adrian lange & john m. herbert department of chemistry ohio state university molecular...

Adrian Lange & John M. HerbertDepartment of Chemistry

Ohio State University

Molecular Spectroscopy Symposium, 6/21/07

Spurious charge-transfer contamination in large-scale TDDFT calculations:

A public service announcement

JMH group

Leif Jacobson

Dr. ChrisWilliams

AdrianLange

ShoumikChatterjee

The long-range CT problem in TDDFT

*Except those who don’t

• Everyone* knows that TDDFT woefully underestimates long-range CT excitation energies

• But just what, precisely, constitutes “long range” ?


*Except those who don’t

e–

~1.0/R

~0.5/R

~0.2/R

CIS (100% HF exchange)

LDA (0% HF exchange)

BHLYP (50% HF exchange)

B3LYP (20% HF exchange)

R / Å

[ E

(R)

– E

(4.0

Å)

] / e

V ~1.0/

R

~0.5/R

~0.2/R

R / Å

Ex.

en

erg

y /

eV

Long-range intermolecular CTDreuw et al., JCP (2003)




Long-range intramolecular CT



Dreuw & Head-Gordon JACS (2004)

Magyar & TretiakJCTC (2007)

ET

ET

Okay, so long-range ET is out of bounds

• But perhaps the theory is otherwise okay. After all, it works great* for small, gas-phase molecules.

*Typically 0.2–0.3 eV accuracy, for the lowest few valence-type excitations

pote

nti

al energ

y /

eV

N1–H bond length / Å

uracil singlet excited states



• Unfortunately, no. Spurious CT states have been observed for acetone/formamide in liquid water and clusters:– Bernasconi, Sprik, Hutter (JPC-B 2003; CPL 2004) – CPMD

– Besley (CPL 2004) – Q-Chem

– Neugebauer, Gritsenko, Baerends (JCP 2005) – ADF

*Typically 0.2–0.3 eV accuracy, for the lowest few valence-type excitations



• Unfortunately, no. Spurious CT states have been observed for acetone/formamide in liquid water and clusters.

Bernasconi, Sprik, HutterCPL (2004)

• BUT... popular hybrid functionals like B3LYP and PBE0 push these states up by ~1 eV, above the lowest valence bands. In

tensi

ty

/ eV

BLYP

B3LYP

PBE0

n*

CT



• Unfortunately, no. Spurious CT states have been observed for acetone/formamide in liquid water and clusters.

Bernasconi, Sprik, HutterCPL (2004)

• BUT... popular hybrid functionals like B3LYP and PBE0 push these states up by ~1 eV, above the lowest valence bands.

How robust are these hybrids?

A sequence of uracil–water clusters

R = 1.5 ÅNwater = 0







Extracted from a single MD snapshot (T=298 K, =1.0 g/cm3)

TD-PBE0 results vs. cluster sizeEx. energies below 6 eV 40th excitation energy

• QM region: PBE0/6-31+G*

TD-PBE0 results vs. cluster size

• QM region: PBE0/6-31+G*

• MM region: TIP3P charges out to 20 Å

Ex. energies below 6 eV 40th excitation energy

Typical CT excited states

4.5 eV

5.6 eV

4.3 eV

4.5 eV

blue = detachment densitypurple = attachment density

TDDFT/TDA working equations

• Solve eigenvalue eqn. Ax = x for excitation energies , where x = (xia) is a vector of occupied ( |i>) to virtual (|a>) excitation amplitudes

• If |i> and |a> are spatially distant, then [Dreuw et al. JCP (2003)]

• TIP3P charges stabilize water lone pairs on the edge of the cluster, pushing water-to-uracil CT excitations to higher energy

Aia,jb = (a – i) ijab – cHF (ij|ab)

QM/MM: Pure vs. hybrid functionals

QM cluster radius / Å

Ex. energies below 6 eV 40th excitation energy

QM cluster radius / Å

B3LYP (cHF = 0.2) behaves much the same as PBE0

(cHF = 0.25)

(cHF = 0)

(cHF=0.25)

(cHF=0)

QM/MM electronic absorption spectraB3LYP PBE0Size of QM region

R = 1.5 Å(uracil only)

