Line data Source code
1 : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2 : Copyright (c) 2019
3 : National Institute of Advanced Industrial Science and Technology (AIST), Japan.
4 : This file contains module for LogMFD method proposed by Tetsuya Morishita(AIST).
5 :
6 : The LogMFD module is free software: you can redistribute it and/or modify
7 : it under the terms of the GNU Lesser General Public License as published by
8 : the Free Software Foundation, either version 3 of the License, or
9 : (at your option) any later version.
10 :
11 : The LogMFD module is distributed in the hope that it will be useful,
12 : but WITHOUT ANY WARRANTY; without even the implied warranty of
13 : MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 : GNU Lesser General Public License for more details.
15 :
16 : You should have received a copy of the GNU Lesser General Public License
17 : along with plumed. If not, see <http://www.gnu.org/licenses/>.
18 : +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
19 :
20 : //+PLUMEDOC LOGMFDMOD_BIAS LOGMFD
21 : /*
22 : Used to perform LogMFD, LogPD, and TAMD/d-AFED.
23 :
24 : \section LogMFD LogMFD
25 :
26 : Consider a physical system of \f$N_q\f$ particles, for which the Hamiltonian is given as
27 :
28 : \f[
29 : {H_{\rm MD}}\left( {\bf{\Gamma}} \right) = \sum\limits_{j = 1}^{{N_q}} {\frac{{{\bf{p}}_j^2}}{{2{m_j}}}} + \Phi \left( {\bf{q}} \right)
30 : \f]
31 :
32 : where \f${\bf q}_j\f$, \f${\bf p}_j\f$ (\f$\bf{\Gamma}={\bf q},{\bf p}\f$), and \f$m_j\f$ are the position, momentum, and mass of particle \f$j\f$ respectively,
33 : and \f$\Phi\f$ is the potential energy function for \f${\bf q}\f$.
34 : The free energy \f$F({\bf X})\f$ as a function of a set of \f$N\f$ collective variables (CVs) is given as
35 :
36 : \f{eqnarray*}{
37 : F\left( {{\bf X}} \right) &=& - {k_B}T\log \int {\exp \left[ { - \beta {H_{\rm MD}}} \right]\prod\limits_{i = 1}^N {\delta \left( {{s_i}\left( {{\bf q}} \right) - {X_i}} \right)} d{\bf{\Gamma }}} \\
38 : &\simeq& - {k_B}T\log \int {\exp \left[ { - \beta \left\{ {{H_{\rm MD}} + \sum\limits_i^N {\frac{{{K_i}}}{2}{{\left( {{s_i}\left( {{\bf q}} \right) - {X_i}} \right)}^2}} } \right\}} \right]} d{\bf{\Gamma }}
39 : \f}
40 :
41 : where \f$\bf{s}\f$ are the CVs, \f$k_B\f$ is Boltzmann constant, \f$\beta=1/k_BT\f$,
42 : and \f$K_i\f$ is the spring constant which is large enough to invoke
43 :
44 : \f[
45 : \delta \left( x \right) = \lim_{k \to \infty } \sqrt {\beta k/2\pi} \exp \left( -\beta kx^2/2 \right)
46 : \f]
47 :
48 : In mean-force dynamics, \f${\bf X}\f$ are treated as fictitious dynamical variables, which are associated with the following Hamiltonian,
49 :
50 : \f[
51 : {H_{\rm log}} = \sum\limits_{i = 1}^N {\frac{{P_{{X_i}}^2}}{{2{M_i}}} + \Psi \left( {{\bf X}} \right)}
52 : \f]
53 :
54 : where \f${P_{{X_i}}}\f$ and \f$M_i\f$ are the momentum and mass of \f$X_i\f$, respectively, and \f$\Psi\f$ is the potential function for \f${\bf X}\f$.
55 : We assume that \f$\Psi\f$ is a functional of \f$F({\bf X})\f$; \f$Ψ[F({\bf X})]\f$. The simplest form of \f$\Psi\f$ is \f$\Psi = F({\bf X})\f$,
56 : which corresponds to TAMD/d-AFED \cite AbramsJ2008, \cite Maragliano2006 (or the extended Lagrangian dynamics in the limit of the adiabatic decoupling between \f$\bf{q}\f$ and \f${\bf X}\f$).
