Unraveling Substituent E ects on Frontier Orbitals of ... · python script. • Step I: prepare...

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Supplementary Information for “Unraveling Substituent Effects on Frontier Orbitals of Conjugated Molecules Using an Absolutely Localized Molecular Orbital Based Analysis” Yuezhi Mao, 1 Martin Head-Gordon, 1 and Yihan Shao 2, a) 1) Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, CA 94720 2) Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, USA (Dated: 17 September 2018) a) Author to whom correspondence should be addressed; Electronic mail: [email protected] 1 Electronic Supplementary Material (ESI) for Chemical Science. This journal is © The Royal Society of Chemistry 2018

Transcript of Unraveling Substituent E ects on Frontier Orbitals of ... · python script. • Step I: prepare...

Page 1: Unraveling Substituent E ects on Frontier Orbitals of ... · python script. • Step I: prepare unpolarized fragment MOs on naphthalene (Naph) 1)From the optimized Naph-X geometry,

Supplementary Information for “Unraveling Substituent Effects on Frontier Orbitals

of Conjugated Molecules Using an Absolutely Localized Molecular Orbital Based

Analysis”

Yuezhi Mao,1 Martin Head-Gordon,1 and Yihan Shao2, a)

1)Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry,

University of California at Berkeley, Berkeley, CA 94720

2)Department of Chemistry and Biochemistry, University of Oklahoma, Norman,

Oklahoma 73019, USA

(Dated: 17 September 2018)

a)Author to whom correspondence should be addressed; Electronic mail: [email protected]

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Electronic Supplementary Material (ESI) for Chemical Science.This journal is © The Royal Society of Chemistry 2018

Page 2: Unraveling Substituent E ects on Frontier Orbitals of ... · python script. • Step I: prepare unpolarized fragment MOs on naphthalene (Naph) 1)From the optimized Naph-X geometry,

Section S1. PREPARATION OF THE FRAG STATE IN THE ALMO

ANALYSIS

Here we shall use a substituted naphthalene (Naph-X) as an example. The “FRAG”

state involves two “tailored-then-capped” fragments, whose generation is automated using a

python script.

• Step I: prepare unpolarized fragment MOs on naphthalene (Naph)

1) From the optimized Naph-X geometry, construct an unsubstituted naphthalene

(Naph-H) molecule, where the substituent group X is replaced by a hydrogen

atom. The H atom lies along the C-X bond at 1.086 A(as in fully optimized

Naph-H) from the carbon atom, while all other atoms retain the same coordinates

as in Naph-X.

2) Perform a standard SCF calculation on Naph-H.

3) Carry out Pipek-Mezey localization for the occupied orbitals, and identify the

orbital corresponding to the C-H σ-bond.

4) Truncate the C-H bond so that it is spanned only by AO functions on the asso-

ciated C and H atoms, then renormalize it.

5) Truncate all other orbitals on the Naph ring by zeroing out all coefficients for AO

functions on the terminal H atom; orthonormalize the occupied ones and create

their complementary virtuals in the full AO space of Naph (without the terminal

H).

6) Using these truncated orbitals as an initial guess, perform a generalized SCF-MI

calculation to obtain optimized fragment orbitals on the Naph ring, in which the

orbital for the C-H bond is kept frozen.

• Step II: prepare linking-bond and substituent group orbitals

7) From the optimized Naph-X geometry, construct a Ph-X molecule where the Naph

ring is replaced by a phenyl ring, where R(C-C) = 1.400 A, R(C–H)=1.086 A.

The phenyl ring is constrained to be in the same plane as the Naph ring, and the

carbon atom in the C–X bond is retained at the same position.

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8) Perform a standard SCF calculation on Ph-X.

9) Carry out Pipek-Mezey localization for the occupied orbitals, and identify the

orbital for the C-X bond and all other orbitals on the substituent.

10) Truncate the C-X bond orbital so that it is spanned only by AO functions on

the associated carbon atom (on the phenyl ring) and substituent atoms, then

renormalize it.

11) Truncate all other substituent/phenyl orbitals to make them absolutely local-

ized (spanned by AO functions on the substituent/phenyl ring only); as in step

#5 above, orthonormalize the occupied orbitals and create the complementary

virtuals on both fragments.

12) Perform a generalized SCF-MI calculation to optimize orbitals on the substituent

group (those on the phenyl ring are allowed to relax as well) with the C-X bond

orbital remaining frozen.

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Section S2. EFFECT OF THE DIMETHYLAMINO GROUP EVALUATED

USING THE 6-31+G(D) BASIS SET

FIG. S1. Effect of the dimethylamino group on the HOMO and LUMO of naphthalene calcu-

lated with B3LYP and the 6-31+G(d) basis. All orbital energies are in eV. Numbers in bottom

parentheses show the total energy of each intermediate state relative to that of the fully converged

state.

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FIG. S2. Interaction between polarized naphthalene and dimethylamino orbitals to yield the fully

converged molecular orbitals calculated with B3LYP/6-31+G(d). All orbital energies are in eV.

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Section S3. FROM 6-(PROPIONYL)NAPHTHALENE TO PRODAN

FIG. S3. Effect of the electron-donating dimethylamino group on the frontier orbitals of the 6-

(propionyl)naphthalene. All orbital energies are in eV. Numbers in bottom parentheses show the

total energy of each intermediate state relative to that of the fully converged state. Due to slightly

different geometries, HOMO and LUMO energies of the FRAG state are not exactly the same as

the values for the FULL state in Fig. 5.

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FIG. S4. Interaction between polarized 6-(propionyl)naphthalene and dimethylamino orbitals to

yield the fully converged molecular orbitals. All orbital energies are in eV.

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Section S4. FROM 2-(DIMETHYLAMINO)NAPHTHALENE TO PRODAN

FIG. S5. Effect of the electron-withdrawing propionyl group on the frontier orbitals of the 2-

(dimethylamino)naphthalene. All orbital energies are in eV. Numbers in bottom parentheses show

the total energy of each intermediate state relative to that of the fully converged state. Due to the

slightly different geometries, HOMO and LUMO energies of the FRAG state are not exactly the

same as the values for the FULL state in Fig. 3.

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FIG. S6. Interaction between polarized 2-(dimethylamino)naphthalene and propionyl orbitals to

yield the fully converged molecular orbitals. All orbital energies are in eV.

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Section S5. 2-(TRIFLUOROMETHYL)NAPHTHALENE

FIG. S7. Effect of the trifluoromethyl group (–CF3) on the frontier orbitals of naphthalene. All or-

bital energies are in eV. Numbers in bottom parentheses show the total energy of each intermediate

state relative to that of the fully converged state.

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