Unraveling substituent effects on frontier orbitals of conjugated molecules using an absolutely localized molecular orbital based analysis.

It is common to introduce electron-donating or electron-withdrawing substituent groups into functional conjugated molecules (such as dyes) to tune their electronic structure properties (such as frontier orbital energy levels) and photophysical properties (such as absorption and emission wavelengths). However, there lacks a generally applicable tool that can unravel the underlying interactions between orbitals from a substrate molecule and those from its substituents in modern electronic structure calculations, despite the long history of qualitative molecular orbital theory. In this work, the absolutely localized molecular orbitals (ALMO) based analysis is extended to analyze the effects of substituent groups on the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of a given system. This provides a bottom-up avenue towards quantification of effects from distinct physical origins (e.g. permanent electrostatics/Pauli repulsion, mutual polarization, inter-fragment orbital mixing). For the example case of prodan (a typical dye molecule), it is found that inter-fragment orbital mixing plays a key role in narrowing the HOMO-LUMO gap of the naphthalene core. Specifically, an out-of-phase mixing of high-lying occupied orbitals on the naphthalene core and the dimethylamino group leads to an elevated HOMO, whereas an in-phase combination of LUMOs on the naphthalene core and the propionyl group lowers the LUMO energy of the entire molecule. We expect this ALMO-based analysis to bridge the gap between concepts from qualitative orbital interaction analysis and quantitative electronic structure calculations

Measurement Models For Sailboats Price vs. Features And Regional Areas

In this study, we investigated the relationship between sailboat technical specifications and their prices, as well as regional pricing influences. Utilizing a dataset encompassing characteristics like length, beam, draft, displacement, sail area, and waterline, we applied multiple machine learning models to predict sailboat prices. The gradient descent model demonstrated superior performance, producing the lowest MSE and MAE. Our analysis revealed that monohulled boats are generally more affordable than catamarans, and that certain specifications such as length, beam, displacement, and sail area directly correlate with higher prices. Interestingly, lower draft was associated with higher listing prices. We also explored regional price determinants and found that the United States tops the list in average sailboat prices, followed by Europe, Hong Kong, and the Caribbean. Contrary to our initial hypothesis, a country's GDP showed no direct correlation with sailboat prices. Utilizing a 50% cross-validation method, our models yielded consistent results across test groups. Our research offers a machine learning-enhanced perspective on sailboat pricing, aiding prospective buyers in making informed decisions.Comment: 20 pages, 17 figure

Factorization of the Hückel Hamiltonian Matrix for Highly Symmetrical Molecules

A simple approach to the group-theoretical factorizing of the Hamiltonian matrix of highly symmetrical molecules is presented. This approach, which is based on the Lanczos method, requires only a symmetry-adapted linear combination (SALC) for each category of irreducible representation (IR) of the molecular point-group, while it reduces the size of the problem by more than one order of magnitude. We demonstrate the treatment by applying it to the study of electronic structures of the Goldberg type-II fullerenes, Cgo, C1go, C320, C50o and Cggo within the Hückel tight-binding framework. The results, in terms of the factor characteristic polynomial (or the subspectrum) for each category of irreducible representation, are presented for these giant molecules

Analytic derivative couplings between configuration-interaction-singles states with built-in electron-translation factors for translational invariance

We present a method for analytically calculating the derivative couplings between a pair of configuration-interaction-singles (CIS) excited states obtained in an atom-centered basis. Our theory is exact and has been derived using two completely independent approaches: one inspired by the Hellmann-Feynman theorem and the other following from direct differentiation. (The former is new, while the latter is in the spirit of existing approaches in the literature.) Our expression for the derivative couplings incorporates all Pulay effects associated with the use of an atom-centered basis, and the computational cost is minimal, roughly comparable to that of a single CIS energy gradient. We have validated our method against CIS finite-difference results and have applied it to the lowest lying excited states of naphthalene; we find that naphthalene derivative couplings include Pulay contributions sufficient to have a qualitative effect. Going beyond standard problems in analytic gradient theory, we have also constructed a correction, based on perturbative electron-translation factors, for including electronic momentum and eliminating spurious components of the derivative couplings that break translational symmetry. This correction is general and can be applied to any level of electronic structure theory

Analytic Derivatives of Quartic-Scaling Doubly Hybrid XYGJ-OS Functional: Theory, Implementation, and Benchmark Comparison with M06-2X and MP2 Geometries for Nonbonded Complexes

Analytic first derivative expression of opposite-spin (OS) ansatz-adapted quartic scaling doubly hybrid XYGJ-OS functional is derived and implemented into Q-Chem. The resulting algorithm scales quartically with system size as in OS-MP2 gradient, by utilizing the combination of Laplace transformation and density fitting technique. The performance of XYGJ-OS geometry optimization is assessed by comparing the bond lengths and the intermolecular properties in reference coupled cluster methods. For the selected nonbonded complexes in the S22 and S66 data sets used in the present benchmark test, it is shown that XYGJOS geometries are more accurate than M06-2X and RI-MP2, the two quantum chemical methods widely used to obtain accurate geometries for practical systems, and comparable to CCSD(T) geometries

Analysis of Localized Diabatic States beyond the Condon Approximation for Excitation Energy Transfer Processes

In a previous paper [Fatehi, S.; et al. J. Chem. Phys. 2013, 139, 124112], we demonstrated a practical method by which analytic derivative couplings of Boys-localized CIS states can be obtained. In this paper, we now apply that same method to the analysis of triplet–triplet energy transfer systems studied by Closs and collaborators [Closs, G. L.; et al. J. Am. Chem. Soc.1988, 110, 2652]. For the systems examined, we are able to conclude that (i) the derivative coupling in the BoysOV basis is negligible, and (ii) the diabatic coupling will likely change little over the configuration space explored at room temperature. Furthermore, we propose and evaluate an approximation that allows for the inexpensive calculation of accurate diabatic energy gradients, called the “strictly diabatic” approximation. This work highlights the effectiveness of diabatic state analytic gradient theory in realistic systems and demonstrates that localized diabatic states can serve as an acceptable approximation to strictly diabatic states

Accelerated Computation of Free Energy Profile at ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semi-Empirical Reference Potential. I. Weighted Thermodynamics Perturbation

Free energy profile (FE Profile) is an essential quantity for the estimation of reaction rate and the validation of reaction mechanism. For chemical reactions in condensed phase or enzymatic reactions, the computation of FE profile at ab initio (ai) quantum mechanical/molecular mechanics (QM/MM) level is still far too expensive. Semiempirical (SE) method can be hundreds or thousands of times faster than the ai methods. However, the accuracy of SE methods is often unsatisfactory, due to the approximations that have been adopted in these methods. In this work, we proposed a new method termed MBAR+wTP, in which the ai QM/MM free energy profile is computed by a weighted thermodynamic perturbation (TP) correction to the SE profile generated by the multistate Bennett acceptance ratio (MBAR) analysis of the trajectories from umbrella samplings (US). The weight factors used in the TP calculations are a byproduct of the MBAR analysis in the post-processing of the US trajectories, which are often discarded after the free energy calculations. The results show that this approach can enhance the efficiency of ai FE profile calculations by several orders of magnitude