

THEORETICAL NANOPHYSICS Group 




JengDa Chai
(蔡政達)
Professor
Department of Physics
National Taiwan University
No. 1, Sec. 4, Roosevelt Road
Taipei 10617, Taiwan
Office: R534, New Physics Building, NTU
Phone: +886233665586
Fax: +886223639984
Email: jdchai@phys.ntu.edu.tw
Website: http://web.phys.ntu.edu.tw/jdchai/

Academic Websites:
Professional Experience:
 Professor, Department of Physics, National Taiwan University (2017.8present)
 Associate Professor, Department of Physics, National Taiwan University (2013.82017.7)
 Assistant Professor, Department of Physics, National Taiwan University (2009.82013.7)
 Postdoctoral Fellow, Department of Chemistry, University of California, Berkeley and Chemical Sciences Division, Lawrence Berkeley National Laboratory (2006.12009.6)
Education:
 Ph.D. in Chemical Physics, University of Maryland, College Park (2002.72005.12)
 M.S. in Physics (Ph.D. Candidate), The Ohio State University (1999.92002.6)
 B.S. in Physics (with a minor in Mathematics), National Taiwan University (1993.91997.6)
Awards and Honors:
 Excellence in Teaching Award, National Taiwan University, Taiwan (2023)
 Excellence in Teaching Award, National Taiwan University, Taiwan (2021)
 Excellence in Teaching Award, National Taiwan University, Taiwan (2019)
 Project for Excellent Junior Research Investigators, Ministry of Science and Technology, Taiwan (20182021)
 Excellence in Teaching Award, National Taiwan University, Taiwan (2018)
 Junior Research Investigators Award, Academia Sinica, Taiwan (2017)
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 Outstanding Young Physicist Award, The Physical Society of Taiwan (2016)
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 Project for Excellent Junior Research Investigators, Ministry of Science and Technology, Taiwan (20152018)
 Career Development Award, National Taiwan University, Taiwan (20152016)
 Youth Medal, China Youth Corps, Taiwan (2015)
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 TWAS Young Affiliate, The World Academy of Sciences (TWAS)  for the advancement of science in developing countries (20132017)
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 Career Development Award, National Taiwan University, Taiwan (20132015)
 Young Theorist Award, National Center for Theoretical Sciences, Taiwan (2012)
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 EPSON Scholarship Award, The International Society for Theoretical Chemical Physics (2011)
Software Development:
 Developer, QChem Inc. (2008present)
[Theoretical methods developed in our group may be available in QChem ]
Journal Editorial Boards:
 Editorial Board, International Journal of Quantum Chemistry (2018.3present)
 Editorial Board, London Journals Press (2016.9present)
 Editorial Board, International Journal of Advanced Research in Physical Science (2016.8present)
 Editorial Board, The Open Access Journal of Science and Technology (2016.3present)
 Editorial Board, Mediterranean Journal of Physics (2016.1present)
 Editorial Board, Journal of Lasers, Optics & Photonics (2015.9present)
 Editorial Board, Open Journal of Physical Chemistry (2011.3present)
 Editorial Board, Chinese Journal of Physics (2017.122022.4)
Journal Referees:
 Nature Chemistry
 Nature Communications
 Scientific Reports
 Journal of Chemical Physics
 Journal of Chemical Theory and Computation
 Physical Chemistry Chemical Physics
 Journal of Physical Chemistry Letters
 Journal of Physical Chemistry
 Chemical Science
 Nanoscale
 Journal of Materials Chemistry C
 RSC Advances
 The Chemical Record
 Journal of Computational Chemistry
 International Journal of Quantum Chemistry
 Theoretical Chemistry Accounts
 Molecular Physics
 Chemical Physics Letters
 Journal of Applied Physics
 Communications Chemistry
 Chemistry—A European Journal
 Journal of the Taiwan Institute of Chemical Engineers
 Bulletin of the Chemical Society of Japan
 Molecular Simulation
 Molecules
 Synthetic Metals
 Journal of Electronic Materials
 Symmetry
 Entropy
 Chinese Journal of Physics
 Acta PhysicoChimica Sinica
 Journal of Molecular Graphics and Modelling
 Structural Chemistry
 Journal of Theoretical and Computational Chemistry
 Computation
Research Interests:
"The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry
are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too
complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics
should be developed, which can lead to an explanation of the main features of complex atomic systems without too much
computation." P. A. M. Dirac (1929)
To meet the challenge, our group has focused on the development of new quantummechanical methods (e.g.,
thermallyassistedoccupation density functional theory) suitable for the study of nanoscale systems (with 100~1,000,000 electrons),
and their applications to novel systems at the nanoscale (e.g., Möbius molecules, triangleshaped graphene nanoflakes, linear and cyclic carbon chains,
linear and cyclic boron nanoribbons) and materials for new energy (e.g., solar cells, hydrogen storage materials).
