THEORETICAL NANOPHYSICS Group
Department of Physics
National Taiwan University
No. 1, Sec. 4, Roosevelt Road
Taipei 10617, Taiwan
Office: R534, New Physics Building, NTU
- Professor, Department of Physics, National Taiwan University (2017.8-present)
- Associate Professor, Department of Physics, National Taiwan University (2013.8-2017.7)
- Assistant Professor, Department of Physics, National Taiwan University (2009.8-2013.7)
- Postdoctoral Fellow, Department of Chemistry, University of California, Berkeley and Chemical Sciences Division, Lawrence Berkeley National Laboratory (2006.1-2009.6)
- Ph.D. in Chemical Physics, University of Maryland, College Park (2002.7-2005.12)
- M.S. in Physics (Ph.D. Candidate), The Ohio State University (1999.9-2002.6)
- B.S. in Physics (with a minor in Mathematics), National Taiwan University (1993.9-1997.6)
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 (2018-2021)
- Excellence in Teaching Award, National Taiwan University, Taiwan (2018)
- Junior Research Investigators Award, Academia Sinica, Taiwan (2017)
- Outstanding Young Physicist Award, The Physical Society of Taiwan (2016)
- Project for Excellent Junior Research Investigators, Ministry of Science and Technology, Taiwan (2015-2018)
- Career Development Award, National Taiwan University, Taiwan (2015-2016)
- Youth Medal, China Youth Corps, Taiwan (2015)
- TWAS Young Affiliate, The World Academy of Sciences (TWAS) - for the advancement of science in developing countries (2013-2017)
E2 (p. 8),
- Career Development Award, National Taiwan University, Taiwan (2013-2015)
- Young Theorist Award, National Center for Theoretical Sciences, Taiwan (2012)
- EPSON Scholarship Award, The International Society for Theoretical Chemical Physics (2011)
- Developer, Q-Chem Inc. (2008-present)
[Theoretical methods developed in our group may be available in Q-Chem ]
Journal Editorial Boards:
- Editorial Board, International Journal of Quantum Chemistry (2018.3-present)
- Editorial Board, London Journals Press (2016.9-present)
- Editorial Board, International Journal of Advanced Research in Physical Science (2016.8-present)
- Editorial Board, The Open Access Journal of Science and Technology (2016.3-present)
- Editorial Board, Mediterranean Journal of Physics (2016.1-present)
- Editorial Board, Journal of Lasers, Optics & Photonics (2015.9-present)
- Editorial Board, Open Journal of Physical Chemistry (2011.3-present)
- Editorial Board, Chinese Journal of Physics (2017.12-2022.4)
- 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
- 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
- Synthetic Metals
- Journal of Electronic Materials
- Chinese Journal of Physics
- Acta Physico-Chimica Sinica
- Journal of Molecular Graphics and Modelling
- Structural Chemistry
- Journal of Theoretical and Computational Chemistry
"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 quantum-mechanical methods (e.g.,
thermally-assisted-occupation 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, triangle-shaped 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. Kohn-Sham Density Functional Theory (KS-DFT)
a. Exchange Energy Density Functional
b. Correlation Energy Density Functional
c. Linear-Scaling Methods
a. Self-Interaction 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. Thermally-Assisted-Occupation Density Functional Theory (TAO-DFT)
A. Density Functional Approximations
B. Fictitious Temperature
C. Fundamental Properties
D. Real-Time Extension (for Electron Dynamics)
E. Ab Initio Molecular Dynamics
F. Other Extensions
G. Strongly Correlated Electron Systems at the Nanoscale
For systems with strong static correlation effects (i.e., systems possessing radical character or multi-reference systems), KS-DFT employing the LDA, GGA, MGGA,
hybrid, and double-hybrid exchange-correlation energy functionals can provide unreliable results, due to the inappropriate treatment of static correlation.
To accurately predict the properties of these systems, high-level ab initio multi-reference electronic structure methods are typically needed. However,
accurate multi-reference 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 ground-state (GS) properties of strongly correlated electron systems at the nanoscale with minimum computational complexity, we have
recently developed TAO-DFT .
