2,435 research outputs found
Extended M{\o}ller-Plesset perturbation theory for dynamical and static correlations
We present a novel method that appropriately handles both dynamical and
static electron correlation in a balanced manner, using a perturbation theory
on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a
suitable candidate for degenerate systems where static correlation is
ubiquitous, it is known that most of dynamical correlation is neglected in EHF.
In this work, we derive a perturbative correction to a fully spin-projected
self-consistent wave function based on second-order M{\o}ller-Plesset
perturbation theory (MP2). The proposed method efficiently captures the ability
of EHF to describe static correlation in degeneracy, combined with MP2's
ability to treat dynamical correlation effects. We demonstrate drastic
improvements on molecular ground state and excited state potential energy
curves and singlet-triplet splitting energies over both EHF and MP2 with
similar computational effort to the latter.Comment: 5 pages, 3 figures, 2 table
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
Narrative of Chain cruise #17, phase I : St. George, Bermuda, to Freetown, Sierra Leone, 19 February - 22 March 1961
The journal of a cruise of R/V CHAIN from Bermuda to Freetown, Sierra Leone during February and March, 1961, is the basis of this report. Location of observations are given. The portion of the Mid- Atlantic Ridge lying along the equator was surveyed from 10° to 19°W, and new information concerning the slope and orientation of rift zones was obtained. A detailed bathymetric survey of the Romanche Trench was made. A continuous temperature-depth profile, from the surface to 100 meters, was made along the ship 's track with a thermistor chain. Surface shear was measured with pitotmeters mounted on the chain (surface water velocity relative to the water velocity at the depth of the pitotmeter), to determine the strength and direction of the equatorial undercurrent.The Office of Naval Research under Contract Nonr-, 2196 (00
Accurate densities of states for disordered systems from free probability: Live Free or Diagonalize
We investigate how free probability allows us to approximate the density of
states in tight binding models of disordered electronic systems. Extending our
previous studies of the Anderson model in neighbor interactions [J. Chen et
al., Phys. Rev. Lett. 109, 036403 (2012)], we find that free probability
continues to provide accurate approximations for systems with constant
interactions on two- and three-dimensional lattices or with
next-nearest-neighbor interactions, with the results being visually
indistinguishable from the numerically exact solution. For systems with
disordered interactions, we observe a small but visible degradation of the
approximation. To explain this behavior of the free approximation, we develop
and apply an asymptotic error analysis scheme to show that the approximation is
accurate to the eighth moment in the density of states for systems with
constant interactions, but is only accurate to sixth order for systems with
disordered interactions. The error analysis also allows us to calculate
asymptotic corrections to the density of states, allowing for systematically
improvable approximations as well as insight into the sources of error without
requiring a direct comparison to an exact solution
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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
Nonlocal van der Waals density functional: The simpler the better
We devise a nonlocal correlation energy functional that describes the entire
range of dispersion interactions in a seamless fashion using only the electron
density as input. The new functional is considerably simpler than its
predecessors of a similar type. The functional has a tractable and robust
analytic form that lends itself to efficient self-consistent implementation.
When paired with an appropriate exchange functional, our nonlocal correlation
model yields accurate interaction energies of weakly-bound complexes, not only
near the energy minima but also far from equilibrium. Our model exhibits an
outstanding precision at predicting equilibrium intermonomer separations in van
der Waals complexes. It also gives accurate covalent bond lengths and
atomization energies. Hence the functional proposed in this work is a
computationally inexpensive electronic structure tool of broad applicability
Parsimony and Quantum Mechanics: An Analysis of the Copenhagen and Bohmian Interpretations
Parsimony, sometime referred to as simplicity, is an effective criterion of theory choice in the case of Quantum Mechanics. The Copenhagen and Bohmian interpretations are rival theories, with the Bohmian interpretation being more parsimonious. More parsimonious theories have a higher probability of being true than less parsimonious rivals. The Bohmian interpretation should thus be preferred on these grounds
The Infinite and the Finite: An Analysis of the United States’ Energy Future
Last year the New York Times published a newsworthy article stating that the United States could become “Energy Independent” from the tumultuous OPEC countries. This groundbreaking revelation, supported by statistics from the International Energy Agency, claimed that newfound energy resources were spread throughout North America in the form of shale oil and gas. Politicians and the public clung to this possibility in the face of strenuous relations with the Middle East as the Arab Spring and the War on Terror waged on. However, the consequences of becoming “energy independent” have not been considered. What are the geopolitical implications of pursuing energy independence? What are the effects the search for shale oil and gas will have on more sustainable energy sources, like renewable energy? What will happen as the search for unconventional fuels begin? This research project will focus on these geopolitical questions of renewable energy and the rise of unconventional fossil fuels and end with a policy recommendation based on the information provided in this essay to promote a sustainable energy future
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