Specific research topics are the following.
1. KohnSham Density Functional Theory (KSDFT)
A. Goal:
a. Exchange Energy Density Functional
b. Correlation Energy Density Functional
c. LinearScaling Methods
B. Direction:
a. SelfInteraction Error
b. Noncovalent Interaction Error
c. Static Correlation Error
C. Suitable Systems:
Systems with 100~1,000 electrons (the Schrödinger equation and highly accurate ab initio methods are inappropriate due to their expensive computational costs)
2. ThermallyAssistedOccupation Density Functional Theory (TAODFT)
A. Density Functional Approximations
B. Fictitious Temperature
C. Fundamental Properties
D. RealTime Extension (for Electron Dynamics)
E. Ab Initio Molecular Dynamics
F. Other Extensions
G. Strongly Correlated Electron Systems at the Nanoscale
Description:
For systems with strong static correlation effects (i.e., systems possessing radical character or multireference (MR) systems), KSDFT employing the LDA, GGA,
MGGA, hybrid, and doublehybrid exchangecorrelation (xc) energy functionals can provide unreliable results, due to the inappropriate treatment of static
correlation. To accurately predict the properties of these systems, highlevel ab initio MR electronic structure methods are typically needed. However, accurate
MR calculations are prohibitively expensive for large systems (especially for geometry optimization). Consequently, it remains very challenging to investigate
the properties of strongly correlated electron systems at the nanoscale using conventional electronic structure methods.
Aiming to study the groundstate (GS) properties of strongly correlated electron systems at the nanoscale with minimum computational complexity, we have recently
developed TAODFT [1]. Unlike finitetemperature density functional theory, TAODFT is developed for GS systems at zero (physical) temperature (just like KSDFT).
In contrast to KSDFT, TAODFT is a density functional theory with fractional orbital occupations produced by the FermiDirac distribution (controlled by
a fictitious (reference) temperature), wherein strong static correlation is shown to be explicitly described by the entropy contribution. Similar to the static
correlation energy of a system, the entropy contribution in TAODFT is always nonpositive, yielding an insignificant contribution for a singlereference (SR) system
(i.e., a system possessing nonradical character), and significantly lowering the total energy of an MR system. TAODFT has similar computational cost as KSDFT
for singlepoint energy and analytical nuclear gradient calculations, and reduces to KSDFT in the absence of strong static correlation effects.
Besides, existing xc energy functionals and dispersion correction schemes in KSDFT may also be adopted in TAODFT [2].
Recently, we have defined the exact exchange in TAODFT, and developed the corresponding global and rangeseparated hybrid schemes in TAODFT for an improved
description of nonlocal exchange effects [3]. With some simple modifications, global hybrid functionals [3] and rangeseparated hybrid functionals [3, 5] in
KSDFT can be combined seamlessly with TAODFT. Relative to TAODFAs (i.e., TAODFT with the density functional approximations), global hybrid functionals in
TAODFT are generally superior in performance for a wide range of applications, such as thermochemistry, kinetics, reaction energies, and optimized geometries.
