TY - JOUR
T1 - Free energy profile along a discretized reaction path via the hyperplane constraint force and torque
AU - Kudin, Konstantin N.
AU - Car, Roberto
N1 - Funding Information:
This material is based upon work supported in part by the U.S. Army Research Office Multidisciplinary University Research Initiative (ARO/MURI) under Grant No. W911NF-04-1-0170. The work was also partially supported by NSF Award No. CHE-0121432.
PY - 2005/3/15
Y1 - 2005/3/15
N2 - By employing mechanical work analogies, we derive a convenient computational approach for evaluation of the free energy profile (FEP) along some discretized path defined as a sequence of hyperplanes. A hyperplane is fully specified by any of its point and a tangent vector. The FEP is obtained as an integral of two components. The translational component of the free energy is computed by integrating the hyperplane constraint force. The rotational component is evaluated via the hyperplane torque. Both ingredients-the constraint force and the hyperplane torque-are evaluated on each hyperplane independently. The integration procedure utilizes a set of reference points defining a point of rotation on each hyperplane, and these points can be chosen before or after the sampling takes place. A shift in the reference points redistributes the FEP contributions between the translational and rotational components. For systems where the FEP is dominated by the potential energy differences, reference points residing on the minimum energy path present a natural choice. We demonstrate the validity of our approach on two examples, a simple two-dimensional (2D) potential, and a seven-atom Lennard-Jones cluster. In each case, we compare the numerical FEP with the harmonic approximation estimates. Our results for the 2D potential are also verified by the data available in the literature. In both cases, the rotational component of the FEP represents a sizable contribution to the total FEP, so ignoring it would yield clearly incorrect results.
AB - By employing mechanical work analogies, we derive a convenient computational approach for evaluation of the free energy profile (FEP) along some discretized path defined as a sequence of hyperplanes. A hyperplane is fully specified by any of its point and a tangent vector. The FEP is obtained as an integral of two components. The translational component of the free energy is computed by integrating the hyperplane constraint force. The rotational component is evaluated via the hyperplane torque. Both ingredients-the constraint force and the hyperplane torque-are evaluated on each hyperplane independently. The integration procedure utilizes a set of reference points defining a point of rotation on each hyperplane, and these points can be chosen before or after the sampling takes place. A shift in the reference points redistributes the FEP contributions between the translational and rotational components. For systems where the FEP is dominated by the potential energy differences, reference points residing on the minimum energy path present a natural choice. We demonstrate the validity of our approach on two examples, a simple two-dimensional (2D) potential, and a seven-atom Lennard-Jones cluster. In each case, we compare the numerical FEP with the harmonic approximation estimates. Our results for the 2D potential are also verified by the data available in the literature. In both cases, the rotational component of the FEP represents a sizable contribution to the total FEP, so ignoring it would yield clearly incorrect results.
UR - http://www.scopus.com/inward/record.url?scp=18644361869&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=18644361869&partnerID=8YFLogxK
U2 - 10.1063/1.1874832
DO - 10.1063/1.1874832
M3 - Article
C2 - 15836202
AN - SCOPUS:18644361869
SN - 0021-9606
VL - 122
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 11
M1 - 114108
ER -