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
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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