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We find that for thermodynamic integration\u2010type free energy calculations as much as a nanosecond or more molecular dynamics sampling is required to obtain a fully converged value for a <jats:italic>single<\/jats:italic> \u03bb point of the integrand. The concept of \u201cfree energy derivatives\u201d with respect to the individual parameters of the force field is introduced. This formalism allows the total convergence of the simulation to be deconvoluted into components. A determination of the statistical \u201csampling ratio\u201d from these simulations indicates that for window\u2010type free energy calculations carried out in a periodic waterbox of typical size at least 0.6 ps of sampling should be performed at each window (0.7 ps if constraint contributions to the free energy are being determined). General methods to estimate and reduce the error in thermodynamic integration and free energy perturbation calculations are discussed. We show that the difficulty in applying such methods is determining a reliable estimate of the correlation length from a short series of data. \u00a9 1994 by John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jcc.540150112","type":"journal-article","created":{"date-parts":[[2005,1,2]],"date-time":"2005-01-02T00:56:30Z","timestamp":1104627390000},"page":"105-123","source":"Crossref","is-referenced-by-count":53,"title":["Free energy derivatives: A new method for probing the convergence problem in free energy calculations"],"prefix":"10.1002","volume":"15","author":[{"given":"David A.","family":"Pearlman","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,9,7]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1039\/fs9821700055"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0097-8485(84)85020-2"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.449208"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.3576184"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/bip.360290810"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1021\/ar00176a002"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.bi.52.070183.001403"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1021\/j150644a002"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.460608"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.461148"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/jcc.540120218"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1080\/08927029108022136"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1051\/jcp\/1991882617"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.455988"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.459753"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.463456"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.463650"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.457251"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1021\/j100165a045"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1021\/j100170a054"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1021\/j100176a002"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1021\/j100177a006"},{"key":"e_1_2_1_24_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.bb.18.060189.002243"},{"key":"e_1_2_1_25_2","volume-title":"Numerical Recipes","author":"Press W. 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