For MR systems, KSDFT with the traditional xc energy functionals can yield wrong spin densities and related properties. For instance, for the dissociation of
H2 and N2, the spinrestricted and spinunrestricted solutions obtained from the same xc energy functional in KSDFT can be distinctly different, leading to
the unphysical spinsymmetry breaking effects in the spinunrestricted solutions. Very recently, we have developed a response theory [11] based on TAODFT to
demonstrate that TAODFT with a sufficiently large fictitious temperature can always resolve the aforementioned spinsymmetry breaking problems (which are
"challenging problems" for KSDFT).
Also, we have recently proposed a simple model [8] to define the optimal systemindependent fictitious temperature of a given energy functional in TAODFT.
Besides, we have employed this model to determine the optimal systemindependent fictitious temperature of a global hybrid functional in TAODFT as a function
of the fraction of exact exchange. Furthermore, we have discussed the role of exact exchange and an optimal systemindependent fictitious temperature in TAODFT.
In addition, we have recently proposed a selfconsistent scheme [4] for the determination of the fictitious temperature in TAODFT. Relative to the
systemindependent fictitious temperature scheme in TAODFT, the selfconsistent fictitious temperature scheme in TAODFT is generally superior in performance
for a very broad range of applications.
To obtain excitedstate properties within the framework of TAODFT, a frequencydomain formulation of linearresponse timedependent TAODFT (TDTAODFT) has
been recently proposed by Yeh et al. [6]. While some progress has been made, the underlying assumption of TDTAODFT (i.e., that the timedependent (TD) density
is assumed to be associated with the TD "pure state" of a noninteracting reference system) is generally incorrect (e.g., see Ref. [10]).
To resolve the aforementioned inconsistency of TDTAODFT, we have recently developed a realtime (RT) extension of TAODFT (RTTAODFT) [10] based on an ensemble
formalism. RTTAODFT allows the study of TD properties of both SR and MR systems. Since the assumption of a weak perturbation is not required in RTTAODFT,
spinrestricted and spinunrestricted RTTAODFT calculations have been performed to explore the TD properties (e.g., the number of bound electrons, induced dipole
moment, and highorder harmonic generation (HHG) spectrum) of H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly
polarized laser pulse. The TD properties obtained with RTTAODFT have been compared with those obtained with conventional TDDFT. Moreover, issues related to the
possible spinsymmetry breaking effects in the TD properties are also discussed. Furthermore, for clarity, we have also discussed the difference among three
generally different electronic structure methods: KSDFT, TAODFT, and FTDFT (finitetemperature density functional theory, also called the MerminKohnSham (MKS)
method) as well as TAODFTrelated methods.
To explore the equilibrium thermodynamic and dynamical properties of nanosystems with radical character at finite temperatures, we have recently combined TAODFT
with ab initio molecular dynamics (AIMD), yielding TAODFTbased AIMD (TAOAIMD) [7]. In TAOAIMD, the atomic nuclei of an electronic system move based on the
classical Newtonian equations of motion on the GS potential energy surface generated by TAODFT. To show some of the capabilities of TAOAIMD, we have carried out
TAOAIMD simulations to study the instantaneous/average radical character and infrared (IR) spectra of nacenes (containing n = 2–8 fused benzene rings) at 300 K.
On the basis of the TAOAIMD simulations, on average, the smaller nacenes (n = 2–5) exhibit nonradical character, and the larger nacenes (n = 6–8) exhibit
increasing radical character, displaying remarkable similarities to the GS counterparts at 0 K. Moreover, the IR spectra of nacenes obtained with the TAOAIMD
simulations are in qualitative agreement with the existing experimental data. In addition, we have performed preliminary calculations on 8acene to investigate
the possible symmetrybreaking effects in the spinunrestricted TAOAIMD and KSAIMD (i.e., KSDFTbased AIMD) simulations. Based on our results, the
spinunrestricted and spinrestricted KSAIMD simulations can yield distinctly different dynamical information (e.g., distinctly different values of GS electronic
energy, GS potential energy, and total energy at each time), leading to the unphysical symmetrybreaking effects in the spinunrestricted KSAIMD simulations.
