Paper reviews multireference methods and applications to molecular excited states.

In brief:

  • The main multireference (MR) methods available for excited states are reviewed.
  • The review spans ab-initio and semiempirical MR-CI, MR-CC, MR-PT, and MR-DFT.
  • Recent MR applications to several classes of molecules, from diatomic to proteins, are discussed.


It’s a pleasure to announce the publication of Multireference Approaches for Excited States of Molecules in the Chemical Reviews [1].

In this work, led by Hans Lischka, we have extensively reviewed the methods and applications of multireference electronic structure theory. With over 1000 references, you will find everything you ever wanted to know (and possibly more) about MR methods.

Often, the theoretical description of the molecular wave function, especially near the ground state minimum, can take a single Slater determinant as the basic approximation. Several of the most popular quantum chemistry methods (DFT, coupled cluster, MP2) calculate electron dynamic correlation based on this single reference (SR) approximation. Then, excited states are computed (TD-DFT, CC2, ADC(2)) still based on that approximation.

There are, however, many situations when the SR approximation isn’t reasonable anymore, and the ground state description must start from an ensemble of Slater determinants, which is called a multireference (MR) approximation. This means that nondynamical electron correlation (also known as static or strong correlation) must be also computed in addition to dynamic correlation.

Among the main case for which MR approximation is needed, I can mention:

  • molecules with metals (due to their large density of states);
  • dissociative structures;
  • conical intersections with the ground state.

MR methods have been around since the 1970s, but they have never been nearly as popular as the SR methods. They require large expertise to run and demand a lot of computer power.

Conceptually, the most straightforward MR method is the uncontracted MRCI, which calculates ground and excited states from a configuration interaction expansion starting from a multireference configuration space (usually, set by a preliminary CASSCF calculation). But the MR approximation can be used in any framework, like MR-PT (CASPT2 is the most famous example), MR-CC, and MR-DFT.

Today, there are many fascinating developments in the MR field. Methods allowing to increase (a lot) the reference space, program adaptations for GPUs, energy gradients for CASPT2, algorithms for automatic generation of the reference space.

No, MR methods won’t ever be as popular as DFT, but they are ready to take a fair share of computational chemistry calculations.

All these things are discussed in details in our review, whose outline is:

A.      Theory and Methods

A.1.     Configuration Interaction

A.1.1.     Basic concepts
A.1.2.     Single- and Multireference Spaces
A.1.3.     Size-extensivity Problem.
A.1.4.     Contracted CI
A.1.5.     Calculation of Excited States
A.1.6.     Individual Selection Schemes
A.1.7.     Local MRCI Approaches
A.1.8.     Natural Orbitals for Use in MRCI

A.2.     Multiconfiguration Self-Consistent Field Method

A.2.1.     Multiple MCSCF Solutions and Symmetry Breaking

A.3.     Coupled cluster methods

A.3.1.     Single reference coupled cluster methods to describe excited states
A.3.2.     Multireference coupled cluster Methods

A.4.     Mutireference perturbation theory

A.5.     MRCI with semiempirical Hamiltonians

A.6.     Multireference Density Functional Theory

A.6.1.     Nondynamical electron correlation in DFT
A.6.2.     Semiempirical MRCI with DFT
A.6.3.     Hybrid wavefunction and DFT
A.6.4.     Multiconfigurational DFT
A.6.5.     Ensemble DFT

A.7.     Emerging algorithms

A.7.1.     DMRG
A.7.2.     FCIQMC

A.8.     Aspects of analytic gradients and nonadiabatic couplings

A.9.     Diagnostics of multireference character, analysis of excited states

B.      Applications of multireference methods to molecular excited states

B.1.     Diatomics and small molecules

B.2.     Singlet oxygen photosensitization

B.3.     Conjugated π systems

B.3.1.     Excited States of Polyenes
B.3.2.     Protonated Schiff bases
B.3.3.     Nucleic acids: from nucleobases to double strands
B.3.4.     Aminoacids and proteins
B.3.5.     Polycyclic aromatic systems: monomers and dimers
B.3.6.     Transition metal complexes: metalloporphyrins

In addition to Hans, I’d like to thank my coworkers Dana, Adelia, Peter, Felix, and Franciso for their hard work putting this review together.



[1] H. Lischka, D. Nachtigallová, A. J. A. Aquino, P. G. Szalay, F. Plasser, F. B. C. Machado, and M. Barbatti, Multireference Approaches for Excited States of Molecules, Chem. Rev. DOI: 10.1021/acs.chemrev.8b00244 (2018).