|molcas|, Quantum Chemistry Software
====================================

|molcas| is a Quantum Chemistry software package developed by scientists to be used by
scientists. It is neither a commercial product nor is it sold for significant profit gain
by its owner, Lund University. The authors
of |molcas| have assembled their collected experience and knowledge in
computational Quantum Chemistry to produce a research product which is used
as a platform by the scientists in the |molcas| network to
develop new and improved computational tools in Quantum Chemistry. Several of
the codes in the |molcas| software have newly developed leading-edge features. Along with these new
capabilities, users should not be surprised to ocasionally discover bugs when using |molcas|.

The basic philosophy behind |molcas| is to develop methods that allow
accurate *ab initio* treatment of very general electronic structure problems
for molecular systems in both ground and excited states which is not an easy
task. Nowadays, knowledge about how to obtain accurate properties for single-reference
dominated ground states is well developed, and |molcas| contains
a number of codes that can perform such calculations (MP2, CC, CPF, DFT etc).
All these methods treat the electron correlation starting from a single
determinant (closed or open shell) reference state. Such codes are today's
standard in most Quantum Chemistry program.

However, |molcas| is to be able to treat,
highly degenerate states, such as those occurring in
excited states, transition states in chemical reactions, diradicaloid systems, heavy metal systems,
as well as other chemically important problems, all at the same level of accuracy.
This is a much more difficult problem,
since a single-determinant approach does not work well in these cases. The key
feature of |molcas| is the multiconfigurational approach. |molcas| contains
codes for general and effective multi-configurational SCF calculations at the
Complete Active Space (CASSCF) level, but also employs more restricted MCSCF
wave functions such as the Restricted Active Space, RASSCF, and the Generalized Active Space, GASSCF.
It is also possible using either CASSCF or RASSCF to
employ optimization techniques and obtain equilibrium geometries, transition-state structures,
force fields, and vibrational energies using gradient techniques.

Since |molcasviii| the Stochastic-CASSCF method :cite:`limanni2016` is also available to treat systems requiring large active spaces.
Routine calculations have been presented with active spaces of size of 40 electrons in 40 orbitals :cite:`limanni2018,limanni2019` and larger active space are currently tested.

Although the RASSCF approach is known to give reasonable structures for
degenerate systems both in ground and excited states, in
general it is not capable of recovering more than a fraction of the correlation
energy. Therefore, it becomes necessary to supplement the multi-configurational SCF
treatment with a calculation of dynamic correlation effects. In the earliest
version of |molcas|, this was achieved by means of the multi-reference (MR) CI
method. This method has severe limitations in the number of electrons
that can be correlated and the size of the reference space which limits
study to excited states of small molecules.
However, the MRCI code in |molcas| does have the capacity to produce very accurate wave functions and
potential energy surfaces, and is used by many groups for this purpose.
In fact, it is also possible to run the COLUMBUS MRCI code together with |molcas|.

During the period of 1986--90, a new method called CASPT2 was developed, which
computes dynamic electron correlation effects for multi-configurational wave
functions based on second order perturbation theory and was included into the second version of
|molcas|. From the beginning it was not clear whether or not the CASPT2 method would be
sufficiently accurate to be useful in practice, but it turned out to be surprisingly
accurate in a number of different types of chemical applications.
The CASPT2 approach has become especially important in
studies of excited states and spectroscopic properties of large
molecules, where no other *ab initio* method has, so far, been applicable.
Since the CASPT2 method is based on second order perturbation theory and has, therefore,
limitations in accuracy, the error limits have been investigated in a
large number of applications. The relative energy errors are
small in almost all cases leading to results which can be used for conclusive
predictions of molecular properties in ground and excited states.
Important application areas for the CASPT2 method are potential energy
surfaces for chemical reactions, photochemistry, transition metal chemistry, and
heavy element chemistry.

Several quasi-degenerate versions of CASPT2 are available, which allow for the simultaneous
study of several electronic states, including their interaction to second order.
This code is especially useful in cases where two or more energy surfaces are
close in energy. An analytical CASPT2 gradient code (nuclear energy gradients and
derivative coupling vector) supporting all these variants is available, allowing
automatic geometry optimization at the CASPT2 level of theory.
It is applicable to all states and systems for which the CASPT2 energy can be computed,
whereas the calculation of vibrational frequencies can be carried out with the
numerical procedure. It is important to note that the CASPT2 method is under constant
development.

