Enhanced diastereocontrol via strong light-matter interactions in an optical cavity Nam Vu Grace M. McLeod Kenneth Hanson and A. Eugene DePrince IIIa

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Enhanced diastereocontrol via strong light-matter interactions in an optical

cavity

Nam Vu, Grace M. McLeod, Kenneth Hanson, and A. Eugene DePrince IIIa)

Department of Chemistry and Biochemistry, Florida State University, Tallahassee,

FL 32306-4390

The enantiopuriﬁcation of racemic mixtures of chiral molecules is important for a range of applications.

Recent work has shown that chiral group-directed photoisomerization is a promising approach to enantioenrich

racemic mixtures of BINOL, but increased control of the diasteriomeric excess (de) is necessary for its broad

utility. Here we develop a cavity quantum electrodynamics (QED) generalization of time-dependent density

functional theory and demonstrate computationally that strong light-matter coupling can alter the de of chiral

group-directed photoisomerization of BINOL. The relative orientation of the cavity mode polarization and the

molecules in the cavity dictates the nature of the cavity interactions, which either enhance the de of the (R)-

BINOL diasteriomer (from 17% to ≈40%) or invert the favorability to the (S)-BINOL derivative (to ≈34%

de). The latter outcome is particularly remarkable because it indicates that the preference in diasteriomer can

be inﬂuenced via orientational control, without changing the chirality of the directing group. We demonstrate

that the observed eﬀect stems from cavity-induced changes to the Kohn-Sham orbitals of the ground state.

I. INTRODUCTION

Chiral molecules are ubiquitous in food additives,

pharmaceuticals, catalysts, and elsewhere; the genera-

tion of enantiopure molecules is thus critical for these

applications.1Molecules containing axial chirality like

BINOL ([1,1’-binaphthalene]-2,2’-diol) and its deriva-

tives are of particular interest because they are popu-

lar chiral ligands for a wide range of asymmetric cat-

alytic reactions.2,3 Enantiopure BINOL (i.e., either pure

Ror S) is typically obtained via chiral chromatography,

strategic recrystallization, or direct asymmetric synthe-

sis. However, separation methods often require large

quantities of solvent or result in substantial loss of start-

ing material (i.e. the undesired isomer), while syn-

thetic means rely upon already enantiopure catalysts.2

Recently, chiral-group-directed photoisomerization was

introduced as an alternative means of enantioenriching

racemic mixtures of BINOL, and this strategy could the-

oretically result in 100% yield and 100% diastereomeric

excess (de).4Upon excitation in the presence of a base,

BINOL is known to isomerize via an excited-state pro-

ton transfer (ESPT) mechanism.5–7 When one of its two

-OH groups is functionalized with a chiral directing group

[such as (S)-Boc-Proline, see Fig. 1] the isomerization is

biased such that the de at the photostationary state is

dictated by the nature of this group and its impact on

the energetics of the excited state diastereomers. While

this approach shows promise, the best de observed in

Ref. 4 (63%) was below the enantiopurity necessary for

most applications (>95%). Ultimately one would like

to not only enhance this de but also to exert some con-

trol over the chirality of the resulting product. Toward

these aims, the present study explores how strong light-

matter coupling can modulate the obtainable de and di-

a)Electronic mail: adeprince@fsu.edu

astereomeric preferences in ESTP-driven puriﬁcation of

BINOL derivatives.

Recently, there has been an explosion in interest har-

nessing strong light-matter interactions in optical cavities

for chemical applications,8–11 with a number of exper-

imental and computational studies demonstrating vari-

ous aspects of control over chemical transformations.12–20

Cavity-induced changes to electronic structure could be

particularly impactful in the areas of asymmetric syn-

thesis and puriﬁcation where even small changes in en-

ergy can have a large eﬀect on the resulting enan-

tiomeric/diastereomeric excess. Several recent com-

putational studies have demonstrated that >1 kcal

mol−1changes to spin-state splittings21 or reaction bar-

rier heights22,23 can be realized via strong coupling of

molecules to an optical cavity. In the context of the

ESPT-driven enantiopuriﬁcation depicted in Fig. 1, en-

ergy changes of this magnitude would result in dra-

matic changes to the observed de. As an example, as-

suming that the de reported in Ref. 4 are determined

solely by the relative energies of the ﬁrst excited states

of the (S)-Boc-Pro-(R)-BINOL and (S)-Boc-Pro-(S)-

BINOL diastereomers, the 63% de observed in that work

would correspond to a roughly 0.9 kcal mol−1diﬀerence

in energies in these states (see Eqs. 6 and 7 below). A

>95% de would require increasing this energy diﬀer-

ence by roughly 1.3 kcal mol−1. Given the magnitudes

of energy changes predicted in other computational stud-

ies of cavity-bound molecules, it is reasonable to expect

that suﬃciently strong light-matter interactions could al-

ter the relative energies of these states such that a >95%

de would be attainable via the ESPT mechanism consid-

ered here.

In this work, we use ab initio cavity quantum electro-

dynamics (QED) methods to explore how cavity inter-

actions can inﬂuence the outcome of the ESPT-driven

diastereomeric enrichment protocol shown in Fig. 1. We

develop a cavity QED generalization of time-dependent

density functional theory (TDDFT) for this problem in

arXiv:2210.04991v1 [physics.chem-ph] 10 Oct 2022

(S)-Boc-Pro-(R/S)-BINOL

(S)-Boc-Pro-(R)-BINOL

(S)-Boc-Pro-(S)-BINOL

Et3N, toluene, rt

hν

86%, %de=31(R)

FIG. 1. Enantioenrichment of (S)-Boc-Proline functionalized BINOL [(S)-Boc-Pro-(R/S)-BINOL] by ESPT. The yield (86%)

and de (31%) correspond to those reported in Ref. 4.