Unlike finite-temperature density functional theory, TAO-DFT is developed for GS systems at zero (physical) temperature (just like KS-DFT).
In contrast to KS-DFT, TAO-DFT is a density functional theory with fractional orbital occupations produced by the Fermi-Dirac 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 TAO-DFT is always nonpositive, yielding insignificant contributions for a single-reference system
(i.e., a system possessing non-radical character), and significantly lowering the total energy of a multi-reference system. TAO-DFT has similar computational
cost as KS-DFT for single-point energy and analytical nuclear gradient calculations, and reduces to KS-DFT in the absence of strong static correlation effects.
Besides, existing exchange-correlation energy functionals and dispersion correction schemes in KS-DFT may also be adopted in TAO-DFT .
Recently, we have defined the exact exchange in TAO-DFT, and developed the corresponding global and range-separated hybrid schemes in TAO-DFT for an improved
description of nonlocal exchange effects . With some simple modifications, global hybrid functionals  and range-separated hybrid functionals [3, 5] in
KS-DFT can be combined seamlessly with TAO-DFT. Relative to TAO-DFAs (i.e., TAO-DFT with the density functional approximations), global hybrid functionals in
TAO-DFT are generally superior in performance for a wide range of applications, such as thermochemistry, kinetics, reaction energies, and optimized geometries.
Very recently, we have proposed a simple model to define the optimal system-independent fictitious temperature of a given energy functional in TAO-DFT .
Besides, we have employed this model to determine the optimal system-independent fictitious temperature of a global hybrid functional in TAO-DFT as a function
of the fraction of exact exchange. Furthermore, we have discussed the role of exact exchange and an optimal system-independent fictitious temperature in TAO-DFT.
In addition, we have recently proposed a self-consistent scheme for the determination of the fictitious temperature in TAO-DFT . Relative to the
system-independent fictitious temperature scheme in TAO-DFT, the self-consistent fictitious temperature scheme in TAO-DFT is generally superior in performance
for a very broad range of applications.
To obtain excited-state properties within the framework of TAO-DFT, a frequency-domain formulation of linear-response time-dependent TAO-DFT (TDTAO-DFT) has
been recently proposed by Yeh et al. . While some progress has been made, the underlying assumption of TDTAO-DFT (i.e., that the time-dependent (TD) density
is assumed to be associated with the TD "pure state" of a noninteracting reference system) is generally incorrect (e.g., see Ref. ).
To resolve the aforementioned inconsistency of TDTAO-DFT, we have recently developed a real-time (RT) extension of TAO-DFT (RT-TAO-DFT)  based on an
ensemble formalism. RT-TAO-DFT allows the study of TD properties of both single-reference and multi-reference systems. Since the assumption of a weak
perturbation is not required in RT-TAO-DFT, spin-restricted and spin-unrestricted RT-TAO-DFT calculations have been performed to explore the TD properties
(e.g., the number of bound electrons, induced dipole moment, and high-order 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 RT-TAO-DFT have been compared with
those obtained with conventional TD-DFT. Moreover, issues related to the possible spin-symmetry breaking effects in the TD properties are also discussed.
Futhermore, for clarity, we have also discussed the difference among three generally different electronic structure methods: KS-DFT, TAO-DFT, and
FT-DFT (finite-temperature density functional theory, also called the Mermin-Kohn-Sham (MKS) method) as well as TAO-DFT-related methods.