These issues can be resolved by the TAOAIMD simulations.
To study solvation effects on the GS properties of nanomolecules with MR character at a minimal computational cost, we have recently combined TAODFT with the
polarizable continuum model (PCM), leading to TAODFTbased PCM (TAOPCM) [9]. In TAOPCM, the solute is treated quantummechanically with TAODFT, and the
solvation effect is modeled implicitly with the PCM. To show its usefulness, TAOPCM has been adopted to study the electronic properties of linear acenes in
three different solvents (toluene, chlorobenzene, and water).
To demonstrate the applicability of TAODFT, we have recently employed TAODFT to study the GS properties of various strongly correlated electron systems at the
nanoscale.
First, in our recent study [13], the orbital occupation numbers obtained from TAODFT have been shown to be qualitatively similar to the natural orbital
occupation numbers (NOONs) obtained from the variational twoelectron reduceddensitymatrixdriven completeactivespace selfconsistentfield (v2RDMCASSCF)
method (i.e., an accurate multireference electronic structure method that can be applied to treat active spaces that are too large for conventional CASSCF),
yielding a similar trend for the radical character of the 24 alternant polycyclic aromatic hydrocarbons (PAHs) studied.
Besides, we have investigated the role of Kekulé and nonKekulé structures in the radical character of several alternant PAHs using TAODFT. Our results have
revealed that the studies of Kekulé and nonKekulé structures qualitatively describe the radical character of alternant PAHs, which could be useful when
electronic structure calculations are infeasible due to the expensive computational cost.
Second, we have employed TAODFT to study the electronic properties of zigzag graphene nanoflakes (GNFs) and graphene quantum rings (GQRs) of different shapes and
sizes, such as the zigzag graphene nanoribbons (ZGNRs) [12], graphene nanoparallelograms (GNPs) [26], hexagonshaped GNFs with n fused benzene rings at each
side (ncoronenes) [18], triangleshaped GNFs with n fused benzene rings at each side (ntriangulenes) [21], diamondshaped GNFs with n benzenoid rings fused
together at each side (npyrenes) [22], and hexagonal GQRs with n aromatic rings fused together at each side (nHGQRs) [25].
On the basis of our TAODFT results, the electronic properties of ZGNRs, GNPs, ncoronenes, ntriangulenes, npyrenes, and nHGQRs are distinctly different. For
example, ZGNRs/GNPs exhibit an oscillatory polyradical nature with increasing ZGNR/GNP length, and the polyradical nature is also highly dependent on the ZGNR/GNP width.
The edge localization of active orbitals has been found for the wider and longer ZGNRs, while the edge/corner localization of active orbitals has been observed for the
wider and longer GNPs. By contrast, with increasing system size, there is a monotonic transition from the nonradical nature of the smaller ncoronenes/nHGQRs to the
increasing polyradical nature of the larger ncoronenes/nHGQRs. Moreover, the latter should be closely related to the localization of active orbitals at the zigzag
edges, which increases with the increase of the side length. On the other hand, ntriangulenes possess a very significant polyradical nature (e.g., the occupation
numbers of active spin orbitals are all very close to 0.5), yielding approximately (n − 1) unpaired electrons in their ground states. Note that npyrene (i.e.,
a diamondshaped GNF) can be viewed as two interconnected triangleshaped GNFs. When n increases, there is a smooth transition from the nonradical character of the
smaller npyrenes to the increasing polyradical nature of the larger npyrenes. Furthermore, the latter is shown to be related to the increasing concentration of active
orbitals on the zigzag edges of the larger npyrenes. These examples clearly support the statement that the radical nature of GNFs/GQRs is intimately correlated with the
shapes, edges, and sizes of GNFs/GQRs.