R = 2.5 Å(“microhydrated”)

R = 4.5 Å(full solvation

shell)

40 excited states req’d to reach 6.8

eV

Spurious intensity stealing

Excitation energies (i) and oscillator strengths (ƒi ) from QM/MM

blue = detachment density

purple = attachment density

Spurious intensity stealing --------------------------------------------------- TDDFT/TDA Excitation Energies ---------------------------------------------------

Excited state 1: excitation energy (eV) = 4.2793 Total energy for state 1: -2322.842189693738 Multiplicity: Singlet Trans. Mom.: -0.0640 X -0.0680 Y -0.0578 Z Strength : 0.0013 D(154) --> V( 2) amplitude = 0.9738

Excited state 7: excitation energy (eV) = 5.0455 Total energy for state 7: -2322.814030524368 Multiplicity: Singlet Trans. Mom.: 0.1804 X -0.6829 Y -0.1392 Z Strength : 0.0641 D(151) --> V( 2) amplitude = 0.3653 D(152) --> V( 1) amplitude = 0.3714 D(152) --> V( 2) amplitude = 0.7596

Excited state 8: excitation energy (eV) = 5.0531 Total energy for state 8: -2322.813753118397 Multiplicity: Singlet Trans. Mom.: -0.1953 X 0.4639 Y -0.0488 Z Strength : 0.0317 D(151) --> V( 1) amplitude = -0.5382 D(151) --> V( 2) amplitude = -0.2623 D(152) --> V( 1) amplitude = 0.6666 D(152) --> V( 2) amplitude = -0.2499

...

Excited state 9: excitation energy (eV) = 5.0822 Total energy for state 9: -2322.812684185100 Multiplicity: Singlet Trans. Mom.: 0.0763 X -0.3729 Y -0.0894 Z Strength : 0.0190 D(147) --> V( 2) amplitude = 0.3182 D(149) --> V( 2) amplitude = -0.2723 D(151) --> V( 2) amplitude = 0.6347 D(152) --> V( 2) amplitude = -0.5571

Excited state 10: excitation energy (eV) = 5.1582 Total energy for state 10: -2322.809891225142 Multiplicity: Singlet Trans. Mom.: -0.1382 X 0.3452 Y 0.0368 Z Strength : 0.0176 D(140) --> V( 2) amplitude = 0.2390 D(147) --> V( 2) amplitude = 0.5259 D(149) --> V( 2) amplitude = -0.4967 D(151) --> V( 2) amplitude = -0.4595

Excited state 11: excitation energy (eV) = 5.2025 Total energy for state 11: -2322.808260470356 Multiplicity: Singlet Trans. Mom.: -0.0665 X -0.2645 Y -0.2073 Z Strength : 0.0150 D(151) --> V( 2) amplitude = 0.2279 D(154) --> V( 5) amplitude = 0.8782 D(154) --> V( 6) amplitude = -0.3163...

Another small system with long-range problems

black = attachment density

TD-PBE0/6-31+G* calculations on a gas-phase GC base pair

Summary: Long-range CT in TDDFT

• “Long range” is any time (squares of) orbitals do not overlap. Uracil–(H2O)4 is large enough.



• Spurious states impose a major memory bottleneck: Nwords ~ 2 NO NV Nroots Niter / 1.5




• QM/MM absorption spectra look okay below 6 eV, even with > 120 QM atoms, but watch out for spurious intensity stealing.




• QM/MM absorption spectra look okay below 6 eV, even with > 120 QM atoms, but watch out for spurious intensity stealing.

• This is a work in progress. Long-range K, subspace truncation, asymptotic correction, etc., are required to make TDDFT a robust method.

Long list of spurious charge-transfer states

Gaussian user

Just because it came from B3LYP doesn’t make it right...

Thanks:

Spectra from gas-phase clusters

Absorption spectrum(Gas-phase QM region)

Absorption spectrum(QM/MM)

Density of states (Gas-phase QM region)

40 excited states to reach 5.4

eV

microhydrated

full solvationshell

adrian lange & john m. herbert department of chemistry ohio state university molecular...

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