Extension and applications of the GVVPT2 method to the study of transition metals

The ground and low-lying excited electronic states of molecules of the first ( 2 Sc , 2 Cr , 2 Mn , and 2 Ni ) and second ( 2 Y , 2 Mo , and 2 Tc ) row of transition elements have been investigated for the first time with the generalized Van Vleck second order multireference perturbation theory (GVVPT2) method, a variant of MRPT. All potential energy curves (PECs) obtained in these studies were smooth and continuous; that is, they are free from wiggles or inflexion points. In order to account for relativistic effects, which become important in heavy elements, the GVVPT2 method was extended to include scalar relativistic effects through the spin-free exact two component (sf-X2C) method and used in the studies of all molecules of second row transition elements and some of those of the first row considered in this present work. GVVPT2 studies of triatomic lithium and beryllium were also done as a first step to studies of small clusters of transition metals. The spectroscopic constants (bond lengths, harmonic frequencies, bond energies, and adiabatic transition energies) obtained for all PECs at the GVVPT2 level were in good agreement with experimental data, where available, and with results from previous studies using other high level ab initio methods. Optimized geometries of the triatomics were also in good agreement with previous findings. The studies included electronic states (e.g., the g 1 g 1 2 Σ and 3 Σ states of 2 Y as well as the g 5 1 Σ and g 9 1 Σ states of 2 Tc ) not previously discussed in the literature. As a first step to applying GVVPT2 to the study of relatively larger systems, the present work includes the results of efforts on improving DFT-in-DFT embedding theory. New equations were determined which involved an additional constraint of orthogonality of the orbitals of one subsystem to those of the complementary subsystem as warranted by formal arguments based on the formulation of DFT-in-DFT embedding. A computer program was realized using the new embedding equations and test calculations performed. Analyses of electron density deformations in embedding theory, in comparison with conventional Kohn-Sham (KS)-DFT densities, were performed using the new embedding program and a computer code that was also written to compute electron densities of molecules in real space, given reduced one particle density matrices. The results revealed that whereas the current formulation of DFT-in-DFT embedding theory generally underestimates electron density, at the interface between subsystems in comparison with conventional KS-DFT calculations of the supermolecule, the new DFT-in-DFT embedding scheme with the external orthogonality constraint was found to remedy the situation. Worthy of special note in this new embedding protocol is the fact that the nonadditive kinetic potential ( T v ), thought to be a major cause of weaknesses in DFT-in-DFT embedding and to which many previous research efforts have been devoted, can be set exactly to zero. The present work therefore realized, for the first time, a new DFT-in-DFT embedding theory that neither relies on kinetic functionals nor requires a supermolecular DFT calculation. Test calculations using the new embedding theory and supermolecular basis set expansion of KS orbitals reproduced conventional KS-DFT energies to at least the 7th decimal place (and even exactly at many geometries). A new way of expanding KS orbitals was also employed in the new embedding protocol, which is intermediate between the usual supermolecular and monomer basis expansions, referred to as the “extended monomer expansion”. The monomer basis expansion scheme was inadequate for the new DFT-in-DFT embedding protocol. Test calculations found this novel, computationally cheaper, extended monomer approach to give results quite close to those from supermolecular basis expansions

Effect of Binding Geometry on Charge Transfer in CdSe Nanocrystals Functionalized by N719 Dyes to Tune Energy Conversion Efficiency

Semiconductor quantum dots (QDs) functionalized by metal–organic dyes show great promise in photocatalytic and photovoltaic applications. However, the charge transfer direction and rateskey processes governing the efficiency of energy conversionare strongly affected by the QD–dye interactions, insights on which are challenging to obtain experimentally. We use density functional theory (DFT) and constrained DFT calculations to investigate a degree of sensitivity of the electronic level alignment and related QD–dye electronic couplings to binding conformations of N719 dye at the surface of the 1.5 nm CdSe QD. Our calculations reveal a lack of direct correlations between the strength of the QD–dye interaction in terms of their binding conformations and the donor–acceptor electronic couplings. While the QD–dye binding conformations are the most stable when the N719 dye is attached to the QD via two carboxylate groups, the strongest electronic coupling between the QD as an electron donor and the dye as an electron acceptor is observed in structures bonded via the isocyanate ligands. Such strong electronic couplings also are responsible for significant stabilization of the dye’s occupied orbitals deep inside in the valence band of the QD making the hole transfer from the photoexcited QD to the dye thermodynamically unfavorable in structures bound via isocyanates. Our results suggest that the most probable binding conformations are those occurring via two carboxylate linkers, which exhibit very weak electronic couplings contributing to the electron transfer from the photoexcited CdSe QD to the N719 dye but provide the most favorable conditions for the hole transfer. Overall, our computational work provides an insightful view about the surface chemistry of CdSe regarding the donor–acceptor interaction, energy level alignment, and charge transfer between CdSe and dye molecule, which can guide the rational design of QD-based materials for energy conversion applications

Relativistic GVVPT2 Multireference Perturbation Theory Description of the Electronic States of Y₂ and Tc₂

The multireference generalized Van Vleck second-order perturbation theory (GVVPT2) method is used to describe full potential energy curves (PECs) of low-lying states of second-row transition metal dimers Y₂ and Tc₂, with scalar relativity included via the spin-free exact two-component (sf-X2C) Hamiltonian. Chemically motivated incomplete model spaces, of the style previously shown to describe complicated first-row transition metal diatoms well, were used and again shown to be effective. The studied states include the previously uncharacterized 2¹Σ_g⁺ and 3¹Σ_g⁺ PECs of Y₂. These states, together with 1¹Σ_g⁺, are relevant to discussion of controversial results in the literature that suggest dissociation asymptotes that violate the noncrossing rule. The ground state of Y₂ was found to be X⁵Σ_u^– (similar to Sc₂) with bond length <i>R</i>_e = 2.80 Å, binding energy <i>D</i>_e = 3.12 eV, and harmonic frequency ω_e = 287.2 cm^–1, whereas the lowest 1¹Σ_g⁺ state of Y₂ was found to lie 0.67 eV above the quintet ground state and had spectroscopic constants <i>R</i>_e = 3.21 Å, <i>D</i>_e = 0.91 eV, and ω_e = 140.0 cm^–1. Calculations performed on Tc₂ include study of the previously uncharacterized relatively low-lying 1⁵Σ_g⁺ and 1⁹Σ_g⁺ states (i.e., 0.70 and 1.84 eV above 1¹Σ_g⁺, respectively). The ground state of Tc₂ was found to be X³Σ_g^– with <i>R</i>_e = 2.13 Å, <i>D</i>_e = 3.50 eV, and ω_e = 336.6 cm^–1 (for the most stable isotope, Tc-98) whereas the lowest ¹Σ_g⁺ state, generally accepted to be the ground state symmetry for isovalent Mn₂ and Re₂, was found to lie 0.47 eV above the X³Σ_g^– state of Tc₂. The results broaden the range of demonstrated applicability of the GVVPT2 method