Third, to investigate the significance of cyclic and Möbius topologies, we have studied the electronic properties of cyclacenes [15] and Möbius cyclacenes [19]
using TAODFT, and have also compared these properties with the respective properties of acenes, containing the same number of fused benzene rings. Similar to
acenes, the ground states of cyclacenes and Möbius cyclacenes are singlets for all the cases studied. In contrast to acenes, the electronic properties of
cyclacenes and Möbius cyclacenes, however, exhibit oscillatory behavior for the smaller cyclacenes and Möbius cyclacenes in the approach to the corresponding
properties of acenes with increasing number of benzene rings. The larger cyclacenes and Möbius cyclacenes should exhibit increasing polyradical character in
their ground states, with the active orbitals being mainly localized at the peripheral carbon atoms. Interestingly, the GS geometry of Möbius cyclacene is
composed mainly of an essentially untwisted open chain plus a highly twisted stripe. In other words, the twist is not evenly distributed along the whole chain.
Fourth, we have employed TAOLDA to investigate the electronic properties of linear carbon chains and cyclic carbon chains [23], possessing polyradical nature
when the system size is sufficiently large. For all the cases studied, linear and cyclic carbon chains are GS singlets; cyclic carbon chains are energetically
more stable than linear carbon chains. Note that among them, the cyclic carbon chains containing 18 carbon atoms have been recently synthesized. Very recevently,
we have also adopted TAODFT with exact exchange to examine the electronic properties of cyclic carbon chains [8]. Owing to the much reduced selfinteraction
error, TAODFT with exact exchange can accurately predict the radical character and bond length alternation of cyclic carbon chains (with even number of carbon
atoms), showing consistency with the results of reliably accurate electronic structure methods (e.g., the CCSD, CASSCF, and QMC methods).
Fifth, we have used TAODFT to predict the electronic properties of CBelt[n], i.e., the carbon nanobelts with n fused 12membered carbon rings [24].
CBelt[n] have singlet ground states. Generally, the larger the size of CBelt[n], the more pronounced the MR nature of groundstate CBelt[n].
Sixth, we have adopted TAODFT to study the electronic properties of twoatomwide linear boron nanoribbons and cyclic boron nanoribbons [20], which exhibit
polyradical character when the system size is considerably large. The electronic properties of the cyclic boron nanoribbons exhibit more pronounced oscillatory
patterns than those of the linear boron nanoribbons when the system size is small, and converge to the respective properties of linear boron nanoribbons when
the system size is sufficiently large. The active orbitals are delocalized along the length of linear boron nanoribbons or the circumference of cyclic boron
nanoribbons. Since materials with several delocalized electrons tend to be highly conductive, the delocalized electrons of the boron nanoribbons are expected to
enable enhanced electrical conductivity. From our TAODFT results, the cyclic boron nanoribbons are more stable than the linear boron nanoribbons for all the
cases studied, revealing the role of cyclic topology.
Besides, TAODFT has been recently used to study the electronic properties of nacenes in oriented external electric fields (OEEFs), where the OEEFs of various
electric field strengths are applied along the long axes of nacenes [27]. The MR character of groundstate nacenes in OEEFs increases with the increase in the
acene length and/or the electric field strength.
In addition, we have shown that Liadsorbed acenes [14], Literminated linear carbon chains [16], and Literminated linear boron chains [17] can be highcapacity
hydrogen storage materials (HSMs) for reversible hydrogen uptake and release at ambient (or nearambient) conditions using dispersioncorrected TAODFT.
Accordingly, the search for ideal HSMs can be readily extended to large systems with strong static correlation effects.
References:
a. TAODFT:
[1]
J.D. Chai*, J. Chem. Phys. 136, 154104 (2012).
b. Extensions of TAODFT:
[2]
J.D. Chai*, J. Chem. Phys. 140, 18A521 (2014).
