10 Molecular Properties and Analysis

10.9 Harmonic Vibrational Analysis

Vibrational analysis is an extremely important tool for the quantum chemist, supplying a molecular fingerprint which is invaluable for aiding identification of molecular species in many experimental studies. Q-Chem includes a vibrational analysis package that can calculate vibrational frequencies and their RamanJohnson:1995 and infrared activities. Vibrational frequencies are calculated by either using an analytic Hessian (if available; see Table 9.1) or, numerical finite difference of the gradient. The default setting in Q-Chem is to use the highest analytical derivative order available for the requested theoretical method.

When calculating analytic frequencies at the HF and DFT levels of theory, the coupled-perturbed SCF equations must be solved. This is the most time-consuming step in the calculation, and also consumes the most memory. The amount of memory required is 𝒪(N2M) where N is the number of basis functions, and M the number of atoms. This is an order more memory than is required for the SCF calculation, and is often the limiting consideration when treating larger systems analytically. Q-Chem incorporates a new approach to this problem that avoids this memory bottleneck by solving the CPSCF equations in segments.Korambath:2002 Instead of solving for all the perturbations at once, they are divided into several segments, and the CPSCF is applied for one segment at a time, resulting in a memory scaling of 𝒪(N2M/Nseg), where Nseg is the number of segments. This option is invoked automatically by the program.

Following a vibrational analysis, Q-Chem computes useful statistical thermodynamic properties at standard temperature and pressure, including: zero-point vibration energy (ZPVE) and, translational, rotational and vibrational, entropies and enthalpies.

The performance of various ab initio theories in determining vibrational frequencies has been well documented; see Refs. Murray:1992, Scott:1996, Johnson:1993d.