Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities

• Published in: Journal of computational chemistry 2017-06, Vol.38 (16), p.1376-1388
• Main Authors: Kearns, Fiona L., Hudson, Phillip S., Woodcock, Henry L., Boresch, Stefan
• Format: Article
• Language: English
• Subjects: BAR; free energy simulations; nonequilibrium work; QM/MM; QM‐NBB
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.24706

We demonstrate that Jarzynski's equation can be used to reliably compute free energy differences between low and high level representations of systems. The need for such a calculation arises when employing the so‐called “indirect” approach to free energy simulations with mixed quantum mechanical/molecular mechanical (QM/MM) Hamiltonians; a popular technique for circumventing extensive simulations involving quantum chemical computations. We have applied this methodology to several small and medium sized organic molecules, both in the gas phase and explicit solvent. Test cases include several systems for which the standard approach; that is, free energy perturbation between low and high level description, fails to converge. Finally, we identify three major areas in which the difference between low and high level representations make the calculation of ΔAlow→high difficult: bond stretching and angle bending, different preferred conformations, and the response of the MM region to the charge distribution of the QM region. © 2016 Wiley Periodicals, Inc. Although highly desirable, the use of quantum mechanics to compute free energy differences is typically prohibitively expensive. Fortunately, the so‐called “indirect” thermodynamic cycle, to compute quantities of interest at an affordable cost and ultimately connect these to higher accuracy results, can circumvent this limitation. Using results from a series of medium‐sized organic molecules, we highlight several major challenges that need to be overcome to effectively use high‐level methods in combination with this indirect methodology.