Constrained density functional theory in Q -Chem · PDF fileQ-Chem Workshop APCTCC6, Gyeong...
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Q Q - - Chem Chem Workshop Workshop APCTCC6, APCTCC6, Gyeong Gyeong - - ju ju , Korea , Korea July 10, 2013 July 10, 2013 Tim Tim Kowalczyk Kowalczyk Nagoya University Nagoya University Constrained density functional theory Constrained density functional theory in Q in Q - - Chem Chem
Transcript of Constrained density functional theory in Q -Chem · PDF fileQ-Chem Workshop APCTCC6, Gyeong...
QQ--ChemChem WorkshopWorkshop
APCTCC6, APCTCC6, GyeongGyeong--juju, Korea, Korea
July 10, 2013July 10, 2013
Tim Tim KowalczykKowalczyk
Nagoya UniversityNagoya University
Constrained density functional theoryConstrained density functional theory
in Qin Q--ChemChem
Acknowledgments
Troy Van Voorhis
Ben KadukQin Wu
Brookhaven National Laboratory
MIT Chemistry
MIT Kerberos Consortium
Why Constrained DFT?
Density functional approximations suffer from selfself--interaction errorinteraction error (SIE)
• Mixed-valence compounds:
unphysical charge delocalization
• Highly delocalized excited states:
underestimate excitation energies
• Barrier heights are too low
Strategies to overcome self-interaction error (and other flaws of XC functionals):
1. Make better functionals
2. Abandon DFT, go ab initio
3. Adopt strategies to work around SIE with existing work around SIE with existing functionalsfunctionals
Constrained density functional theory
We identify charge-localized states with ground states of constrained systems
• Introduce charge/spin constraints
on the density
• Constraints force density to conform toconform to
chemical intuitionchemical intuition by design
• Constrained energy is obtained at roughly
the cost of a ground state calculation
Constrained density functional theory
[ ] [ ] ( ) ( )
−+→ ∫∑∑
σ
σσ ρρρkk
k
kNdwVEE rrr
3
wk – weight operators defining the constraint region (Becke weights)
Vk – Lagrange multipliers to enforce the constraint
Nk – value of the desired charge/spin constraint
We identify charge-localized states with ground states of constrained systems
• Introduce charge/spin constraints
on the density
• Constraints force density to conform toconform to
chemical intuitionchemical intuition by design
• Constrained energy is obtained at roughly
the cost of a ground state calculation
Constrained density functional theory
Some rules of thumb:
CDFT delivers diabatic states
• Density-based weight operators (e.g. Becke) are more stable than AO-based
operators (Mulliken, Lowdin)
• Larger fragments give more stable energies and couplings
• CDFT may give unreliable results for very small donor-acceptor distances
States maintain their electronic maintain their electronic
charactercharacter over the reaction
coordinate of interest
CDFT Applications
Sticking curves for O2 incident on the
Al(111) surface
Charge distribution in the
intramolecular charge-transfer
excited state of a fluorescent
sensor dye
Constrained density functional theory –configuration interaction (CDFT-CI)
Electronic couplings between CDFT states
KSKSKS
2
)(ˆ)(ˆ
2
ˆ
B
BBAA
AAB
BA
BAAB
wVwVS
FF
HH
Φ+
Φ−+
≈
ΨΨ=
rr
Constrained density functional theory –configuration interaction (CDFT-CI)
Electronic couplings between CDFT states
KSKSKS
2
)(ˆ)(ˆ
2
ˆ
B
BBAA
AAB
BA
BAAB
wVwVS
FF
HH
Φ+
Φ−+
≈
ΨΨ=
rr
• Need to approximate approximate wavefunctionwavefunction of interacting systemof interacting system with Kohn-Sham
wavefunction – an uncontrolled approximation
• Can build and diagonalizediagonalize HamiltonianHamiltonian in basis of nonorthogonal CDFT states
to get adiabatic ground, excited states
Barrier heights in CDFT-CI
A ― XB AX ― B[A ― X ― B]‡
• Most XC functionals overdelocalizeoverdelocalize the electron densitythe electron density of [A ― X ― B]‡
• 22--state descriptionstate description of the transition state avoids overdelocalization;
reactant and product diabatic states are both well-described by XC functionals
• More realistic charge/spin constraints via promoleculepromolecule densitiesdensities:
CDFT-CI Applications
Qualitatively correct
description of conical intersections
Electronic couplings that show
the correct distance dependence
CASSCF
CDFT-CI
TDDFT
Summary
CDFT is a DFT prescriptionCDFT is a DFT prescription
for for diabaticdiabatic electronic stateselectronic states
•• CDFT energies, gradients, and HessiansCDFT energies, gradients, and Hessians
•• CDFTCDFT--CI energiesCI energies
Availability in QAvailability in Q--ChemChem 4.x:4.x:
Charge and spin constraints are appliedCharge and spin constraints are applied
to a groundto a ground--state Kohnstate Kohn--Sham calculationSham calculation
•• Gradients and Hessians are on the wayGradients and Hessians are on the way……
Improved description of: mixed-valence complexes, spin-frustrated systems, CT excited states, barrier heights…
Thanks!Thanks!