[3]
J.D. Chai*, J. Chem. Phys. 146, 044102 (2017).
[4]
C.Y. Lin, K. Hui, J.H. Chung, and J.D. Chai*, RSC Adv. 7, 50496 (2017).
[5]
F. Xuan, J.D. Chai*, and H. Su*, ACS Omega 4, 7675 (2019).
[6]
S.H. Yeh, A. Manjanath, Y.C. Cheng, J.D. Chai*, and C.P. Hsu*, J. Chem. Phys. 153, 084120 (2020).
[7]
S. Li and J.D. Chai*, Front. Chem. 8, 589432 (2020).
[8]
B.J. Chen and J.D. Chai*, RSC Adv. 12, 12193 (2022).
[9]
S. Seenithurai and J.D. Chai*, Nanomaterials 13, 1593 (2023).
[10]
H.Y. Tsai and J.D. Chai*, Molecules 28, 7247 (2023).
[11]
Y.Y. Wang and J.D. Chai*, Phys. Rev. A 109, 062808 (2024).
c. Applications of TAODFT:
[12]
C.S. Wu and J.D. Chai*, J. Chem. Theory Comput. 11, 2003 (2015).
[13]
C.N. Yeh and J.D. Chai*, Sci. Rep. 6, 30562 (2016).
[14]
S. Seenithurai and J.D. Chai*, Sci. Rep. 6, 33081 (2016).
[15]
C.S. Wu, P.Y. Lee, and J.D. Chai*, Sci. Rep. 6, 37249 (2016).
[16]
S. Seenithurai and J.D. Chai*, Sci. Rep. 7, 4966 (2017).
[17]
S. Seenithurai and J.D. Chai*, Sci. Rep. 8, 13538 (2018).
[18]
C.N. Yeh, C. Wu, H. Su*, and J.D. Chai*, RSC Adv. 8, 34350 (2018).
[19]
J.H. Chung and J.D. Chai*, Sci. Rep. 9, 2907 (2019).
[20]
S. Seenithurai and J.D. Chai*, Sci. Rep. 9, 12139 (2019).
[21]
Q. Deng and J.D. Chai*, ACS Omega 4, 14202 (2019).
[22]
H.J. Huang, S. Seenithurai, and J.D. Chai*, Nanomaterials 10, 1236 (2020).
[23]
S. Seenithurai and J.D. Chai*, Sci. Rep. 10, 13133 (2020).
[24]
S. Seenithurai and J.D. Chai*, Nanomaterials 11, 2224 (2021).
[25]
C.C. Chen and J.D. Chai*, Nanomaterials 12, 3943 (2022).
[26]
S. Seenithurai and J.D. Chai*, Molecules 29, 349 (2024).
[27]
C.Y. Chen and J.D. Chai*, Molecules 29, 4245 (2024).
[Presentation:
Webinar on TAODFT
]
[Availability:
TAODFT (for singlepoint energy and analytical nuclear gradient calculations) is available in
QChem 4.3 or higher
]
[Some features of TAODFT are briefly summarized in the QChem 5 paper
(
J. Chem. Phys. 155, 084801 (2021)) and in the
QChem Highlights
]
3. OrbitalFree Density Functional Theory
A. Goal:
a. Kinetic Energy Density Functional
b. Pseudopotentials
B. Direction:
a. Linear Response Theory
b. KEDFs in Certain Situations
c. Transferable Pseudopotentials
C. Suitable Systems:
Systems with 1,000~1,000,000 electrons (KohnSham density functional theory is inappropriate due to its high computational cost)
4. TimeDependent Density Functional Theory
A. ExchangeCorrelation Action Functional
B. Excited States
C. RealTime Electron Dynamics
D. Quantum Transport
E. Quantum Hydrodynamics
5. Materials for New Energy
A. Organic Solar Cells
B. Hydrogen Storage Materials