To explore the equilibrium thermodynamic and dynamical properties of nanosystems with radical character at finite temperatures, we have recently combined
TAO-DFT with ab initio molecular dynamics (AIMD), yielding TAO-DFT-based AIMD (TAO-AIMD) . In TAO-AIMD, the atomic nuclei of an electronic system move
based on the classical Newtonian equations of motion on the GS potential energy surface generated by TAO-DFT. To show some of the capabilities of TAO-AIMD,
we have carried out TAO-AIMD simulations to study the instantaneous/average radical character and infrared (IR) spectra of n-acenes (containing n = 2–8 fused
benzene rings) at 300 K. On the basis of the TAO-AIMD simulations, on average, the smaller n-acenes (n = 2–5) exhibit nonradical character, and the larger
n-acenes (n = 6–8) exhibit increasing radical character, displaying remarkable similarities to the GS counterparts at 0 K. Moreover, the IR spectra of n-acenes
obtained with the TAO-AIMD simulations are in qualitative agreement with the existing experimental data. In addition, we have performed preliminary
calculations on 8-acene to investigate the possible symmetry-breaking effects in the spin-unrestricted TAO-AIMD and KS-AIMD (i.e., KS-DFT-based AIMD)
simulations. Based on our results, the spin-unrestricted and spin-restricted KS-AIMD 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 symmetry-breaking effects in
the spin-unrestricted KS-AIMD simulations. These issues can be resolved by the TAO-AIMD simulations.
To study solvation effects on the GS properties of nanomolecules with MR character at a minimal computational cost, we have recently combined TAO-DFT with the
polarizable continuum model (PCM), leading to TAO-DFT-based PCM (TAO-PCM) . In TAO-PCM, the solute is treated quantum-mechanically with TAO-DFT, and the
solvation effect is modeled implicitly with the PCM. To show its usefulness, TAO-PCM has been adopted to study the electronic properties of linear acenes in
three different solvents (toluene, chlorobenzene, and water).
To demonstrate the applicability of TAO-DFT, we have recently employed TAO-DFT to study the GS properties of various strongly correlated electron systems
at the nanoscale.
First, in our recent study , the orbital occupation numbers obtained from TAO-DFT have been shown to be qualitatively similar to the natural orbital
occupation numbers (NOONs) obtained from the variational two-electron reduced-density-matrix-driven complete-active-space self-consistent-field (v2RDM-CASSCF)
method (i.e., an accurate multi-reference 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 non-Kekulé structures in the radical character of several alternant PAHs using TAO-DFT. Our results have
revealed that the studies of Kekulé and non-Kekulé 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 TAO-DFT 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) , hexagon-shaped GNFs with n fused benzene rings at each side (n-coronenes) , triangle-shaped GNFs
with n fused benzene rings at each side (n-triangulenes) , diamond-shaped GNFs with n benzenoid rings fused together at each side (n-pyrenes) , and
hexagonal GQRs with n aromatic rings fused together at each side (n-HGQRs) . On the basis of our TAO-DFT results, the electronic properties of ZGNRs,
n-coronenes, n-triangulenes, n-pyrenes, and n-HGQRs are distinctly different. For example, ZGNRs exhibit an oscillatory polyradical nature with increasing ribbon
length, and the polyradical nature is also highly dependent on the ribbon width. By contrast, with increasing system size, there is a monotonic transition from
the non-radical nature of the smaller n-coronenes/n-HGQRs to the increasing polyradical nature of the larger n-coronenes/n-HGQRs. 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,
n-triangulenes 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 n-pyrene (i.e., a diamond-shaped graphene nanoflake) can be viewed as two interconnected
triangle-shaped graphene nanoflakes. When n increases, there is a smooth transition from the nonradical character of the smaller n-pyrenes to the increasing
polyradical nature of the larger n-pyrenes. Furthermore, the latter is shown to be related to the increasing concentration of active orbitals on the zigzag edges
of the larger n-pyrenes. 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  and Möbius cyclacenes 
using TAO-DFT, 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 TAO-LDA to investigate the electronic properties of linear carbon chains and cyclic carbon chains , 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 TAO-DFT with exact exchange to examine the electronic properties of cyclic carbon chains . Owing to the much reduced self-interaction
error, TAO-DFT 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 TAO-DFT to predict the electronic properties of C-Belt[n], i.e., the carbon nanobelts with n fused 12-membered carbon rings .
C-Belt[n] have singlet ground states. Generally, the larger the size of C-Belt[n], the more pronounced the MR nature of ground-state C-Belt[n].
Sixth, we have adopted TAO-DFT to study the electronic properties of two-atom-wide linear boron nanoribbons and cyclic boron nanoribbons , 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 TAO-DFT results, the cyclic boron nanoribbons are more stable than the linear boron nanoribbons for all the
cases studied, revealing the role of cyclic topology.