Sec. II and outline the details of our calculations in

Sec. III. In Sec. IV, we apply QED-TDDFT to this

diastereomeric enrichment problem, and we ﬁnd that

strong light-matter coupling can drive the de toward

either diastereomer, depending on orientation of the

molecule relative to the cavity mode polarization. After

some concluding remarks in Sec. V, a complete deriva-

tion of the QED-TDDFT approach that we employ can

be found in Appendices A and B.

II. THEORY

Computational cavity QED studies often use simple

model Hamiltonians24,25 that describe interactions be-

tween quantized radiation modes and few-level quantum

emitters. A more rigorous description of molecular de-

grees of freedom can be obtained from ab initio cav-

ity QED approaches, which resemble familiar electronic

structure methods, but are generalized to describe both

electron-electron and electron-photon interactions. Ex-

amples of calculations performed using cavity QED ex-

tensions of density functional theory,26–41 coupled-cluster

theory,22,42–49 conﬁguration interaction,50 or reduced-

density-matrix methods21 are becoming increasingly

commonplace. In this work, we adopt a QED-TDDFT

formalism that most closely resembles the Gaussian-basis

formalism described in Ref. 39. A detailed derivation of

working equations for QED-TDDFT can be found in that

work, and we present our own derivation, which results in

slightly diﬀerent equations, in Appendix B. In this sec-

tion, our aim is to describe the approach with enough

detail such that slight diﬀerences between the formalism

outlined in Ref. 39 and that which we use can be under-

stood.

Interactions between electronic degrees of freedom

and quantized radiation ﬁelds associated with an op-

tical cavity can be described by the Pauli-Fierz (PF)

Hamiltonian.51,52 We limit our considerations to a cavity

that supports a single photon mode, and we express this

Hamiltonian in the length gauge and under the dipole

and cavity Born-Oppenheimer approximations as

ˆPF =H

ˆe+ωcavb

ˆ†b

ˆ−ωcav

2(λ·ˆµ)(b

ˆ†+b

ˆ)

2(λ·ˆµ)2(1)

Here, the ﬁrst two terms are the usual electronic Hamilto-

nian (H

ˆe) and the Hamiltonian for the photon mode; ωcav

is the fundamental frequency associated with this mode,

and b

ˆ†and b

ˆrepresent bosonic creation and annihilation

operators, respectively. The third and fourth terms in

Eq. 1 represent the bilinear coupling between the elec-

tron and photon degrees of freedom and the dipole self-

energy, respectively. The symbol ˆµrepresents the total

molecular dipole operator (electronic plus nuclear, i.e.,

ˆµ=ˆµe+ˆµn), and the coupling vector, λ, parametrizes

the strength of the photon-electron interactions. We are

interested in single-molecule coupling, in which case we

take λ=λu, where uis a unit vector describing the po-

larization of the cavity mode, and the magnitude of the

coupling vector, λ, relates to the eﬀective cavity mode

volume as13

λ=1

ϵ0Veﬀ

(2)

Here, ϵ0is the permittivity of free-space. At this point,

we can note one diﬀerence between the present formal-

ism and that outlined in Ref. 39. In Ref. 39, the expec-

tation value of the dipole operator enters Eq. 1, rather

than the dipole operator itself; in that case, as described

below, cavity interactions do not perturb the ground-

state Kohn-Sham orbitals. On the other hand, with the

Hamiltonian in Eq. 1, the Kohn-Sham orbitals can relax

to account for the presence of the cavity. For this reason,

we refer to QED-TDDFT based on the formalisms out-

lined in Ref. 39 and herein as “unrelaxed” and “relaxed”

QED-TDDFT, respectively.

Similar to the case in Kohn-Sham DFT, the ground-

state in QED-DFT maps onto a non-interacting reference

function of the form

|Ψ⟩=|0e⟩⊗|0p⟩(3)

where |0e⟩refers to a Kohn-Sham determinant of elec-

tronic spin orbitals, and |0p⟩represents a zero-photon

state. These functions can be determined via a mod-

iﬁed Roothaan-Hall procedure: (i) |0e⟩can be deter-

mined as the Kohn-Sham determinant that minimizes

the electronic energy, given a ﬁxed |0p⟩, and (ii) |0p⟩

can be determined as the lowest-energy eigenfunction of

⟨H

ˆPF⟩e, where the subscript “e” indicates that we have

integrated out the electronic degrees of freedom. For the

ﬁrst step, electron correlation and exchange eﬀects can

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Enhanceddiastereocontrolviastronglight-matterinteractionsinanopticalcavityNamVu,GraceM.McLeod,KennethHanson,andA.EugeneDePrinceIIIa)DepartmentofChemistryandBiochemistry,FloridaStateUniversity,Tallahassee,FL32306-4390Theenantiopurificationofracemicmixturesofchiralmoleculesisimportantforarangeofapplic...

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Enhanced diastereocontrol via strong light-matter interactions in an optical cavity Nam Vu Grace M. McLeod Kenneth Hanson and A. Eugene DePrince IIIa

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