arXiv subjects

Weitao Yang

Publications and source records attributed to Weitao Yang.

At least 55 records · Page 3Linked to original sources

arXiv2015

Accurate atomic quantum defects from particle-particle random phase approximation

The accuracy of calculations of atomic Rydberg excitations cannot be judged by the usual measures, such as mean unsigned errors of many transitions. We show how to use quantum defect theory to (a) separate errors due to approximate ionization potentials, (b) extract smooth quantum defects to compare with experiment, and (c) quantify those defects with a few characteristic parameters. The particle-particle random phase approximation (pp-RPA) produces excellent Rydberg transitions that are an order of magnitude more accurate than those of time-dependent density functional theory with standard approximations. We even extract reasonably accurate defects from the lithium Rydberg series, despite the reference being open-shell. Our methodology can be applied to any Rydberg series of excitations with 4 transitions or more to extract the underlying threshold energy and characteristic quantum defect parameters. Our pp-RPA results set a demanding challenge for other excitation methods to match.

physics.chem-ph↗

arXiv2013

Layer-dependent Electrocatalysis of MoS2 for Hydrogen Evolution

The quantitative correlation of the catalytic activity with microscopic structure of heterogeneous catalysts is a major challenge for the field of catalysis science. It requests synergistic capabilities to tailor the structure with atomic scale precision and to control the catalytic reaction to proceed through well-defined pathways. Here we leverage on the controlled growth of MoS2 atomically thin films to demonstrate that the catalytic activity of MoS2 for the hydrogen evolution reaction decreases by a factor of ~4.47 for the addition of every one more layer. Similar layer dependence is also found in edge-riched MoS2 pyramid platelets. This layer-dependent electrocatalysis can be correlated to the hopping of electrons in the vertical direction of MoS2 layers over an interlayer potential barrier, which is found to be 0.119V and consistent with theoretical calculations. Our results point out that increasing the hopping efficiency of electrons in the vertical direction is a key for the development of high-efficiency two-dimensional material catalysts.

cond-mat.mtrl-sci↗

arXiv2013

Equivalence of Particle-Particle Random Phase Approximation Correlation Energy and Ladder-Coupled-Cluster-Double

We present an analytical proof and numerical demonstrations of the equivalence of the correlation energy from particle-particle random phase approximation (pp-RPA) and ladder-couple-cluster-doubles (ladder-CCD). These two theories reduce to the identical algebraic matrix equation and correlation energy expressions, under the assumption that the pp-RPA equation is stable. The numerical examples illustrate that the correlation energy missed by pp-RPA in comparison with couple-cluster single and double is largely canceled out when considering reaction energies. This theoretical connection will be beneficial to future pp-RPA studies based on the well established couple cluster theory.

physics.chem-ph↗

arXiv2013

Exchange-Correlation Energy from Pairing Matrix Fluctuation and the Particle-Particle Random Phase Approximation

We formulate an adiabatic connection for the exchange-correlation energy in terms of pairing matrix fluctuation. This connection opens new channels for density functional approximations based on pairing interactions. Even the simplest approximation to the pairing matrix fluctuation, the particle-particle Random Phase Approximation (pp-RPA), has some highly desirable properties. It has no delocalization error with a nearly linear energy behavior for systems with fractional charges, describes van der Waals interactions similarly and thermodynamic properties significantly better than particle-hole RPA, and eliminates static correlation error for single-bond systems. Most significantly, the pp-RPA is the first known functional that has an explicit and closed-form dependence on the occupied and unoccupied orbitals and captures the energy derivative discontinuity in strongly correlated systems. These findings illlustrate the potential of including pairing interactions within a density functional framework.

physics.chem-ph↗

arXiv2013

Extension of many-electron theory and approximate density functionals to fractional charges and fractional spins

The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are not normally expressed in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of $G^{0}$, the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, $G^{0}$. We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the LDA and GGA; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental band gaps with approximate functionals and many-electron theories through the energy derivatives with respect to the fractional charge.

