Introduction
************

Since AMS2020, ADF is only accessible through the AMS driver program
[5]. ADF (Amsterdam Density Functional) is an AMS engine for
calculations on atoms and molecules (in gas phase or solution). It can
be used for the study of such diverse fields as molecular
spectroscopy, organic and inorganic chemistry, and pharmacochemistry.
The AMS engine BAND is available for the study of periodic systems:
crystals, surfaces, and polymers. The separate COSMO-RS program is
used for calculating thermodynamic properties of (mixed) fluids.

The underlying theory is the Kohn-Sham approach to Density-Functional
Theory (DFT). This implies a one-electron picture of the many-electron
systems but yields, in principle, the exact electron density (and
related properties) and the total energy.

If ADF is new for you, we recommend that you carefully read the
section Technical remarks and Terminology, which presents a discussion
of a few ADF-typical aspects and terminology. This will help you
understand the output of an ADF calculation.

ADF has been developed since the early 1970s (at that time called HFS,
later AMOL, see also refs. [1] [2] [3] [5]), mainly by the two
theoretical chemistry groups of, respectively, the Vrije Universiteit
in Amsterdam and the University of Calgary, Canada. Other researchers
have also contributed. As a major research tool of these academic
development groups, ADF is in continuous development and retains a
firm basis in the academic world.

Maintenance and distribution of the commercial (export) version of the
program is done by Software for Chemistry & Materials B.V. (SCM)
(https://www.scm.com), a company based in Amsterdam, formally split
off from the theoretical chemistry group in Amsterdam but practically
still very much a part of it. Documentation such as user manuals,
installation instructions, examples, and theoretical documents can be
found at the SCM website.

Publications based on research with ADF should include appropriate
references to the program. We recommend that references are made both
to the program itself and to publications related to its development
and structure. See the Required Citations.

The installation of the Amsterdam Modeling Suite (AMS) program package
is explained in the Installation manual. This User's Guide describes
how to use the program, how input is structured, what files are
produced, and so on. Some special applications of ADF are described in
the Examples.

Where references are made to the operating system (OS) and to the file
system on your computer, the terminology of UNIX-type OSs is used.

The AMS package is in continuous development to extend its
functionality and applicability, to increase its efficiency and user-
friendliness, and of course to correct errors. We appreciate comments
and suggestions for improvement of the software and the documentation.


ADF is an AMS Engine
====================

The most important change in AMS2020 is that ADF is only accessible
via the AMS driver program. We recommend you first read the General
section of the AMS Manual. More details can be found in the section
AMSification of ADF.


Functionality
=============

* Computation of any electronic configuration

* Excitation energies, oscillator strengths, transition dipole
  moments, (hyper)polarizabilities, Van der Waals dispersion
  coefficients, CD spectra, ORD, MCD, VCD, magnetizabilities, Verdet
  constants, using Time-Dependent Density Functional Theory (TDDFT)

* ESR (EPR) g-tensors, A-tensors, NQCCs

* NMR chemical shifts and spin-spin coupling constants

* Mössbauer spectroscopy

* Transport properties: charge transfer integrals, NEGF

* Various other molecular properties

* Treatment of large systems and/or environments by the QM/MM (Quantum
  Mechanics / Molecular Mechanics) hybrid approach.


Applicability
=============

All elements of the periodic table can be used (Z = 1-120). For each
of the elements, basis sets of different sizes are available, ranging
from minimal to high quality. Special basis sets are provided for
relativistic calculations within the ZORA approach and for response
calculations that require additional diffuse basis functions.


Model Hamiltonian
=================

* A range of Density Functionals is available, including Local Density
  Approximation (LDA), Generalized Gradient Approximation (GGA),
  (range-separated) hybrid functionals (not for all properties
  available), meta-GGA functionals (not for all properties available),
  double-hybrids (not for all properties available). The MBPT methods
  MP2 and GW are available (not for all properties available).

* Spin: restricted or unrestricted

* Relativistic effects: scalar approximation and spin-orbit (double-
  group symmetry), using the (now recommended) ZORA or the (previously
  used) Pauli formalism, X2C

* Environment: Solvent Effects, Homogeneous Electric Field, Point
  Charges (Madelung Fields), QM/MM method, FDE

* (Fragment-based) Constrained Density Functional Theory


Analysis
========

* Decomposition of the bond energy in 'chemical' components (steric
  interaction, Pauli repulsion, orbital interactions, ...)

* Natural orbitals for chemical valence (ETS-NOCV)

* Representation of data (Molecular Orbital coefficients, Mulliken
  Populations) in terms of the constituent chemical fragments in the
  molecule, along with the conventional representation in elementary
  basis functions

* Atomic charge determination by Hirshfeld analysis and by Voronoi
  analysis, multipole-derived charges, along with the classical
  Mulliken populations, and Mayer bond orders

* QTAIM analysis based on local, atomic and non-local descriptors for
  describing bonding.

* Conceptual DFT descriptors, including global, atomic, and non-local
  descriptors, as well as a detailed analysis of the dual descriptor’s
  domains (predominantly electrophilic or nucleophilic regions).

