Editorial

In quantum chemistry, it is well-accepted that coupled cluster theory and related many-body perturbation approaches are systematically improvable frameworks that permit calculations whose error can be smaller than the holy grail of chemical accuracy (1 kcal per mole root mean square (RMS) error for bonded interactions – and much smaller for non-bonded interactions). For example, in Molecular Physics, over the past year, let me mention three papers that address the question of establishing benchmark values using such methods. Boese et al. report benchmark numbers for the strength of hydrogen-bond interactions [1], which help in the assessment of approximate ground-state methods such as density functional theory (DFT). Turning to ionisation energies, Krause et al. have reported benchmark ionisation energies [2] using coupled cluster theory on over 100 molecules, while Piecuch et al. assess their new many-body excited-state methods against benchmark excitation energies [3]. Enabling better benchmarks at the complete basis set limit, new larger basis sets for such calculations were reported at the quintuple zeta level modified for the increasingly popular F12 methods [4].

The only catch is that due to the steep increase of computational cost with molecular size in standard coupled cluster theory, these benchmark quality calculations are typically only reported for rather small molecules. A pressing frontier of quantum chemistry is therefore the quest for reduced scaling approximations for coupled cluster theory. In the issue you are reading, we are pleased to present a review on this topic [5] as the latest article in our ongoing series of Invited Topical Reviews. The review is entitled the ‘Cluster-in-molecule local correlation method for post-Hartree–Fock calculations of large systems’, and is authored by Prof. Shuhua Li, of Nanjing University. He describes a very promising approach that he and his group have developed to reduce the computational cost of coupled cluster or many-body perturbation calculations by using localised orbitals to obtain additive increments to the correlation energy. As Prof. Li describes in his review, it is still possible to avoid introducing significant numerical errors, while greatly speeding up the calculations. Other recent Topical Reviews describe the remarkable roaming mechanism in gas phase chemical dynamics [6], simulations of dynamic nuclear polarisation [7], and multireference F12 methods in quantum chemistry [8].

In addition to the excellent review in this issue [5], the general topic of local correlation is also addressed in other interesting recent papers in Molecular Physics. I will mention just a few examples here. An alternative approach is to fragment the molecule itself, as in the ‘molecules-in-molecules’ approach, illustrated for Raman spectra by Jose and Raghavachari [9], and using the molecular subunits of a cluster as a natural building block for low-scaling methods [10]. Adaptive methods are another class of approaches which develop intelligent criteria for discarding numerically insignificant terms, as illustrated, for instance, in the density matrix renormalisation group approach, discussed by Kurashige in a New Views article [11]. Two very different adaptive approaches are the stochastic full configuration interaction (CI) quantum Monte Carlo method discussed by Booth et al. [12] (winner of our 2014 Longuet-Higgins Early Career Researcher Prize), and the selection procedure described by Knowles [13]. On the other hand, there is also intense activity on the design of very compact wavefunctions, such as geminals [14,15] that contain the essential strong correlations. One other extremely interesting possibility is to combine DFT with a compact wavefunction that describes strong electron correlation, as discussed by Fromager in another New Views article [16]. In light of the diversity of alternative approaches, local correlation is a vigorous area of quantum chemistry where not only has great progress been made, as exemplified by the cluster-in-molecule approach [5], but there remains much scope for new innovations in the future.

For readers with a general interest in quantum chemistry, I would like to highlight a few of the very interesting Special Issues that we have published in the area recently. There were three during 2015, of which the most recent (numbers 19, 20 of vol. 113) was in Honor of Sourav Pal [17]. Numbers 13, 14 of vol. 113 comprised a Special Issue in Honor of Nicholas Handy [18], a former editor of Molecular Physics, and numbers 3, 4 of vol. 113 comprised the Proceedings of the 54th Sanibel Meeting [19].

Molecular Physics continues to encourage the submission of original research papers in both methods and applications of quantum chemistry, as well as suggestions for future appropriate Topical Reviews, or Special Issues in the field.