Accurate Excited-State Geometries: A CASPT2 and Coupled-Cluster Reference Database for Small Molecules

We present an investigation of the excited-state structural parameters determined for a large set of small compounds with the dual goals of defining reference values for further works and assessing the quality of the geometries obtained with relatively cheap computational approaches. In the first stage, we compare the excited-state geometries obtained with ADC(2), CC2, CCSD, CCSDR(3), CC3, and CASPT2 and large atomic basis sets. It is found that CASPT2 and CC3 results are generally in very good agreement with one another (typical differences of ca. 3 × 10^–3 Å) when all electrons are correlated and when the aug-cc-pVTZ atomic basis set is employed with both methods. In a second stage, a statistical analysis reveals that, on the one hand, the excited-state (ES) bond lengths are much more sensitive to the selected level of theory than their ground-state (GS) counterparts and, on the other hand, that CCSDR(3) is probably the most cost-effective method delivering accurate structures. Indeed, CCSD tends to provide too compact multiple bond lengths on an almost systematic basis, whereas both CC2 and ADC(2) tend to exaggerate these bond distances, with more erratic error patterns, especially for the latter method. The deviations are particularly marked for the polarized CO and CN bonds, as well as for the puckering angle in formaldehyde homologues. In the last part of this contribution, we provide a series of CCSDR(3) GS and ES geometries of medium-sized molecules to be used as references in further investigations

Quantifying Electron Delocalization in Electrides

Electrides are ionic solids whose anions are electrons confined to crystal voids. We show that our electron delocalization range function EDR­(<i>r⃗</i>;<i>d</i>), which quantifies the extent to which an electron at point <i>r⃗</i> in a calculated wave function delocalizes over distance <i>d</i>, provides useful insights into electrides. The EDR quantifies the characteristic delocalization length of electride electrons and provides a chemically intuitive real-space picture of the electrons’ distribution. It also gives a potential diagnostic for whether a given formula unit will form a solid electride at ambient pressure, quantifies the effects of electron–electron correlation on confined electrons’ interactions, and highlights analogies between covalent bonding and the interaction of interstitial quasi-atoms in high-pressure electrides. These results motivate adding the EDR to the toolbox of theoretical methods applied to electrides

Quantifying Electron Delocalization in Electrides

Electrides are ionic solids whose anions are electrons confined to crystal voids. We show that our electron delocalization range function EDR­(<i>r⃗</i>;<i>d</i>), which quantifies the extent to which an electron at point <i>r⃗</i> in a calculated wave function delocalizes over distance <i>d</i>, provides useful insights into electrides. The EDR quantifies the characteristic delocalization length of electride electrons and provides a chemically intuitive real-space picture of the electrons’ distribution. It also gives a potential diagnostic for whether a given formula unit will form a solid electride at ambient pressure, quantifies the effects of electron–electron correlation on confined electrons’ interactions, and highlights analogies between covalent bonding and the interaction of interstitial quasi-atoms in high-pressure electrides. These results motivate adding the EDR to the toolbox of theoretical methods applied to electrides

Quantifying Electron Delocalization in Electrides

Electrides are ionic solids whose anions are electrons confined to crystal voids. We show that our electron delocalization range function EDR­(<i>r⃗</i>;<i>d</i>), which quantifies the extent to which an electron at point <i>r⃗</i> in a calculated wave function delocalizes over distance <i>d</i>, provides useful insights into electrides. The EDR quantifies the characteristic delocalization length of electride electrons and provides a chemically intuitive real-space picture of the electrons’ distribution. It also gives a potential diagnostic for whether a given formula unit will form a solid electride at ambient pressure, quantifies the effects of electron–electron correlation on confined electrons’ interactions, and highlights analogies between covalent bonding and the interaction of interstitial quasi-atoms in high-pressure electrides. These results motivate adding the EDR to the toolbox of theoretical methods applied to electrides

Electronic Couplings for Resonance Energy Transfer from CCSD Calculations: From Isolated to Solvated Systems

Quantum mechanical (QM) calculations of electronic couplings provide great insights for the study of resonance energy transfer (RET). However, most of these calculations rely on approximate QM methods due to the computational limitations imposed by the size of typical donor–acceptor systems. In this work, we present a novel implementation that allows computing electronic couplings at the coupled cluster singles and doubles (CCSD) level of theory. Solvent effects are also taken into account through the polarizable continuum model (PCM). As a test case, we use a dimer of indole, a common model system for tryptophan, which is routinely used as an intrinsic fluorophore in Förster resonance energy transfer studies. We consider two bright π → π* states, one of which has charge transfer character. Lastly, the results are compared with those obtained by applying TD-DFT in combination with one of the most popular density functionals, B3LYP

