Research Activity in Nakai Group
TargetAlgorithm

TheoryNuclearWavefunction

NOMO

Ground StateDCElectron
Correlation

DC

Excited StateDC

Ground-State
Dynamics
Non-adiabatic
Dynamics
Relativity

MD

MachineLearning

ML

NOMO-HF
NOMO-MBPTNOMO-CC
DC-HF
DC-DFT
DC-DFTB
DC-MP2
DC-CCSD
DC-CCSD(T)
DC-TDDFT
DC-CCLR
DC-TDDFTB
DC-DFTB-MD
DC-DFTB-MetaD
DC-TDDFTB-FSSH
DC-SF-TDDFTB-FSSH
LUT-IOTC
LUT-IOTC/LUT-IOTC
ML-EC
ML-KEDF

FSSH
LUT

Program

DCDFTBMD??

1Programing in Nakai Groupz … Mark seems to like LUT more than

GAMESS Documentation

the other relativistic methods.
$CONTRL group…
RELWFN
Selects all-electron scalar relativity treatment.
See the $RELWFN input group for more information,including nuclear derivative availability.
= NONE use the basic Schrodinger equation (default)= LUT-IOTC local unitary transformation modificationof IOTC, due to H.Nakai, J.Seino, Y.Nakajima.
This is the fastest and most numericallyreliable scalar relativity method, so it ispreferred over RESC, DK, or IOTC.
= IOTC infinite-order two-component method of …
= DK
Douglas-Kroll transformation, available at …
= RESC relativistic elimination of small component,…
= NESC normalised elimination of small component,…
2

Function of DCDFTBMD Program
Function
Energy, Gradient, Hessian Closed-shell system: DFTB1/2/3, Orbital resolved SCC
Open-shell system: Spin-polarized DFTB
Linear-scaling method

Divide and conquer (DC)Charge-charge interaction

Ewald, FMM, Spline interpolation

SCC corrections

SCC convergence

Chemical potential equalization, DFTB+U,
Weighted Mulliken scheme, On-site corrected DFTB,
Long-range correction (LC-DFTB2),
Finite-temperature calculation,
Point charge for external field effect,
Static electric field for external field effect
Implicit solvation model (GBSA/ALPB)
Broyden, Simple mixing, Anderson, DIIS

Excited-state calculation

Time-dependent DFTB, Spin-flip time-dependent DFTBDispersion correction

Slater-Kirkwood, Lennard-Jones, DFT-D2/D3/D4,DFT-ulg, dDMC, D3H4, D3H5, D3X, DFT-TS, MBD

Property evaluation

Mulliken charge, CM3/CM5 charge, Mayer bond order,
Dipole moment, Static polarizability, Atom resolved
energy3Function of DCDFTBMD Program (cnt’d)
Function
Local geometry
optimization
Global optimization

BFGS, Steepest descent, Conjugate gradient,
Quick-min, FIRE
Monte Carlo minimization (Basin hopping)

Reaction path finding

Nudged elastic band (NEB)

Transition state search

Dimer method

Vibrational analysis

Harmonic frequency, IR intensity, Raman activity,
Thermochemical quantities
NVE, NVT, NPT

MD ensemble
MD thermostat

Non-adiabatic MD

Velocity scaling, Nose-Hoover chain, Berendsen,
Andersen
RATTLE, Soft potential, Lagrange interpolation initial
guess charge, Least square fitting initial guess charge
Metadynamics (MetaD), Well-tempered metaD,Multiple-walkers metaD, Replica exchange MD,
Parallel-tempering metaD
Fewest switches trajectory surface hopping (FSSH)

Quantum dynamics

Path Integral MD (PIMD), Ring Polymer MD (RPMD)

MD option
MD sampling4Release of DCDFTBMD Program
Release as academic-free softwarez http://www.chem.waseda.ac.jp/dcdftbmd
z November 1st, 2018

Worldwide users（2020.10.10）

Y. Nishimura, H. Nakai, J. Comput. Chem., 40, 1538 (2019).
Y. Nishimura, T. Yoshikawa, H. Nakai, J. Comput. Chem. Jpn., 17, A21 (2018).

5Large-Scale Reaction Simulation
Bond formation/cleavagez Electron transfer
z Dynamical behaviorz Tens of thousands of atoms
zQuantum Mechanics (QM)
Molecular Dynamics (MD)Linear-Scaling Method

QM-MD

Classical MD
MM

WFT

DFT

DFTB

DC-DFTB

Cluster collision

Electrolyte
decomposition

Growth ofnanotubeCO2chemisorption

Virus

< 100

< 1,000< 1,000~1,000,000~10,000,000

Big gap!!
6

Massive-Parallel DC-DFTB Code…
…
H0α, Sα, γα, Γα
SCCFαMPI： all-to-all
Determine common Fermi level1) Assign each fragment to each node2) Determine localization region and save itsinformation3) Calculate Erep4) Calculate H0α & Sα5) Calculate γα & Γα6) Calculate EDFTB7) Construct Fock matrix, Fα8) Diagonalize FαDα9) Construct subsystem’s density matrix, Dαqα10) Calculate subsystem’s charge, qα
MPI： all-to-allq11) Calculate total charge, q

H. Nishizawa, Y. Nishimura, K. Kobayashi, S. Irle, H. Nakai, J. Comput. Chem., 37, 1983(2016).

7

Applications of DCDFTBMD ProgramWater box(~23×106 atoms)

