4.2.2. DFT and Time-Dependent DFT Calculations

All DFT calculations are carried out with Gaussian 09 Revision C.01 suite [74]. The geometry optimization of SP and MC is performed in a gas phase using the B3LYP/DGDZVP basis set with a tight self-consistent field convergence threshold. This functional is widely and successfully employed in studies of spiropyran-containing molecules [10,11,49,57,58,59,60]. Next, the ground state geometries are optimized by applying the integral equation formalism variant of the polarizable continuum model to simulate the solvent environment [72]. In this model, the molecular cavity is constructed applying the Universal Force Field [73]; the shape of the cavity is defined by interlocking spheres centered on each solute atom having van der Waals radii scaled by a factor 1.1. Harmonic vibrational frequency calculations are used to confirm that the structure of each isomer in vacuum and in IEFPCM/UFF solvent is a true minimum, to obtain the standard enthalpy of formation and to calculate the zero-point energy correction at 298 K. The solvents mimicked in the DFT calculations are: chloroform (ϵ = 4.7113 ), ethanol (ϵ = 24.852), acetonitrile (ϵ = 35.688), dimethyl sulfoxide (ϵ = 46.826), and water (ϵ = 78.3553).

The vertical transition energies to the first 100 excited states are calculated for each isomer having optimized geometries in a particular solvent using time-dependent DFT with the B3LYP [58], PBE [87] functionals and the DGDZVP and 6-311G* basis set, correspondingly. The DGDZVP basis set is shown to predict the energies close with respect to the experiment transition energies, e.g., for merocyanines [88]. The combination B3LYP/6-311G* has also shown a good agreement with measured spectra [75]. The electronic spectra are simulated employing Gaussian functions with the half-width at half height of 0.333 eV to build a continuous spectrum from a collection of transition peaks corresponding to the time-dependent DFT transition energies and oscillator strengths. For the qualitative description of the electronic transitions, the natural transition orbitals [98] for the excited state of interest are analyzed.

The solvent-accessible surface area of the TMAB head (a) and the occupied molecular volumes (v) are calculated for the optimized geometries in implicit water [96]. The rolling probe radius is 1.4 Å for water [99]. These quantities, as well as the length of the hydrophobic tail (l) of the amphiphile are further used for the calculation of the Israelachvili’s critical packing parameter P [94], as described in our previous publications [3,100]. The p value predicts possible micellar structures that could be built by a surfactant in water (Equation (2)):

The electrostatic potential V(r) is calculated using the Merz-Singh-Kollman procedure [101] for the molecular cations and for the cations paired with bromine anion and mapped onto a surface with an electron density isovalue of 0.02 au. The ESP (Equation (3)) is defined as the interaction energy between the electrical charge generated from the molecule electrons and a positive point charge as a probe located at the position r:

Here zA is the charge of the nucleus A, which is a point charge located at RA. The term ρ(r′) is the electron density function. The sign of the electrostatic potential is correlated to the partial charges on the atoms/atomic groups, i.e., the value at the minimum of V(r) quantifies the electron-rich character of that region, and vice versa. The initial guess for the Br− anion placement next to the molecular cation is made using the analysis of the partial ESP charges.