cond-mat.other↗

arXiv2013

The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r^4) scaling

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI) tensor and the two-particle excitation amplitudes used in the parametric reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).

physics.chem-ph↗

arXiv2012

Using tensor hypercontraction density fitting to achieve an O(L^4) CISD algorithm

Recently, Hohenstein et al[1] introduced tensor hypercontraction density fitting to decompose the rank-4 electron repulsion integral tensor as the product of five rank-2 tensors. In this paper, we use this methodology to construct an algorithm which calculates the approximate ground state energy in O(L^4) operations. We test our method using several small molecules and show that we quickly approach the CISD limit with a small number of auxiliary functions.

physics.chem-ph↗

arXiv2010

Time-Dependent Transport Through Molecular Junctions

We investigate transport properties of molecular junctions under two types of bias--a short time pulse or an AC bias--by combining a solution for the Green functions in the time domain with electronic structure information coming from ab initio density functional calculations. We find that the short time response depends on lead structure, bias voltage, and barrier heights both at the molecule-lead contacts and within molecules. Under a low frequency AC bias, the electron flow either tracks or leads the bias signal (capacitive or resistive response) depending on whether the junction is perfectly conducting or not. For high frequency, the current lags the bias signal due to the kinetic inductance. The transition frequency is an intrinsic property of the junctions.

cond-mat.mes-hall↗

arXiv2009

The Role of the Exchange-Correlation Potential in ab initio Electron Transport Calculations

The effect of the exchange-correlation potential in ab initio electron transport calculations is investigated by constructing optimized effective potentials (OEP) using different energy functionals or the electron density from second-order perturbation theory. We calculate electron transmission through two atomic chain systems, one with charge transfer and one without. Dramatic effects are caused by two factors: changes in the energy gap and the self-interaction error. The error in conductance caused by the former is about one order of magnitude while that caused by the latter ranges from several times to two orders of magnitude, depending on the coupling strength and charge transfer. The implications for accurate quantum transport calculations are discussed.

cond-mat.mes-hall↗

arXiv2009

Quantum Interference Controlled Molecular Electronics

Quantum interference in coherent transport through single molecular rings may provide a mechanism to control current in molecular electronics. We investigate its applicability by using a single-particle Green function method combined with ab initio electronic structure calculations. We find that the quantum interference effect (QIE) depends strongly on the interaction between molecular pi states and contact sigma states. It is absent in small molecular rings with Au leads, such as benzene, due to strong pi-sigma hybridization, while it is preserved in large rings, such as [18]annulene, which then could be used to realize QIE transistors.

cond-mat.mes-hall↗

arXiv2009

Failure of the random phase approximation correlation energy

The random phase approximation (RPA) to the correlation energy is extended to fractional occupations and its performance examined for exact conditions on fractional charges and fractional spins. RPA satisfies the constancy condition for fractional spins that leads to correct bond dissociation and no static correlation error for H$_2$ but massively fails for fractional charges, with an enormous delocalization error even for a one-electron system such as H$_2^+$. Other methods such as range-separated RPA can reduce this delocalization error but only at the cost of increasing the static correlation error. None of the RPA methods seem to have the discontinuous nature required to satisfy both exact conditions and the full unified condition, emphasizing the need to go further than just smooth functionals of the orbitals.

cond-mat.other↗

arXiv2008

The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems

Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading to static correlation error. These two conditions are now unified for states with both fractional charge and fractional spin: the exact energy functional is a plane, linear along the fractional charge coordinate and constant along the fractional spin coordinate with a line of discontinuity at the integer. This sheds light on the nature of the derivative discontinuity and calls for explicitly discontinuous functionals of the density or orbitals that go beyond currently used smooth approximations. This is key for the application of DFT to strongly correlated systems.