57 : In the case of LogMFD, the following form of \f$\Psi\f$ is introduced \cite MorishitaLogMFD;
58 :
59 :
60 : \f[
61 : {\Psi _{\rm log}}\left( {{\bf X}} \right) = \gamma \log \left[ {\alpha F\left( {{\bf X}} \right) + 1} \right]
62 : \f]
63 :
64 : where \f$\alpha\f$ (ALPHA) and \f$\gamma\f$ (GAMMA) are positive parameters. The logarithmic form of \f$\Psi_{\rm log}\f$ ensures the dynamics of \f${\bf X}\f$ on a much smoother energy surface [i.e., \f$\Psi_{\rm log}({\bf X})\f$] than \f$F({\bf X})\f$, thus enhancing the sampling in the \f${\bf X}\f$-space. The parameters \f$\alpha\f$ and \f$\gamma\f$ determine the degree of flatness of \f$\Psi_{\rm log}\f$, but adjusting only \f$\alpha\f$ is normally sufficient to have a relatively flat surface (with keeping the relation \f$\gamma=1/\alpha\f$).
65 :
66 : The equation of motion for \f$X_i\f$ in LogMFD (no thermostat) is
67 :
68 : \f[
69 : {M_i}{\ddot X_i} = - \left( {\frac{{\alpha \gamma }}{{\alpha F + 1}}} \right)\frac{{\partial F}}{{\partial {X_i}}}
70 : \f]
71 :
72 : where \f$-\partial F/\partial X_i\f$ is evaluated as a canonical average under the condition that \f${\bf X}\f$ is fixed;
73 :
74 : \f{eqnarray*}{
75 : - \frac{{\partial F}}{{\partial {X_i}}} &\simeq& \frac{1}{Z}\int {{K_i}\left( {{s_i}\left( {{\bf q}} \right) - {X_i}} \right)\exp \left[ { - \beta \left\{ {{H_{\rm MD}} + \sum\limits_i^N {\frac{{{K_i}}}{2}{{\left( {{s_i}\left( {{\bf q}} \right) - {X_i}} \right)}^2}} } \right\}} \right]} d{\bf{\Gamma }}\\
76 : &\equiv& {\left\langle {{K_i}\left( {{s_i}\left( {{\bf q}} \right) - {X_i}} \right)} \right\rangle _{{\bf X}}}
77 : \f}
78 :
79 : where
80 :
81 : \f[
82 : Z = \int {\exp \left[ { - \beta \left\{ {{H_{\rm MD}} + \sum\limits_i^N {\frac{{{K_i}}}{2}{{\left( {{s_i}\left( {{\bf q}} \right) - {X_i}} \right)}^2}} } \right\}} \right]} d{\bf{\Gamma }}
83 : \f]
84 :
85 : The mean-force (MF) is practically evaluated by performing a shot-time canonical MD run of \f$N_m\f$ steps each time \f${\bf X}\f$ is updated according to the equation of motion for \f${\bf X}\f$.
86 :
87 : If the canonical average for the MF is effectively converged, the dynamical variables \f${\bf q}\f$ and \f${\bf X}\f$ are decoupled and they evolve adiabatically, which can be exploited for the on-the-fly evaluation of \f$F({\bf X})\f$. I.e., \f$H_{\rm log}\f$ should be a constant of motion in this case, thus \f$F({\bf X})\f$ can be evaluated each time \f${\bf X}\f$ is updated as
88 :
89 :
90 : \f[
91 : F\left( {{{\bf X}}\left( t \right)} \right) = \frac{1}{\alpha} \left[
92 : \exp \frac{1}{\gamma} \left\{ \left( H_{\rm log} - \sum_i \frac{P_{X_i}^2}{2M_i} \right) \right\} - 1 \right]
93 : \f]
94 :
95 :
96 : This means that \f$F({\bf X})\f$ can be constructed without post processing (on-the-fly free energy reconstruction). Note that the on-the-fly free energy reconstruction is also possible in TAMD/d-AFED if the Hamiltonian-like conserved quantity is available (e.g., the Nose-Hoover type dynamics).
97 :
98 :
99 :
100 : \section LogPD LogPD
101 :
102 :
103 : The accuracy in the MF is critical to the on-the-fly free energy reconstruction. To improve the evaluation of the MF, parallel-dynamics (PD) is incorporated into LogMFD, leading to logarithmic parallel-dynamics (LogPD) \cite MorishitaLogPD.