Na+/K+hydrate-melt(ACIE, 2019)107
Number of atoms

OH- containing
aqueous solution(JPCB, 2017)

Bacteriorhodopsin
embedded in lipid
membrane withwater

106

Achievementof “K”

Target of“Fukaga”

Photoactive
yellow protein(JCCJ, 2018)

105
104
103

Lead iodide
perovskite
material(PCCP, 2020)

Superconcentrated
electrolyte solution(JPCB, 2018)

1 fs 1 ps 1 ns 1 μs 1 ms

Bacteriorhodopsin
in gas phase(JPCB, 2020)

Simulation timeNa+ containing
electrolytesolution(ACIE, 2019)

CO2 capturein amine solution(BCSJ, 2017)

Carbonaceous species diffusion
on γ-Al2O3 surface(ACS Omega, 2020)

8Excited-State Calculation of PYP
z DC-type Excited-State Calculations

Methods: DC-TDDFTB, DC-TDDFT, DC-SACCIz Model: Whole PYP
zMethod
DC-TDDFTB
DC-TDLCDFTB
DC-TDBLYP
DC-TDB3LYP
DC-TDLCBLYP
DC-SACCI
Exptl.

Excitation
Energy [eV]
2.17
2.80
2.33
3.12
2.85
2.89
2.78

(diff.)(-0.61)(0.02)(-0.45)(0.35)(0.07)(0.11)―

Wall Time
[sec]
1.25
2.04
663.82776.401017.042484.00―

T. Yoshikawa, N. Komoto, j. Ono, Y. Nishimura, H. Nakai, J. Chem. Theory Comput., 15,1719 (2019).

9Perovskite Solar Cell Materialsz

Photoexcited-State Dynamics
zSurface hopping simulations probed charge separation processes

CsPbI3

MAPbI3•

Potential energy surfaces•Separation of hole (+, red) and electron (-, blue)

H. Uratani, H. Nakai, J. Phys. Chem. Lett. 11, 4448 (2020).

10RAQET Programz Efficient 1c & 2c Rel QC Program
Functions
HF
MP2
DFTCorrelation
Excited State
Hamiltonian
Initial Guess
Hamil. Gradient
HF Gradient
MP2 Gradient
Basis Function
1E Integral
2E Integral
Integral AlgorithmCore Potential
SCF Conv.
Linear Scaling
Optimization
Others

Details
R, U, RO, KR, KU, KRO, G (disk, direct)
R, U, RO, KR, KU, KRO, G (disk, direct)
R, U, RO, KR, KU, KRO, G (collinear, non-collinear, PCC)
MPn, CI, CC
EOM-CC, TDDFT(R, U, G)
NR, DKHn/NR, IODKH/NR(SF/SD, LUT), IODKH/IODKH (SF/SD, LUT)
Hcore, Extended Hückel, Atomic density, Small basis, MO read, DM readGradientNR, IODKH/NR(SF/SD, LUT), IODKH/IODKH (SF/SD, LUT)R, U, RO, KR, KU, KRO, GR, U, RO, KR, KU, KRO, G
Cartesian, Spherical harmonics
Overlap, Kinetic, V, pVp (derivative)
ERI, pVp, ppVpp (derivative), FMM
ACE-RR, ACE-TRR (GC/SC), Gauss-Rys, PH+MD (SMASH)
MCP, AIMP, FCP, FCP-MP
C1-DIIS, C2-DIIS, E-DIIS, SO-SCF, Level shifting, Fock extrapolation, Damping, FON
DC-SCF, DC-correlation
BFGS, RFO, Cartesian coordinate, Redundant coordinate, G-DIIS, Hessian
Expectation values, Electric/Magnetic properties, Solvent effect

M. Hayami, J. Seino, Y. Nakajima, M. Nakano, Y. Ikabata, T. Yoshikawa, T. Oyama, K. Hiraga, S. Hirata,
H. Nakai, J. Comput. Chem., 39, 2333 (2018).

11Feature of RAQET Programz

Overall Linear-Scaling
Rel QC Method

Accompanying Coordinate Expansion& Transferred Recurrence Relation(ACE-TRR)
for efficient evaluation of OEI & TEI

Local Unitary Transformation(LUT)
for efficient constructionof 2c Rel Hamiltonian
Divide-and-Conquer(DC)for efficient calculationof HF & Post-HF schemes
M. Hayami, J. Seino, H. Nakai, J. Comput. Chem., 35, 1517 (2014).
J. Seino, H. Nakai, J. Chem. Phys., 136, 244102 (2012).

12Performance of RAQET Programz CPU Time of (HCl)n Molecule[5]BS: Primitive 6-311G**
z DC-HF Buffer: 5 unitsz DC-Corr. Buffer: 2 unitsz

4c Dirac-Coulomb

4c Dirac-Coulomb

2c MMF×××

LUT-SF-IODK/IODK

LUT-SFIODK/IODK
DC-NR/C
DC-LUT-SFIODK/IODK×××

CPU time for MP2 calculations.
J. Seino, H. Nakai, J. Chem. Phys., 139, 034109 (2013).

DC-LUT-SFIODK/IODK××××

DC-NR/C××

CPU time for CCSD calculations.
13Download of RAQET Programz Download at www.chem.waseda.ac.jp/raqet/
zRegistration (1 License for 1 Group)14