Toward an Accurate Modeling of Optical Rotation for Solvated Systems: Anharmonic Vibrational Contributions Coupled to the Polarizable Continuum Model Franco Egidi and Vincenzo Barone Scuola Normale Superiore, Piazza dei Cavalieri, 7 I-56126 Pisa, Italy Julien Bloino CNR, Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organometallici, UOS di Pisa, Via G. Moruzzi, 1 I-56124, Italy Chiara Cappelli* Scuola Normale Superiore, Piazza dei Cavalieri, 7 I-56126 Pisa, Italy and Dipartimento di Chimica e Chimica Industriale, Universita ̀ di Pisa, via Risorgimento, 35 I-56126 Pisa, Italy ABSTRACT: We present a newly implemented methodology to evaluate vibrational contributions (harmonic and anharmonic) to the optical rotation of solvated systems described by means of the polarizable continuum model (PCM). Proper account of an incomplete solvation regime in the treatment of both the electronic property and the molecular vibrations is considered, as well as the inclusion of cavity field effects. In order to assess the quality of our approach, test calculations on (R)-methyloxirane in various solvents and (S)-N-acetylproline amide in cyclohexane and aqueous solution are presented. The comparison with experimental findings is also shown. I. INTRODUCTION Chiroptical techniques, such as the measurement of optical activity (OR) or optical rotatory dispersion (ORD), have been around for several decades and have been used mainly by pharmaceutical or organic chemists to determine the enantiomeric purity of their synthesized samples by using empirical rules or heavy chemical derivatization in order to correlate the structure of the enantiomer to the sign of the measured properties. 1 The interest in the correct determination of enantiomeric purity is especially evident in the case of drugs, which in most cases are constituted by pure enantiomers, since only a particular configuration is biologically active, whereas the other may be inactive or even toxic. The use of OR to determine the absolute configuration and predominant conformation has been gaining renewed interest in recent years, due to the availability of quantum mechanical (QM) methods for predicting the OR. In this way, in fact, by comparing calculations and experiments, the assignment is done unequivocally, since the calculated value surely refers to only one of the enantiomerically pure structures. From the point of view of the theoreticians, studying chiroptical properties and spectroscopies offers a unique chance of working in a field where the advancement of the theory opens the way to the investigation of new and more complex systems, and where the strict interplay between theory and experiment is often a real necessity. Also, from the purely theoretical and computational point of view, as chiroptical properties are formally mixed electric and magnetic responses, the underlying QM theory is very challenging, as it requires the same accuracy for the evaluation not only of energetic parameters but also of the response of the molecular system to the electric and especially magnetic component of the radiation. For these reasons, the calculation of chiroptical properties has been viable only in recent years, following the tremendous progress of ab initio quantum chemistry in the recent decades. 2-8 The impact that quantum chemistry has had on the field has been so relevant that Polavarapu spoke of a “Renaissance in chiroptical spectroscopic methods for molec- ular structure determination” following the development of QM computational techniques. 9 In the past decade, much effort has been devoted to develop methods for the accurate calculation of OR. The earliest works 10-14 employed the Hartree-Fock level of theory, but soon the importance of including in the model a treatment of the electron correlation was exposed. 15,16 To date, most of the computational studies on chiroptical properties have been based on response methods within density functional theory (DFT) and time-dependent DFT (TD-DFT), even though more accurate methods such as coupled cluster theory have also been used. 17-20 The basis set dependence was first analyzed by Cheeseman et al., 21 who pointed out the need to include diffuse basis functions in the model and suggested the basis sets aug-cc- Received: November 23, 2011 Published: January 4, 2012 Article pubs.acs.org/JCTC © 2012 American Chemical Society 585 dx.doi.org/10.1021/ct2008473 | J. Chem. TheoryComput. 2012, 8, 585-597