Constrained density functional theory in Q -Chem · PDF fileQ-Chem Workshop APCTCC6, Gyeong...
Transcript of Constrained density functional theory in Q -Chem · PDF fileQ-Chem Workshop APCTCC6, Gyeong...
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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
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Acknowledgments
Troy Van Voorhis
Ben KadukQin Wu
Brookhaven National Laboratory
MIT Chemistry
MIT Kerberos Consortium
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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
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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
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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
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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
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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
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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
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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
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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:
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CDFT-CI Applications
Qualitatively correct
description of conical intersections
Electronic couplings that show
the correct distance dependence
CASSCF
CDFT-CI
TDDFT
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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…
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Thanks!Thanks!