5 research outputs found
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 ÎŁ and 3 ÎŁ states of 2 Y as well as the g 5 1 ÎŁ and g 9 1 ÎŁ 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 ratesî—¸key processes
governing the efficiency of energy conversionî—¸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 Y<sub>2</sub> and Tc<sub>2</sub>
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 Y<sub>2</sub> and Tc<sub>2</sub>, 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 2<sup>1</sup>ÎŁ<sub>g</sub><sup>+</sup> and
3<sup>1</sup>ÎŁ<sub>g</sub><sup>+</sup> PECs of Y<sub>2</sub>. These states, together with 1<sup>1</sup>ÎŁ<sub>g</sub><sup>+</sup>, are relevant to discussion of controversial results in the literature
that suggest dissociation asymptotes that violate the noncrossing
rule. The ground state of Y<sub>2</sub> was found to be X<sup>5</sup>Σ<sub>u</sub><sup>–</sup> (similar to Sc<sub>2</sub>) with bond length <i>R</i><sub>e</sub> = 2.80 Å, binding energy <i>D</i><sub>e</sub> = 3.12 eV, and harmonic frequency ω<sub>e</sub> = 287.2 cm<sup>–1</sup>, whereas the lowest 1<sup>1</sup>Σ<sub>g</sub><sup>+</sup> state of Y<sub>2</sub> was found to lie 0.67 eV above the quintet ground state and
had spectroscopic constants <i>R</i><sub>e</sub> = 3.21
Å, <i>D</i><sub>e</sub> = 0.91 eV, and ω<sub>e</sub> = 140.0 cm<sup>–1</sup>. Calculations performed on
Tc<sub>2</sub> include study of the previously uncharacterized relatively
low-lying 1<sup>5</sup>ÎŁ<sub>g</sub><sup>+</sup> and 1<sup>9</sup>ÎŁ<sub>g</sub><sup>+</sup> states (i.e., 0.70 and 1.84 eV
above 1<sup>1</sup>Σ<sub>g</sub><sup>+</sup>, respectively). The ground state of Tc<sub>2</sub> was found to be X<sup>3</sup>Σ<sub>g</sub><sup>–</sup> with <i>R</i><sub>e</sub> = 2.13 Å, <i>D</i><sub>e</sub> = 3.50
eV, and ω<sub>e</sub> = 336.6 cm<sup>–1</sup> (for the
most stable isotope, Tc-98) whereas the lowest <sup>1</sup>ÎŁ<sub>g</sub><sup>+</sup> state, generally
accepted to be the ground state symmetry for isovalent Mn<sub>2</sub> and Re<sub>2</sub>, was found to lie 0.47 eV above the X<sup>3</sup>Σ<sub>g</sub><sup>–</sup> state of Tc<sub>2</sub>. The results broaden the range of demonstrated
applicability of the GVVPT2 method