Yes, you can use B3LYP/6-31G (d) to find a TS for molecules containing sulfur.
I have done many TS calculations for amoxicillin derivatives (compounds containing sulfur) using B3LYP/6-31G (d,p). But at first I have located the TS using HF/6-31G since the calculations with this basis set are much faster than with B3LYP/6-31G(d,p).
It is much faster to search the TS with a low basis set such as HF/3-21G or HF/6-31G.
The following are some hints for locating the TS:
It's a good idea to start to optimize Transition State structure using the inexpensive computational methods, for example, HF/3-21G to get quickly the initial TS which can be used a starting structure for the TS search using more sophisticated methods.
Since Transition State search involves the frequencies calculations it's a good idea to use tighter convergence criteria. To achieve this in Gaussian you can use opt=tight or even opt=verytight.
Using options opt=tight and especially opt=verytight makes the calculations more computationally expensive, though giving more accurate results.
In the case of the DFT methods it's a good idea to use a more accurate numerical integration grid. To achieve this in Gaussian you can use int=fine or int=ultrafine.
Using options int=fine or int=ultrafine makes the calculations more computationally expensive, though giving more accurate results.
For a case study locating TS, please see the following link:
Yes you can, but in general is better to perform a correlation of the energies within the framework of a more representative set of basis sets, in addition, to a correlation with experimental data towards concrete properties of interest.
It is good, to begin with, the smaller basis set in order to allocate the transition state for most of the systems. However, it is not advisable to generalize the same for all the systems. Moreover, the choice of approximation for the system of interest is dependent on the property to be calculated.
I would like to add some references. The DFT methods are really useful, but they can have limitations. When you have a good TS candidate it is useful to compare it with other Ab initio methods, such MP2. On the other hand, you can improve all the results by computational schemes: Abinitio/highbasisset // DFT/lowerbasisset, where Abinio are MPn, CCSD(T), etc; higher basis sets or CBS and in DFT it could be any functional (which gives accurate geometric and vibrational results) and other basis set that is enough accurate. In my opinion, each system must be validated and tested (trying different basis sets, functionals, methods, reference values, etc). "If I suppose that B3LYP/6-31G(d) is correct for my system, their validation should be perfect and easy without problems, if not, there is a problem."
About DFT, there are many new functionals that are better to calculate barriers. On the other hand, "following my own experience", the basis set of Dunning are computationally more efficient and gives better results with only a slightly increment in the time. (Even so, it depends on time, resources, etc...)
I hope it helps you,
(1) Lynch, B. J.; Truhlar, D. G. How Well Can Hybrid Density Functional Methods Predict Transition State Geometries and Barrier Heights? J. Phys. Chem. A 2001, 105, 2936–2941.
(2) Simon, L.; Goodman, J. M. How Reliable Are DFT Transition Structures? Comparison of GGA, Hybrid-Meta-GGA and Meta-GGA Functionals. Org. Biomol. Chem. 2011, 9, 689–700.
(3) Kang, J. K.; Musgrave, C. B. Prediction of Transition State Barriers and Enthalpies of Reaction by a New Hybrid Density-Functional Approximation. J. Chem. Phys. 2001, 115, 11040–11051.
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Other possibility with the basis set is to use different ones. For example, with an organosulfur TS, you could use different basis set for the atoms: cc-pVDZ for C, H and I; aug-cc-pVTZ for the S and O. With the Pople basis set you could control better the diffusion parameters, etc. In the link you will find all the basis sets for each atom. To use it, you must use the "gen" option in gaussian, and if you use pseudo-potential basis, you must include "b3pw91/gen pseudo=read".