104 :
105 :
106 : In PD, the MF is evaluated by a non-equilibrium path-ensemble based on the Crooks-Jarzynski non-equilibrium work relation. To this end, multiple replicas of the MD system which run in parallel are introduced. The CVs [\f${\bf s}({\bf q})\f$] in each replica is restrained to the same value of \f${\bf X}(t)\f$. A canonical MD run with \f$N_m\f$ steps is performed in each replica, then the MF on \f$X_i\f$ is evaluated using the MD trajectories from all replicas.
107 : The MF is practically calculated as
108 :
109 :
110 : \f[
111 : - \frac{{\partial F}}{{\partial {X_i}}} = \sum\limits_{k = 1}^{{N_r}} {{W_k}} \sum\limits_{n = 1}^{{N_m}} {\frac{1}{{{N_m}}}{K_i}\left[ {{s_i}\left( {{{\bf q}}_n^k} \right) - {X_i}} \right]}
112 : \f]
113 :
114 :
115 :
116 : where \f${\bf q}^k_n\f$ indicates the \f${\bf q}\f$-configuration at time step \f$n\f$ in the \f$N_m\f$-step shot-time MD run in the \f$k\f$th replica among \f$N_r\f$ replicas. \f$W_k\f$ is given as
117 :
118 : \f[
119 : {W_k} = \frac{{{e^{ - \beta {w_k}\left( t \right)}}}}{{\sum\limits_{k=1}^{{N_r}} {{e^{ - \beta {w_k}\left( t \right)}}} }}
120 : \f]
121 :
122 :
123 : where
124 :
125 :
126 : \f[
127 : {w_k}\left( t \right) = \int\limits_{{X_0}}^{X\left( t \right)} {\sum\limits_{i=1}^N {\frac{{\partial H_{\rm MD}^k}}{{\partial {X_i}}}d{X_i}} }
128 : \f]
129 :
130 : \f[
131 : H_{\rm MD}^k\left( {{\bf{\Gamma }},{{\bf X}}} \right) = {H_{\rm MD}}\left( {{{\bf{\Gamma }}^k}} \right) + \sum\limits_{i = 1}^N {\frac{{{K_i}}}{2}{{\left( {s_i^k - {X_i}} \right)}^2}}
132 : \f]
133 :
134 : and \f$s^k_i\f$ is the \f$i\f$th CV in the \f$k\f$th replica.
135 :
136 : \f$W_k\f$ comes from the Crooks-Jarzynski non-equilibrium work relation by which we can evaluate an equilibrium ensemble average from a set of non-equilibrium trajectories. Note that, to avoid possible numerical errors in the exponential function, the following form of \f$W_k\f$ is instead used in PLUMED,
137 :
138 : \f[
139 : {W_k}\left( t \right) = \frac{{\exp \left[ { - \beta \left\{ {{w_k}\left( t \right) - {w_{\min }}\left( t \right)} \right\}} \right]}}{{\sum\nolimits_k {\exp \left[ { - \beta \left\{ {{w_k}\left( t \right) - {w_{\min }}\left( t \right)} \right\}} \right]} }}
140 : \f]
141 :
142 : where
143 :
144 : \f[
145 : {w_{\min }}\left( t \right) = {\rm Min}_k\left[ {{w_k}\left( t \right)} \right]
146 : \f]
147 :
148 :
149 : With the MF evaluated using the PD approach, free energy profiles can be reconstructed more efficiently (requiring less elapsed computing time) in LogPD than with a single MD system in LogMFD. In the case that there exist more than one stable state separated by high energy barriers in the hidden subspace orthogonal to the CV-subspace, LogPD is particularly of use to incorporate all the contributions from such hidden states with appropriate weights (in the limit \f$N_r\to\infty\f$ ).
150 :
151 : Note that LogPD calculations should always be initiated with an equilibrium \f${\bf q}\f$-configuration in each replica, because the Crooks-Jarzynski non-equilibrium work relation is invoked. Also note that LogPD is currently available only with Gromacs, while LogMFD can be performed with LAMMPS, Gromacs, Quantum Espresso, NAMD, and so on.