In addition, we have shown that Li-adsorbed acenes , Li-terminated linear carbon chains , and Li-terminated linear boron chains  can be
high-capacity hydrogen storage materials (HSMs) for reversible hydrogen uptake and release at ambient (or near-ambient) conditions using dispersion-corrected
TAO-DFT. Accordingly, the search for ideal HSMs can be readily extended to large systems with strong static correlation effects.
J.-D. Chai*, J. Chem. Phys. 136, 154104 (2012).
b. Extensions of TAO-DFT:
J.-D. Chai*, J. Chem. Phys. 140, 18A521 (2014).
J.-D. Chai*, J. Chem. Phys. 146, 044102 (2017).
C.-Y. Lin, K. Hui, J.-H. Chung, and J.-D. Chai*, RSC Adv. 7, 50496 (2017).
F. Xuan, J.-D. Chai*, and H. Su*, ACS Omega 4, 7675 (2019).
S.-H. Yeh, A. Manjanath, Y.-C. Cheng, J.-D. Chai*, and C.-P. Hsu*, J. Chem. Phys. 153, 084120 (2020).
S. Li and J.-D. Chai*, Front. Chem. 8, 589432 (2020).
B.-J. Chen and J.-D. Chai*, RSC Adv. 12, 12193 (2022).
S. Seenithurai and J.-D. Chai*, Nanomaterials 13, 1593 (2023).
H.-Y. Tsai and J.-D. Chai*, Molecules 28, 7247 (2023).
c. Applications of TAO-DFT:
C.-S. Wu and J.-D. Chai*, J. Chem. Theory Comput. 11, 2003 (2015).
C.-N. Yeh and J.-D. Chai*, Sci. Rep. 6, 30562 (2016).
S. Seenithurai and J.-D. Chai*, Sci. Rep. 6, 33081 (2016).
C.-S. Wu, P.-Y. Lee, and J.-D. Chai*, Sci. Rep. 6, 37249 (2016).
S. Seenithurai and J.-D. Chai*, Sci. Rep. 7, 4966 (2017).
S. Seenithurai and J.-D. Chai*, Sci. Rep. 8, 13538 (2018).
C.-N. Yeh, C. Wu, H. Su*, and J.-D. Chai*, RSC Adv. 8, 34350 (2018).
J.-H. Chung and J.-D. Chai*, Sci. Rep. 9, 2907 (2019).
S. Seenithurai and J.-D. Chai*, Sci. Rep. 9, 12139 (2019).
Q. Deng and J.-D. Chai*, ACS Omega 4, 14202 (2019).
H.-J. Huang, S. Seenithurai, and J.-D. Chai*, Nanomaterials 10, 1236 (2020).
S. Seenithurai and J.-D. Chai*, Sci. Rep. 10, 13133 (2020).
S. Seenithurai and J.-D. Chai*, Nanomaterials 11, 2224 (2021).
C.-C. Chen and J.-D. Chai*, Nanomaterials 12, 3943 (2022).
Webinar on TAO-DFT
TAO-DFT (for single-point energy and analytical nuclear gradient calculations) is available in
Q-Chem 4.3 or higher
[Some features of TAO-DFT are briefly summarized in the Q-Chem 5 paper
J. Chem. Phys. 155, 084801 (2021)) and in the
3. Orbital-Free Density Functional Theory
a. Kinetic Energy Density Functional
a. Linear Response Theory
b. KEDFs in Certain Situations
c. Transferable Pseudopotentials
C. Suitable Systems:
Systems with 1,000~1,000,000 electrons (Kohn-Sham density functional theory is inappropriate due to its high computational cost)
4. Time-Dependent Density Functional Theory
A. Exchange-Correlation Action Functional
B. Excited States
C. Real-Time Electron Dynamics
D. Quantum Transport
E. Quantum Hydrodynamics
5. Materials for New Energy
A. Organic Solar Cells
B. Hydrogen Storage Materials