7.15.1 Introduction

As methods for ab initio calculations of excited states are becoming increasingly more routine, questions arise concerning how best to extract chemical meaning from such calculations. There are several approaches for analyzing molecular excited states; they are based on reduced one-particle density matrices (OPDMs). The two objects exploited in this analysis are: (i) the difference between the ground- and excited-state OPDMs and (ii) the transition OPDM connecting the ground and excited state. In the case of CIS and TDDFT/TDA wave functions, both quantities are identical and can be directly mapped into the CIS amplitudes; however, for correlated wave functions the two objects are not the same. The most basic analysis includes calculation of attachment and detachment densities ⁴⁷⁶ Head-Gordon M. et al.
J. Phys. Chem.
(1995), 99, pp. 14261. Link (equivalent within TDDFT to particle and hole densities, respectively), and natural transition orbitals. ⁸²⁰ Martin R. L.
J. Chem. Phys.
(2003), 118, pp. 4775. Link These quantities allow one to arrive to a most compact description of an excited state. More detailed analysis allows one to derive additional insight about the nature of the excited state. Detailed description and illustrative examples can be found elsewhere. ⁹⁸⁶ Plasser F., Wormit M., Dreuw A.
J. Chem. Phys.
(2014), 141, pp. 024106. Link ^{, 982} Plasser F. et al.
J. Chem. Phys.
(2014), 141, pp. 024107. Link

This section describes the theoretical background behind attachment/detachment analysis and natural transition orbitals, while details of the input for creating data suitable for plotting these quantities is described separately in Chapter 10, which also describes additional excited-state analysis tools. For historical reasons, there are duplicate implementations of some features. For example, CIS and TDDFT wave functions can be analyzed using an original built-in code and by using a more recent module, libwfa.