We present a systematic theoretical study on the dissociation of diatomic molecules and their spectroscopic constants using our recently presented geminal-based wave function ansätze. Specifically, the performance of the antisymmetric product of rank two geminals (APr2G), the antisymmetric product of 1-reference-orbital geminals (AP1roG) and its orbital-optimized variant (OO-AP1roG) are assessed against standard quantum chemistry methods. Our study indicates that these new geminal-based approaches provide a cheap, robust, and accurate alternative for the description of bond-breaking processes in closed-shell systems requiring only mean-field-like computational cost. In particular, the spectroscopic constants obtained from OO-AP1roG are in very good agreement with reference theoretical and experimental data.

We compared different parametrized bases for computing anharmonic vibrational spectra using a new version of the rectangular collocation-optimization method of Manzhos and Carrington (Can. J. Chem. 2009, 87, 864; Chem. Phys. Lett. 2011, 511, 434). The method enables one to compute a small number of vibrational levels with an ultrasmall basis set without a potential function. To test the ideas, parametrized uncoupled and coupled Gaussian functions as well as direct-product and coupled Hermite basis sets are used to compute four low-lying vibrational energy levels of H2O on model harmonic and anharmonic uncoupled (polynomial) potential energy surfaces. In addition, we compute levels directly from ab initio points and thereby include all coupling and anharmonicity. We conclude that uncoupled parametrized Gaussian and Hermite functions are a good choice for anharmonic and coupled problems.

We present explicit formulas for arbitrary-order derivatives of the energy, grand potential, electron density, and higher-order response functions with respect to the number of electrons, and the chemical potential for any smooth and differentiable model of the energy versus the number of electrons. The resulting expressions for global reactivity descriptors (hyperhardnesses and hypersoftnesses), local reactivity descriptors (hyperFukui functions and local hypersoftnesses), and nonlocal response functions are easy to evaluate computationally. Specifically, the explicit formulas for global/local/nonlocal hypersoftnesses of arbitrary order are derived using Bell polynomials. Explicit expressions for global and local hypersoftness indicators up to fifth order are presented.

We compute frequencies of vibrations of the carboxyl group in acetic acid adsorbed on the anatase (101) surface of TiO2 in two monodentate and the bidentate bridging configurations relevant for the adsorption of dyes on TiO2 in dye-sensitized solar cells (DSSCs). The ability to assign these vibrations and determine the adsorption configurations is critical for the design of DSSCs. Anharmonicity and coupling of four or five modes are taken into account by using a new version of the method of Manzhos and Carrington that computes vibrational spectra directly from discrete ab initio data, bypassing the construction of a potential energy surface, and using parameterized basis functions and rectangular collocation. We show that the method enables a routine analysis of anharmonic vibrations of practical importance in large systems. A sub-cm(-1) accuracy is achieved by using as few as 70 basis functions and 500 single-point energies. The calculations are doable on a desktop computer. This is the first time vibrational spectra for different adsorption sites of an organic molecule have been computed and compared without neglecting anharmonicity and coupling of the attaching group.