cond-mat.str-el↗

arXiv2008

A gradient-directed Monte Carlo approach to molecular design

The recently developed linear combination of atomic potentials (LCAP) approach [M.Wang et al., J. Am. Chem. Soc., 128, 3228 (2006)] allows continuous optimization in discrete chemical space and thus is quite useful in the design of molecules for targeted properties. To address further challenges arising from the rugged, continuous property surfaces in the LCAP approach, we develop a gradient-directed Monte Carlo (GDMC) strategy as an augmentation to the original LCAP optimization method. The GDMC method retains the power of exploring molecular space by utilizing local gradient information computed from the LCAP approach to jump between discrete molecular structures. It also allows random Monte Carlo moves to overcome barriers between local optima on property surfaces. The combined GDMC and LCAP approach is demonstrated here for optimizing nonlinear optical (NLO) properties in a class of donor-acceptor substituted benzene and porphyrin frameworks. Specifically, one molecule with four nitrogen atoms in the porphyrin ring was found to have a larger first hyperpolarizability than structures with the conventional porphyrin motif. 1

physics.chem-ph↗

arXiv2008

Fractional spins and static correlation error in density functional theory

Electronic states with fractional spins arise in systems with large static correlation (strongly correlated systems). Such fractional-spin states are shown to be ensembles of degenerate ground states with normal spins. It is proven here that the energy of the exact functional for fractional-spin states is a constant, equal to the energy of the comprising degenerate pure spin states. Dramatic deviations from this exact constancy condition exist with all approximate functionals, leading to large static correlation errors for strongly correlated systems, such as chemical bond dissociation and band structure of Mott insulators. This is demonstrated with numerical calculations for several molecular systems. Approximating the constancy behavior for fractional spins should be a major aim in functional constructions and should open the frontier for DFT to describe strongly correlated systems. The key results are also shown to apply in reduced density-matrix functional theory.

cond-mat.other↗

arXiv2007

Localization and delocalization errors in density functional theory and implications for band-gap prediction

The band-gap problem and other systematic failures of approximate functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large or bulk systems. Functionals whose energy is convex for fractional charges such as LDA display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an important paradox and opens the possibility to obtain accurate band-gaps from DFT.

cond-mat.mtrl-sci↗

arXiv2007

Fractional charge perspective on the band-gap in density-functional theory

The calculation of the band-gap by density-functional theory (DFT) methods is examined by considering the behavior of the energy as a function of number of electrons. It is found that the incorrect band-gap prediction with most approximate functionals originates mainly from errors in describing systems with fractional charges. Formulas for the energy derivatives with respect to number of electrons are derived which clarify the role of optimized effective potentials in prediction of the band-gap. Calculations with a recent functional that has much improved behavior for fractional charges give a good prediction of the energy gap and also $ε_{\rm homo}\simeq-I$ for finite systems. Our results indicate it is possible, within DFT, to have a functional whose eigenvalues or derivatives accurately predict the band-gap.

cond-mat.mtrl-sci↗

arXiv2007

Electron transport through single conjugated organic molecules: Basis set effects in ab initio calculations

We investigate electron transport through single conjugated molecules - including benzenedithiol, oligo-phenylene-ethynylenes of different lengths, and a ferrocene-containing molecule sandwiched between two gold electrodes with different contact structures - by using a single-particle Green function method combined with density functional theory calculation. We focus on the effect of the basis set in the ab initio calculation. It is shown that the position of the Fermi energy in the transport gap is sensitive to the molecule-lead charge transfer which is affected by the size of basis set. This can dramatically change, by orders of magnitude, the conductance for long molecules, though the effect is only minor for short ones. A resonance around the Fermi energy tends to pin the position of the Fermi energy and suppress this effect. The result is discussed in comparison with experimental data.

cond-mat.mes-hall↗

arXiv2007

Optimized Effective Potentials in Finite Basis Sets

The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of unbalanced, and thus unsuitable, basis sets. A modified functional incorporating a regularizing smoothness measure of the OEP is introduced. This provides a condition on balanced basis sets for the potential, as well as a method to determine the most appropriate OEP potential and energy from calculations performed with any finite basis set.

cond-mat.mtrl-sci↗