On the Assessment of Some New Meta-Hybrid and Generalized Gradient Approximation Functionals for Calculations of Anharmonic Vibrational Frequency Shifts in Hydrogen-Bonded Dimers Vanc ˇo Kocevski and Ljupc ˇo Pejov* Institute of Chemistry, Faculty of Science, Sts. Cyril and Methodius UniVersity, P.O. Box 162, 1001 Skopje, Republic of Macedonia ReceiVed: NoVember 6, 2009; ReVised Manuscript ReceiVed: February 11, 2010 The performance of some recently proposed DFT functionals by Truhlar’s group (mPW1B95, mPWLYP1W, PBELYP1W, and PBE1W [Dahlke, E. E.; Truhlar, D. G. J. Phys. Chem. B 2005, 109, 317. Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 6908.]) was tested primarily with respect to computation of anharmonic vibrational frequency shifts upon hydrogen bond formation in small molecular/ionic dimers. Five hydrogen- bonded systems with varying hydrogen bond strengths were considered: methanol-fluorobenzene, phenol-carbon monoxide in ground neutral (S 0 ) and cationic (D 0 ) electronic states, phenol-acetylene, and phenol-benzene(+). Anharmonic OH stretching frequency shifts were calculated from the computed vibrational potentials for free and hydrogen-bonded proton-donor molecules. To test the basis set convergence properties, all calculations were performed with 6-31++G(d,p) and 6-311++G(2df,2pd) basis sets. The mPW1B95 functional was found to perform remarkably better in comparison to more standard functionals (such as B3LYP, mPW1PW91, PBE1PBE) in the case of neutral dimers. In the case of cationic dimers, however, this is not always the case. With respect to prediction of anharmonic OH stretching frequency shifts upon ionization of free phenol, all DFT levels of theory outperform MP2. Some other aspects of the functional performances with respect to computation of interaction and dissociation energies were considered as well. 1. Introduction In the ongoing quest for an efficient computational methodol- ogy for modeling of condensed phases and molecular clusters, the density functional theory (DFT)-based approaches are of essential importance. This is due to the significantly lower cost of the DFT computations as compared to the wave function- based methods (such as Mpn, CC, and QCI). However, although the density functional theory accounts for the dynamical electron correlation effects, these are included in a more or less semiempirical manner. Ever since the advent of the DFT approach, various combinations of exchange (X) and correlation (C) functionals have been tested for a variety of purposes. 1 Although some of the XC functionals combinations have been proposed for a wide variety of purposes, for rather specific computational tasks, even these may appear quite inefficient. Actually, an a priori approach, which would predict the performance of any combination of XC functionals for a particular computational aim, does not seem to exist. Usually, very extensive careful numerical testing is required, with an emphasis on various aspects in specific systems. For the reasons mentioned before, the refinement of func- tionals for DFT-based computational methodologies is a very active area of research in theoretical physics and chemistry. One of the two alternative approaches in this area, the nonempirical one, seems to be favored in physics, due to its exactness. 2-4 The other one, which is essentially based on choosing a flexible mathematical functional, which depends on several parameters, and subsequent determination of the values of these parameters, usually by a fitting procedure, has been very successful for a wide range of “chemical” problems. 5-7 Of course, apart from the term “empirical” for the latest approach, it should be kept in mind that it is actually only partly empirical. This is so since the general form of the functional is usually guided by theory. A particularly important issue in studies of noncovalently bonded molecular clusters is to establish a computational methodology that would enable accurate calculations of vibra- tional frequency shifts for certain intramolecular modes. This is due to the fact that in experimental studies of such clusters, most often the vibrational frequency shifts with respect to the free molecular species have been used as indicators for the existence and type of noncovalent bonding within the cluster. 8-10 It has been recognized that the straightforwardly calculated harmonic vibrational frequency shifts can lead to fortuitous very good agreement with the experimental spectroscopic data. 11-22 This happens due to cancellations of various types of error. The most important of these are: (i) the known deficiency in the long-range behavior of the more often used “standard” functional combinations, which leads to inappropriate description of the low-density high-gradient region of the electronic density within the molecular clusters, 18 (ii) the inadequacy of harmonic approximation for the oscillators involving motion of low-mass particles, such as hydrogen for example. 15,18 The second error becomes especially significant in cases of hydrogen-bonded systems, where the very existence of the hydrogen bond is often judged on the basis of experimentally measured X-H frequency shift occurring due to cluster formation with respect to the free X-H oscillator. It has been demonstrated in the literature that the anharmonic corrections to the total X-H vibrational frequency shifts can be as large as 30-40% even for weakly bonded systems. 11 On the other hand, the previous studies within our and other research groups have demonstrated that if one * To whom correspondence should be addressed. E-mail: ljupcop@ iunona.pmf.ukim.edu.mk. J. Phys. Chem. A 2010, 114, 4354–4363 4354 10.1021/jp910587y  2010 American Chemical Society Published on Web 03/10/2010