152 :
153 : \section Thermostat Using LogMFD/PD with a thermostat
154 :
155 : Introducing a thermostat on \f${\bf X}\f$ is often recommended in LogMFD/PD to maintain the adiabatic decoupling between \f${\bf q}\f$ and \f${\bf X}\f$. In the framework of the LogMFD approach, the Nose-Hoover type thermostat and the Gaussian isokinetic (velocity scaling) thermostat can be used to control the kinetic energy of \f${\bf X}\f$.
156 :
157 : \subsection Nose-Hoover Nose-Hoover LogMFD/PD
158 :
159 : The equation of motion for \f$X_i\f$ coupled to a Nose-Hoover thermostat variable \f$\eta\f$ (single heat bath) is
160 :
161 : \f[
162 : {M_i}{\ddot X_i} = - \left( {\frac{{\alpha \gamma }}{{\alpha F + 1}}} \right)\frac{{\partial F}}{{\partial {X_i}}} - {M_i}{\dot X_i}\dot \eta
163 : \f]
164 :
165 : The equation of motion for \f$\eta\f$ is
166 :
167 : \f[
168 : Q\ddot \eta = \sum\limits_{i = 1}^N {\frac{{P_{{X_i}}^2}}{{{M_i}}} - N{k_B}T}
169 : \f]
170 :
171 : where \f$N\f$ is the number of the CVs. Since the following pseudo-Hamiltonian is a constant of motion in Nose-Hoover LogMFD/PD,
172 :
173 : \f[
174 : H_{\rm log}^{\rm NH} = \sum\limits_{i = 1}^N {\frac{{P_{{X_i}}^2}}{{2{M_i}}} + \gamma \log \left[ {\alpha F\left( {{\bf X}} \right) + 1} \right] + \frac{1}{2}Q{{\dot \eta }^2} + N{k_B}T\eta}
175 : \f]
176 :
177 : \f$F({\bf X}(t))\f$ is obtained at each MFD step as
178 :
179 : \f[
180 : F\left( {{{\bf X}}\left( t \right)} \right) = \frac{1}{\alpha }\left[ {\exp \left\{ {{{ \frac{1}{\gamma} \left( {H_{\rm log}^{\rm NH} - \sum_i {\frac{{P_{{X_i}}^2}}{{2{M_i}}}} - \frac{1}{2}Q{{\dot \eta }^2} - N{k_B}T\eta} \right)} }} \right\} - 1} \right]
181 : \f]
182 :
183 :
184 :
185 : \subsection VS Velocity scaling LogMFD/PD
186 :
187 : The velocity scaling algorithm (which is equivalent to the Gaussian isokinetic dynamics in the limit \f$\Delta t\to 0\f$) can also be employed to control the velocity of \f${\bf X}\f$, \f$\bf{V}_x\f$.
188 :
189 : The following algorithm is introduced to perform isokinetic LogMFD calculations \cite MorishitaVsLogMFD;
190 :
191 : \f{eqnarray*}{
192 : {V_{{X_i}}}\left( {{t_{n + 1}}} \right)
193 : &=&
194 : V_{X_i}^\prime \left( {{t_n}} \right) + \Delta t \left[
195 : { - \left( {\frac{{\alpha \gamma }}{{\alpha F\left( {{t_n}} \right) + 1}}} \right)
196 : \frac{{\partial F\left( {{t_n}} \right)}}{{\partial {X_i}}}}
197 : \right]\\
198 : S\left( {{t_{n + 1}}} \right)
199 : &=&
200 : \sqrt {\frac{{N{k_B}T}}{{\sum\limits_i {{M_i}V_{{X_i}}^2\left( {{t_{n + 1}}} \right)} }}} \\
201 : {V_{{X_i}}}^\prime \left( {{t_{n + 1}}} \right)
202 : &=&
203 : S\left( {{t_{n + 1}}} \right){V_{{X_i}}}\left( {{t_{n + 1}}} \right)\\
204 : {X_i}\left( {{t_{n + 1}}} \right)
205 : &=&
206 : {X_i}\left( {{t_n}} \right) + \Delta t V_{X_i}^\prime \left( {{t_{n + 1}}} \right)\\
207 : {\Psi_{\rm log}}\left( {{t_{n + 1}}} \right)
208 : &=&
209 : N{k_B}T\log S\left( {{t_{n + 1}}} \right) + {\Psi_{\rm log}}\left( {{t_n}} \right)\\
210 : F\left( {{t_{n + 1}}} \right)
211 : &=&
212 : \frac{1}{\alpha} \left[
213 : \exp \left\{ \Psi_{\rm log} \left( t_{n+1} \right) / \gamma \right\} - 1
214 : \right]
215 : \f}
216 :
217 : Note that \f$V_{X_i}^\prime\left( {{t_0}} \right)\f$ is assumed to be initially given, which meets the following relation,
218 :
219 : \f[
220 : \sum\limits_{i = 1}^N M_i V_{X_i}^{\prime 2} \left( t_0 \right) = N{k_B}{T}
221 : \f]
222 :
223 : It should be stressed that, in the same way as in the NVE and Nose-Hoover LogMFD/PD, \f$F({\bf X}(t))\f$ can be evaluated at each MFD step (on-the-fly free energy reconstruction) in Velocity Scaling LogMFD/PD.
