An Efficient Method for Computing the QTAIM
   Topology of a Scalar Field: The Electron Density Case*,  Journal of
   Computational Chemistry 34, 681 (2013)

Localized molecular orbitals
   J. Autschbach and H.F. King, *Analyzing molecular static linear
   response properties with perturbed localized orbitals*, Journal of
   Chemical Physics 133, 044109 (2010)


Accuracy and efficiency
-----------------------

Linear scaling methods
   C. Fonseca Guerra, J.G. Snijders, G. te Velde and E.J. Baerends,
   *Towards an order-N DFT method*, Theoretical Chemistry Accounts 99,
   391 (1998)

Numerical integration
   M. Franchini, P.H.T. Philipsen, L. Visscher, *The Becke Fuzzy Cells
   Integration Scheme in the Amsterdam Density Functional Program
   Suite*,  Journal of Computational Chemistry 34, 1818 (2013).

Density fitting
   M. Franchini, P.H.T. Philipsen, E. van Lenthe, L. Visscher,
   *Accurate Coulomb Potentials for Periodic and Molecular Systems
   through Density Fitting*,  Journal of Chemical Theory and
   Computation 10, 1994 (2014)


External programs and libraries
===============================

Third party software used in the 2026.1 version of the Amsterdam
Modeling Suite can be found in the file titled "third-party-
software.txt" in the root of your AMS installation.
