^{1}, R. A. McAloney

^{1}, D. Moffatt

^{1}, N. Mora-Diez

^{1,a)}and M. Z. Zgierski

^{1}

### Abstract

Quantitative measurements of second-harmonic generation optical activity (SHG-OA) have been performed for -helical polypeptides poly-(-benzyl--glutamate) and poly-(-ethyl--glutamate) adsorbed at the air∕water interface, with the fundamental frequency . The chiral component of the nonlinear susceptibility is small for both polymers, being comparable in magnitude with the susceptibility of the clean air∕water interface. The microscopic origin of the nonlinear response has been investigated by using semiempirical ZINDO∕S calculations in conjunction with standard time-dependent perturbation theory to evaluate the molecular hyperpolarizability tensor of a model -helix composed of glycine residues. Calculated nonlinear susceptibilities (per monomer unit) are in good agreement with experimental measurements for both the chiral and achiral response. The computational results indicate that charge transfer transitions of the -helix have a large influence on the achiral components of the hyperpolarizability tensor, and produce characteristic features in the response under suitable experimental conditions. The dominant origin of SHG-OA for the model -helix is a structural effect due to the tilt of the plane of each amide group of the helix relative to the helical axis. SHG-OA is associated with the orientational distribution of isolated, achiral chromophores, and is present in the absence of electronic coupling between the amide subunits of the polypeptide -helix.

The authors thank Dr. Albert Stolow for invaluable technical assistance with the laser source that was used in this study.

I. INTRODUCTION

II. EXPERIMENTAL SECTION

III. COMPUTATIONAL METHOD

IV. RESULTS AND DISCUSSION

A. Measurement of nonlinear susceptibilities

B. Calculation of nonlinear susceptibilities

C. Achiral contribution to nonlinearity

D. Chiral contribution to nonlinearity

V. CONCLUSION

### Key Topics

- Chiral symmetries
- 51.0
- Polymers
- 26.0
- Excited states
- 15.0
- Tensor methods
- 15.0
- Optical susceptibility
- 11.0

## Figures

Model right-handed -helix composed of seven glycine residues. (a) Illustration of molecular structure showing carbon, oxygen, and nitrogen atoms in progressively darker shades of gray. Hydrogen atoms are shown in white. (b) Division of model -helix into seven -methylacetamide monomers, with the orientations of the amide groups preserved. (c) End-on view of model -helix, showing only the carbonyl groups. Note that the CO bonds are tilted away from the long axis of the helix.

Model right-handed -helix composed of seven glycine residues. (a) Illustration of molecular structure showing carbon, oxygen, and nitrogen atoms in progressively darker shades of gray. Hydrogen atoms are shown in white. (b) Division of model -helix into seven -methylacetamide monomers, with the orientations of the amide groups preserved. (c) End-on view of model -helix, showing only the carbonyl groups. Note that the CO bonds are tilted away from the long axis of the helix.

Rotation traces for the polypeptides PBLG and PELG and for the achiral surfactant DBSA adsorbed at the air∕water interface. The solid lines are fits of the data to Eq. (8). Note that the traces for the chiral interfaces PBLG and PELG are asymmetric about , and the trace for the achiral interface DBSA is symmetric.

Rotation traces for the polypeptides PBLG and PELG and for the achiral surfactant DBSA adsorbed at the air∕water interface. The solid lines are fits of the data to Eq. (8). Note that the traces for the chiral interfaces PBLG and PELG are asymmetric about , and the trace for the achiral interface DBSA is symmetric.

Calculated nonlinear susceptibilities for the model -helix, shown as a function of the tilt angle of the long axis of the helix relative to the surface normal. The fundamental frequency was . The magnitude of each susceptibility is plotted in the same arbitrary units. Results are shown for an assumed square distribution of the tilt angle about the mean value, with width 10°.

Calculated nonlinear susceptibilities for the model -helix, shown as a function of the tilt angle of the long axis of the helix relative to the surface normal. The fundamental frequency was . The magnitude of each susceptibility is plotted in the same arbitrary units. Results are shown for an assumed square distribution of the tilt angle about the mean value, with width 10°.

(a) and (b) Calculated nonlinear susceptibilities for the model -helix, shown as a function of photon energy of fundamental radiation. The tilt angle of the long axis of the helix relative to the surface normal is 0° for , and , and 90° for . The magnitude of each susceptibility is plotted in the same arbitrary units, with shown expanded. (c) Absorption spectrum of polypeptide -helix. The solid line shows the calculated spectrum and the broken line is an experimental spectrum of poly-(-methyl--glutamate) from Ref. 33 (see the text). Note that the energy scale is in (c) only, to facilitate comparison with the nonlinear susceptibilities.

(a) and (b) Calculated nonlinear susceptibilities for the model -helix, shown as a function of photon energy of fundamental radiation. The tilt angle of the long axis of the helix relative to the surface normal is 0° for , and , and 90° for . The magnitude of each susceptibility is plotted in the same arbitrary units, with shown expanded. (c) Absorption spectrum of polypeptide -helix. The solid line shows the calculated spectrum and the broken line is an experimental spectrum of poly-(-methyl--glutamate) from Ref. 33 (see the text). Note that the energy scale is in (c) only, to facilitate comparison with the nonlinear susceptibilities.

Calculated difference in hyperpolarizability tensor elements , shown as a function of photon energy of fundamental radiation for (a) the model -helix, and (b) the simplified model of seven independent -methylacetamide monomers. The real and imaginary parts and the modulus are plotted in atomic units.

Calculated difference in hyperpolarizability tensor elements , shown as a function of photon energy of fundamental radiation for (a) the model -helix, and (b) the simplified model of seven independent -methylacetamide monomers. The real and imaginary parts and the modulus are plotted in atomic units.

## Tables

Nonlinear susceptibilities of PELG and PBLG monolayer films at the air∕water interface, with . is the density of monomer constituents in the polmer films. and are effective nonlinear susceptibilities normalized to the susceptibility measured for the clean air∕water interface in this work. Two values for and shown on separate lines were derived by using alternative values of for the clean air∕water interface as shown in the table. The linear optical properties of the monolayers were assumed to be those of water.

Nonlinear susceptibilities of PELG and PBLG monolayer films at the air∕water interface, with . is the density of monomer constituents in the polmer films. and are effective nonlinear susceptibilities normalized to the susceptibility measured for the clean air∕water interface in this work. Two values for and shown on separate lines were derived by using alternative values of for the clean air∕water interface as shown in the table. The linear optical properties of the monolayers were assumed to be those of water.

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