Excited State Dipole Moments in Solution: Comparison between State-Specific and Linear-Response TD-DFT Values

We compare different response schemes for coupling continuum solvation models to time-dependent density functional theory (TD-DFT) for the determination of solvent effects on the excited state dipole moments of solvated molecules. In particular, linear-response (LR) and state-specific (SS) formalisms are compared. Using 20 low-lying electronic excitations, displaying both localized and charge-transfer character, this study highlights the importance of applying a SS model not only for the calculation of energies, as previously reported (J. Chem. Theory Comput., 2015, 11, 5782, DOI: 10.1021/acs.jctc.5b00679), but also for the prediction of excited state properties. Generally, when a range-separated exchange–correlation functional is used, both LR and SS schemes provide very similar dipole moments for local transitions, whereas differences of a few Debye units with respect to LR values are observed for CT transitions. The delicate interplay between the response scheme and the exchange–correlation functional is discussed as well, and we show that using an inadequate functional in a SS framework can yield to dramatic overestimations of the dipole moments

Coupled Cluster Calculations in Solution with the Polarizable Continuum Model of Solvation

Coupled cluster theory (CC) provides very accurate estimates of energies and molecular properties. Such calculations are often limited to gas-phase species due to the large computational cost of this level of theory; however, most of the chemical phenomena take place in solution. We propose an efficient implementation of the polarizable continuum model of solvation (PCM) with the coupled cluster singles and doubles method (CCSD) to take into account the solvent effects on the ground-state energy and geometry. Differently from atomistic representations, the PCM approach does not require conformational sampling of the solvent molecules and naturally describes mutual polarization effects between solute and solvent. Applications of the CCSD-PCM method to representative molecules are presented

Electron Delocalization Range in Atoms and on Molecular Surfaces

The electron delocalization range function EDR­(<i>r⃗</i>; <i>d</i>) (<i>J. Chem. Phys.</i> <b>2014</b>, <i>141</i>, 144104) quantifies the extent to which an electron at point <i>r⃗</i> in a calculated wave function delocalizes over distance <i>d</i>. This work illustrates how atomic averages of the EDR, and plots of the EDR on molecule surfaces, provide a chemically intuitive picture of the sizes of occupied orbital lobes in different regions. We show how the surface and atomic delocalization distinguish aminophosphine ligand’s hard N and soft P lone pairs, distinguish the site preference for Ag⁺ cation binding to conjugated oligomers, and provide information that is different from and complementary to conjugation lengths. Applications to strong correlation and the prototropic tautomerization of phosphinylidenes R₁R₂HPO illustrates how the surface and atomic delocalization can work with other tools to provide a nuanced picture of reactivity

Practical Density Functionals beyond the Overdelocalization–Underbinding Zero-Sum Game

Density functional theory (DFT) uses a density functional approximation (DFA) to add electron correlation to mean-field electronic structure calculations. Standard strategies (generalized gradient approximations GGAs, meta-GGAs, hybrids, etc.) for building DFAs, no matter whether based on exact constraints or empirical parametrization, all face a zero-sum game between overdelocalization (fractional charge error, FC) and underestimation of covalent bonding (fractional spin error, FS). This work presents an alternative strategy. Practical “Rung 3.5” ingredients are used to implement insights from hyper-GGA DFAs that reduce both FS and FC errors. Prototypes of this strategy qualitatively improve FS and FC error over 40 years of standard DFAs while maintaining low cost and practical evaluation of properties. Numerical results ranging from transition metal thermochemistry to absorbance peaks and excited-state geometry optimizations highlight this strategy’s promise and indicate areas requiring further development

Comparative Study of Nonhybrid Density Functional Approximations for the Prediction of 3d Transition Metal Thermochemistry

The utility of several nonhybrid density functional approximations (DFAs) is considered for the prediction of gas phase enthalpies of formation for a large set of 3d transition metal-containing molecules. Nonhybrid DFAs can model thermochemical values for 3d transition metal-containing molecules with accuracy comparable to that of hybrid functionals. The GAM-generalized gradient approximation (GGA); the TPSS, M06-L, and MN15-L meta-GGAs; and the Rung 3.5 PBE+ΠLDA(s) DFAs all give root-mean-square deviations below that of the widely used B3LYP hybrid. Modern nonhybrid DFAs continue to show utility for transition metal thermochemistry