Molecular Properties through Polarizable Embedding

Jogvan Magnus Haugaard Olsen1, Arnfinn Hykkerud Steindal2, Kestutis Aidas3 and Jacob Kongsted1

1Department of Physics and Chemistry, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark2Centre of Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway

3Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden

IntroductionWe present a multilevel model which we denote thepolarizable embedding (PE) method(1) and is imple-mented in the DALTON program(2).

Layered model designed for effective inclusion ofan anisotropic environment in a QM calculation

Atomistic representation including terms up tolocalized octupoles and anisotropic dipolepolarizabilities

Fully self-consistent nonequilibrium formulationof the environmental response

Combined with TDQM linear and nonlinearresponse

Parallelized for large scale calculations

Figure 1: The DsRed protein tetramer: the chromophoresubsystem is treated using QM while the protein environmentis represented by a classical potential

TheoryThe PE method accurately models the effects fromthe environment surrounding a central core subsys-tem by including the effects directly in the den-sity/wavefunction of the core. Here we outline thePE-DFT method:

Effective Kohn-Sham operator

feff = fKS + vPE

Polarizable Embedding operator

vPE = v esPE + v ind

PE

Electrostatic contribution

v esPE =

∑s

∑k

(−1)(k+1)

k!Q(k)

s

∑pq

T(k)s,pqEpq

Q(k)s are kth order multipole moments

Q(0)s = qs,Q

(1)s = µs,Q

(2)s = Θs, · · ·

T(k)s,pq are integrals over the interaction tensors

T(k)s =

(∂

∂rx

)kx(∂

∂ry

)ky(∂

∂rz

)kz 1

|r − rs|

Polarization/induction contribution

v indPE = −

∑s

µinds

∑pq

T(1)s,pqEpq

induced dipoles obtained as classical linear response

µinds = αs (Fel(rs) + Fnuc(rs) + Fmul(rs) + Find(rs))

Theory (continued)The PE method is combined with linear, quadraticand cubic response in a fully self-consistent formal-ism. Here we show the linear response PE-TDDFTformalism:

Linear response function

〈〈A; B〉〉ω = −A†(E− ωS

)−1B

Polarizable Embedding contribution

EPEκω = −〈0|[q, Qω

1 + Qω2 |0〉

response from static environment

Qω1 = [κω, v 0

PE] = v 0PE(κω)

dynamical response from the environment

Qω2 = vωPE =

∑s

µinds (Fω)T(1)

s

transformed electric field

Fω = 〈0|[κω, T(1)s ]|0〉 = 〈0|T(1)

s (κω)|0〉

The contributions to the quadratic and cubic responseare obtained in a similar manner.

Typical WorkflowObtain structures

MD snapshotscrystal structuregeometry optimization

Fragment environment (see Fig. 5)amino acid residuesnucleotide fragmentssolvent molecules

Calculate localized properties of fragmentsmultipole moments upto octopolesanisotropic dipole polarizabilities

Merge fragments to create the polarizableembedding potential

Calculate property of interest using PE-DFTexcitation energies with OPA, TPA and 3PA(hyper)polarizabilities: α, β and γexcited state dipole moment and polarizabilitymagnetic properties using GIAOs/LAOs· · ·

Acetone in Water Solution

Solventshift(eV)

0.00

0.10

0.20

0.30

0.40

Force field

M0M1M2M3

M0P1

M1P1

M2P1

M2P2

M2P2BM

M0PCM

M1PCM

M2PCM

AhlströmTIP3P

0.143

PE-CAM-B3LYP/aug-cc-pVDZExperiment (0.22 eV)

0.0920.148

0.219

0.155

0.2300.249

0.224

0.153

0.1230.179

0.178

0.165

0.139

Acetone

Figure 2: Solvent shift of the n→ π∗ excitation in acetonecompared to experiment

Computational details:

Classical MD run using polarizable force fieldextracted 120 snapshot (every 10th ps)

Calculated average n→ π∗ excitation energyLoProp(3) force fieldsCAM-B3LYP/aug-cc-pVDZ

Potential AnalysisHere we present an analysis of the quality of the clas-sical potentials of the H2O and CCl4 molecules. Theplots show the RMSD, with respect to the distancefrom the molecular van-der-Waals surface, of the elec-trostatic potential due the classical potentials com-pared to a QM reference. Kvdw is a factor of the vdwdistance. Mx designates a potential with multipolemoments upto xth order and M* includes only RESPfitted charges.

RMSD

0.000

0.005

0.010

0.015

0.020

0.025

Kvdw

1.0 1.5 2.0 2.5 3.0 3.5 4.0

M*M0M1M2M3

Figure 3: Water

RMSD

0.000

0.005

0.010

0.015

0.020

0.025

Kvdw

1.0 1.5 2.0 2.5 3.0 3.5 4.0

M*M0M1M2M3

Figure 4: Tetrachloromethane

H3N

HN

O

O

R2O

R1

H3N

HN

O

R1

HHc

HcHc

HN

O

R2O

OH

Hc

Hc

HN

HHc

HcH

Hc

O

Figure 5: Outline of a fragmentation procedure for proteins

AcknowledgementsThis work has received support from the Danish Cen-ter for Scientific Computing (DCSC) and the DanishNatural Science Research Council/The Danish Coun-cils for Independent Research.

References(1) J. M. Olsen; K. Aidas; J. Kongsted; J. Chem. Theory Com-put. 2010, 6, 3721.

(2) Development version of DALTON, a molecularelectronic structure program, Release 2.0 (2005), seehttp://daltonprogram.org/

(3) L. Gagliardi, R. Lindh, and G. Karlstrom; J. Chem. Phys.2004, 121, 4494.