Since |molcasviii| the Multiconfiguration Pair-Density Functional Theory, MC-PDFT,
is also available to treat dynamical correlation.

If only a few electrons are correlated, the active space can be quite large
without too many configurations being generated, but in most cases the number of
active electrons is comparable to the number of active orbitals.
Occasionally, a larger active space would be preferred, but would result in too
many configurations (more than a few million CSF's). The more general RASSCF
scheme can be useful, at the price of less efficient calculations, and the risk
of bad convergence properties in the orbital optimization. The CASPT2 program
handles also such wave functions, but will not include correlation within the
active space, i.e., interaction with states that would have been included in
the full CASSCF but are excluded by the RASSCF restrictions. The RASSCF wave
function is regarded as an accurate approximation to the full CASSCF
wave function, and the CASPT2 program evaluates only dynamic correlation that
involves at least one non-active orbital.

|molcas| not only contains the ability to produce various types of wave functions,
but also can compute molecular properties using formulas of expectation values or finite
perturbation theory using the RASSI program.
The RASSI program has the capacity to compute the interaction between several
RASSCF wave functions based on different orbitals which are generally non-orthonormal
(i.e. a non-orthogonal CI). RASSI is routinely used to compute transition dipole
moments in spectroscopy, to study electron transfer, and to obtain eigenstates
of a relativistic Hamiltonian with inclusion of spin-orbit interaction.

Scalar, i.e. spin-averaged, relativistic effects are typically included
in any calculations by using Douglas--Kroll--Hess transformation of one-electron
integrals. The standard basis set library
ANO-RCC :cite:`Roos:03c,Roos:03g,Roos:05a,Roos:05b,Roos:08b`
is optimized for use with these integrals and to include correlation of
semi-core orbitals, and to to have uniform quality across the periodic system
up to element 96, Curium. For heavier elements, typical calculations include
the spin-orbit interaction by using CASSCF wave functions as a many-electron basis
set, letting RASSI compute a Hamiltonian matrix over the set of all spin-components
of these functions, correct for dynamic correlation using CASPT2 and include
a one-electron spin-orbit Hamiltonian. This procedure has been shown to give
accurate results in a number of studies for actinides and other
heavy atom systems :cite:`Roos:03a`.

It is also possible to model solvent effects by adding a
reaction field Hamiltonian (PCM). A new QM/MM model is also included in |molcas|.

The release of |molcasvii| leads to many important enhancements. The sizes of the systems
that can be treated with |molcas| were previously restricted because of limitations in
storing two-electron integrals for large basis sets. This system size limitation has
been substantially reduced by the introduction of a Cholesky decomposition of the
two-electron integrals. This feature is used in |molcasvii| at all levels
of theory :cite:`Aquilante:07b,Aquilante:08a,Aquilante:08b` and speeds up calculations
by orders of magnitude, extending the size of basis sets that can be used.
Accuracy can be controlled by the threshold used in the decomposition. The same
approach can be used to generate RI auxiliary basis sets on the fly,
allowing the calculation of energy derivatives for HF, MP2, DFT, and CASSCF levels of theory.

It is important to emphasize that important problems in Quantum Chemistry cannot be solved
by simply applying :bdit:`black box` techniques.
Nor is |molcas| a :bdit:`black box` tool. A typical |molcas| user should be
someone with a high degree of chemical insight, who has some knowledge of different
Quantum Chemical models in use today, and, most importantly, is able to apply these
models to the appropriate chemical problem while understanding the inherent accuracy
of these methods.
The typical |molcas| user should also apply critical analysis of results, take nothing
for granted, and always check that the results are consistent with the model that was used.
The skill to use |molcas| effectively will not come immediately, but
the user has several resources including this manual and examples which
explain how different key projects were solved using |molcas|.
Users are certain to find them helpful in their own attempts to master the software
for use in chemical applications. The |molcas| group also arranges regular workshops,
which provide a more intimate environment on learning how to use |molcas|.

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