* Bond energy decomposition based on the interacting quantum atoms
  (IQA) approach and using QTAIM real-space partitioning. Any atom-
  atom interaction can be evaluated and decomposed into electrostatic
  (ionic) and exchange (covalent) contributions.

* Localized molecular orbitals


Technical
=========

* The implementation is based upon a highly optimized numerical
  integration scheme for the evaluation of matrix elements of the Fock
  operator, property integrals involving the charge density, etc. The
  code has been vectorized and parallelized.

* Basis functions are Slater-Type Orbitals (STOs). A database is
  available with several basis sets for each atom in the periodic
  table of elements.

* The Coulomb potential is evaluated via an accurate fitting of the
  charge density.

* A frozen core facility is provided for an efficient treatment of the
  inner atomic shells.

* Extensive use is made of point group symmetry. Most of the commonly
  encountered symmetry groups are available.

* Linear scaling techniques are used to speed up calculations on large
  molecules


Fragments
=========

ADF has a fragment-oriented approach: the poly-atomic system to be
computed is conceptually built up from fragments, the molecular one-
electron orbitals are calculated as linear combinations of fragment
orbitals, and final analyses of e.g. the bonding energy are in terms
of fragment properties. The fragments may be single atoms or larger
moieties.

When you compute a system in terms of its constituent fragments, these
fragments must have been computed before and their properties must be
passed on to the current calculation. This is done by attaching
*fragment files*, which contain the necessary information. A fragment
file is simply the standard result file of an ADF calculation on that
fragment.

When using Basic Atoms as fragments, you do not need to create the
fragment files yourself; ADF will create the required fragment files
automatically. We therefore recommend this feature for starting ADF
users.


Basic atoms
-----------

Obviously there must be a set of fundamental fragments that are not
defined in terms of smaller fragments. Therefore ADF has two modes of
execution: the normal mode, using fragments, and the create mode, in
which a fundamental fragment is generated. Such a fundamental fragment
*must* be a single, spherically symmetric, and spin-restricted atom
(i.e. spin-\alpha and spin-\beta orbitals are spatially identical,
they are equally occupied, and fractional occupations are applied, if
necessary, to distribute the electrons equally over symmetry-
degenerate states). Such a fundamental fragment is denoted a *basic
atom*. The basic atoms are the smallest building blocks from which any
'real' calculations are started.

One should realize that the basic atoms are artificial objects that
are convenient in the computational approach but that do not
necessarily represent real atoms very well (in fact, usually not at
all). The bonding energy of a molecule with respect to basic atoms,
for instance, should be corrected for this discrepancy in order to get
a decent comparison against experimental data. See ref. [4] for a
discussion and for examples of applicable values.

A basic atom is computed in the conventional way. The one-electron
orbitals are determined as linear combinations of basis functions; the
frozen core approximation may be applied for the inner atomic states;
a particular type of density functional can be chosen, et cetera. You
may have, for instance, different basic copper atoms by using
different basis sets, by choosing different levels of frozen core
approximations, or by applying different density functionals.


Automatic mode
--------------

If you are using 'Basic Atom' fragments only, you do not need to
prepare the corresponding fragment files yourself; ADF will generate
all the required fragment files for you. This makes your job scripts
and ADF inputs simpler, it ensures that consistent options for the
create runs and molecular runs are used.


Slater-type basis sets
======================

ADF uses Slater-Type Orbitals (STOs) as basis functions. Slaters can
display the correct nuclear cusp and asymptotic decay.

   f(\mathbf{r}) = Y_{lm} r^n e^{-\zeta r}

The center of the function is at a nucleus, the  Y_{lm} are spherical
harmonics, and the exponential factor \zeta (zeta) determines the
long-range decay of the function.

ADF comes with a database of thoroughly tested basis set files,
ranging in quality from single-zeta to quadruple-zeta basis sets with
various diffuse and polarization functions. All-electron and frozen-
core basis sets are available for all elements, including lanthanides
and actinides. The frozen-core approximation can be used to
considerably reduce the computation time for systems with heavy
nuclei, in a controlled manner.

[1] E.J. Baerends, D.E. Ellis and P. Ros, *Self-consistent molecular
    Hartree-Fock-Slater calculations I. The computational procedure*,
    Chemical Physics 2, 41 (1973)

[2] E.J. Baerends and P. Ros, *Evaluation of the LCAO Hartree-Fock-
    Slater method: Applications to transition-metal complexes*,
    International Journal of Quantum Chemistry 14, S12, 169 (1978)

[3] G. te Velde, F.M. Bickelhaupt, E.J. Baerends, C. Fonseca Guerra,
    S.J.A. van Gisbergen, J.G. Snijders, T. Ziegler, *Chemistry with
    ADF*, Journal of Computational Chemistry 22, 931 (2001)

[4] E.J. Baerends, V. Branchadell and M. Sodupe, *Atomic reference-
    energies for density functional calculations*, Chemical Physics
    Letters 265, 481 (1997)

[5] 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)
