30,321 research outputs found
Empirical LCAO parameters for molecular orbitals in planar organic molecules
We present a parametrization within a simplified LCAO model (a type of
Hueckel model) for the description of molecular orbitals in organic
molecules containing -bonds between carbon, nitrogen, or oxygen atoms with
hybridization, which we show to be quite accurate in predicting the
energy of the highest occupied orbital and the first -
transition energy for a large set of organic compounds. We provide four
empirical parameter values for the diagonal matrix elements of the LCAO
description, corresponding to atoms of carbon, nitrogen with one
electron, nitrogen with two electrons, and oxygen. The bond-length
dependent formula (proportional to ) of Harrison is used for the
non-diagonal matrix elements between neighboring atoms. The predictions of our
calculations have been tested against available experimental results in more
than sixty organic molecules, including benzene and its derivatives,
polyacenes, aromatic hydrocarbons of various geometries, polyenes, ketones,
aldehydes, azabenzenes, nucleic acid bases and others. The comparison is rather
successful, taking into account the small number of parameters and the
simplicity of the LCAO method, involving only atomic orbitals, which
leads even to analytical calculations in some cases.Comment: 20 pages, 6 tables, 65 planar organic molecule
Unified Representation of Molecules and Crystals for Machine Learning
Accurate simulations of atomistic systems from first principles are limited
by computational cost. In high-throughput settings, machine learning can
potentially reduce these costs significantly by accurately interpolating
between reference calculations. For this, kernel learning approaches crucially
require a single Hilbert space accommodating arbitrary atomistic systems. We
introduce a many-body tensor representation that is invariant to translations,
rotations and nuclear permutations of same elements, unique, differentiable,
can represent molecules and crystals, and is fast to compute. Empirical
evidence is presented for energy prediction errors below 1 kcal/mol for 7k
organic molecules and 5 meV/atom for 11k elpasolite crystals. Applicability is
demonstrated for phase diagrams of Pt-group/transition-metal binary systems.Comment: Revised version, minor changes throughou
Recommended from our members
Towards Prediction of Non-Radiative Decay Pathways in Organic Compounds I: The Case of Naphthalene Quantum Yields
Many emerging technologies depend on human’s ability to control and manipulate the excited-state properties of molecular systems. These technologies include fluorescent labeling in biomedical imaging, light harvesting in photovoltaics, and electroluminescence in light-emitting devices. All of these systems suffer from non-radiative loss pathways that dissipate electronic energy as heat, which causes the overall system efficiency to be directly linked to quantum yield (Φ) of the molecular excited state. Unfortunately, Φ is very difficult to predict from first principles because the description of a slow non-radiative decay mechanism requires an accurate description of long-timescale excited-state quantum dynamics. In the present study, we introduce an efficient semiempirical method of calculating the fluorescence quantum yield (Φfl) for molecular chromophores, which, based on machine learning, converts simple electronic energies computed using time-dependent density functional theory (TDDFT) into an estimate of Φfl. As with all machine learning strategies, the algorithm needs to be trained on fluorescent dyes for which Φfl’s are known, so as to provide a black-box method which can later predict Φfl’s for chemically similar chromophores that have not been studied experimentally. As a first illustration of how our proposed algorithm can be trained, we examine a family of 25 naphthalene derivatives. The simplest application of the energy gap law is found to be inadequate to explain the rates of internal conversion (IC) or intersystem crossing (ISC) – the electronic properties of at least one higher-lying electronic state (Sn or Tn) or one far-from-equilibrium geometry are typically needed to obtain accurate results. Indeed, the key descriptors turn out to be the transition state between the Franck–Condon minimum a distorted local minimum near an S0/S1 conical intersection (which governs IC) and the magnitude of the spin–orbit coupling (which governs ISC). The resulting Φfl’s are predicted with reasonable accuracy (±22%), making our approach a promising ingredient for high-throughput screening and rational design of the molecular excited states with desired Φ’s. We thus conclude that our model, while semi-empirical in nature, does in fact extract sound physical insight into the challenge of describing non-radiative relaxations
Electronic Spectra from TDDFT and Machine Learning in Chemical Space
Due to its favorable computational efficiency time-dependent (TD) density
functional theory (DFT) enables the prediction of electronic spectra in a
high-throughput manner across chemical space. Its predictions, however, can be
quite inaccurate. We resolve this issue with machine learning models trained on
deviations of reference second-order approximate coupled-cluster singles and
doubles (CC2) spectra from TDDFT counterparts, or even from DFT gap. We applied
this approach to low-lying singlet-singlet vertical electronic spectra of over
20 thousand synthetically feasible small organic molecules with up to eight
CONF atoms. The prediction errors decay monotonously as a function of training
set size. For a training set of 10 thousand molecules, CC2 excitation energies
can be reproduced to within 0.1 eV for the remaining molecules. Analysis
of our spectral database via chromophore counting suggests that even higher
accuracies can be achieved. Based on the evidence collected, we discuss open
challenges associated with data-driven modeling of high-lying spectra, and
transition intensities
Triplet-Tuning: A Novel Family of Non-Empirical Exchange-Correlation Functionals
In the framework of DFT, the lowest triplet excited state, T, can be
evaluated using multiple formulations, the most straightforward of which are
UDFT and TDDFT. Assuming the exact XC functional is applied, UDFT and TDDFT
provide identical energies for T (), which is also a constraint
that we require our XC functionals to obey. However, this condition is not
satisfied by most of the popular XC functionals, leading to inaccurate
predictions of low-lying, spectroscopically and photochemically important
excited states, such as T and S. Inspired by the optimal tuning
strategy for frontier orbital energies [Stein, Kronik, and Baer, {\it J. Am.
Chem. Soc.} {\bf 2009}, 131, 2818], we proposed a novel and non-empirical
prescription of constructing an XC functional in which the agreement between
UDFT and TDDFT in is strictly enforced. Referred to as "triplet
tuning", our procedure allows us to formulate the XC functional on a
case-by-case basis using the molecular structure as the exclusive input,
without fitting to any experimental data. The first triplet tuned XC
functional, TT-PBEh, is formulated as a long-range-corrected hybrid of
PBE and HF functionals [Rohrdanz, Martins, and Herbert, {\it J. Chem. Phys.}
{\bf 2009}, 130, 054112] and tested on four sets of large organic molecules.
Compared to existing functionals, TT-PBEh manages to provide more
accurate predictions for key spectroscopic and photochemical observables,
including but not limited to , , , and
, as it adjusts the effective electron-hole interactions to arrive at the
correct excitation energies. This promising triplet tuning scheme can be
applied to a broad range of systems that were notorious in DFT for being
extremely challenging
Resolving transition metal chemical space: feature selection for machine learning and structure-property relationships
Machine learning (ML) of quantum mechanical properties shows promise for
accelerating chemical discovery. For transition metal chemistry where accurate
calculations are computationally costly and available training data sets are
small, the molecular representation becomes a critical ingredient in ML model
predictive accuracy. We introduce a series of revised autocorrelation functions
(RACs) that encode relationships between the heuristic atomic properties (e.g.,
size, connectivity, and electronegativity) on a molecular graph. We alter the
starting point, scope, and nature of the quantities evaluated in standard ACs
to make these RACs amenable to inorganic chemistry. On an organic molecule set,
we first demonstrate superior standard AC performance to other
presently-available topological descriptors for ML model training, with mean
unsigned errors (MUEs) for atomization energies on set-aside test molecules as
low as 6 kcal/mol. For inorganic chemistry, our RACs yield 1 kcal/mol ML MUEs
on set-aside test molecules in spin-state splitting in comparison to 15-20x
higher errors from feature sets that encode whole-molecule structural
information. Systematic feature selection methods including univariate
filtering, recursive feature elimination, and direct optimization (e.g., random
forest and LASSO) are compared. Random-forest- or LASSO-selected subsets 4-5x
smaller than RAC-155 produce sub- to 1-kcal/mol spin-splitting MUEs, with good
transferability to metal-ligand bond length prediction (0.004-5 {\AA} MUE) and
redox potential on a smaller data set (0.2-0.3 eV MUE). Evaluation of feature
selection results across property sets reveals the relative importance of
local, electronic descriptors (e.g., electronegativity, atomic number) in
spin-splitting and distal, steric effects in redox potential and bond lengths.Comment: 43 double spaced pages, 11 figures, 4 table
Redox potentials of aryl derivatives from hybrid functional based first principles molecular dynamics
Acknowledgements We acknowledge the National Science Foundation of China (No. 41222015, 41273074, 41572027 and 21373166), Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase), the Foundation for the Author of National Excellent Doctoral Dissertation of P. R. China (No. 201228), Newton International Fellowship Program and the financial support from the State Key Laboratory at Nanjing University. We are grateful to the High Performance Computing Center of Nanjing University for allowing us to use the IBM Blade cluster system. Open access via RSC Gold for GoldPeer reviewedPublisher PD
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