224 :
225 :
226 : \par Examples
227 : \section Examples Examples
228 :
229 : \subsection Example-LoGMFD Example of LogMFD
230 :
231 : The following input file tells plumed to restrain collective variables
232 : to the fictitious dynamical variables in LogMFD/PD.
233 :
234 : plumed.dat
235 : \plumedfile
236 : UNITS TIME=fs LENGTH=1.0 ENERGY=kcal/mol MASS=1.0 CHARGE=1.0
237 : phi: TORSION ATOMS=5,7,9,15
238 : psi: TORSION ATOMS=7,9,15,17
239 :
240 : # LogMFD
241 : LOGMFD ...
242 : LABEL=logmfd
243 : ARG=phi,psi
244 : KAPPA=1000.0,1000.0
245 : DELTA_T=1.0
246 : INTERVAL=200
247 : TEMP=300.0
248 : FLOG=2.0
249 : MFICT=5000000,5000000
250 : VFICT=3.5e-4,3.5e-4
251 : ALPHA=4.0
252 : THERMOSTAT=NVE
253 : FICT_MAX=3.15,3.15
254 : FICT_MIN=-3.15,-3.15
255 : ... LOGMFD
256 : \endplumedfile
257 :
258 : To submit this simulation with Gromacs, use the following command line
259 : to execute a LogMFD run with Gromacs-MD.
260 : Here topol.tpr is the input file
261 : which contains atomic coordinates and Gromacs parameters.
262 :
263 : \verbatim
264 : gmx_mpi mdrun -s topol.tpr -plumed
265 : \endverbatim
266 :
267 : This command will output files named logmfd.out and replica.out.
268 :
269 : The output file logmfd.out records free energy and all fictitious dynamical variables at every MFD step.
270 :
271 : logmfd.out
272 :
273 : \verbatim
274 : # LogMFD
275 : # CVs : phi psi
276 : # Mass for CV particles : 5000000.000000 5000000.000000
277 : # Mass for thermostat : 11923.224809
278 : # 1:iter_mfd, 2:Flog, 3:2*Ekin/gkb[K], 4:eta, 5:Veta,
279 : # 6:phi_fict(t), 7:phi_vfict(t), 8:phi_force(t),
280 : # 9:psi_fict(t), 10:psi_vfict(t), 11:psi_force(t),
281 : 0 2.000000 308.221983 0.000000 0.000000 -2.442363 0.000350 5.522717 2.426650 0.000350 7.443177
282 : 1 1.995466 308.475775 0.000000 0.000000 -2.442013 0.000350 -4.406246 2.427000 0.000350 11.531345
283 : 2 1.992970 308.615664 0.000000 0.000000 -2.441663 0.000350 -3.346513 2.427350 0.000350 15.763196
284 : 3 1.988619 308.859946 0.000000 0.000000 -2.441313 0.000350 6.463092 2.427701 0.000351 6.975422
285 : ...
286 : \endverbatim
287 :
288 : The output file replica.out records all collective variables at every MFD step.
289 :
290 : replica.out
291 :
292 : \verbatim
293 : Replica No. 0 of 1.
294 : # 1:iter_mfd, 2:work, 3:weight,
295 : # 4:phi(q)
296 : # 5:psi(q)
297 : 0 0.000000e+00 1.000000e+00 -2.436841 2.434093
298 : 1 -4.539972e-03 1.000000e+00 -2.446420 2.438531
299 : 2 -7.038516e-03 1.000000e+00 -2.445010 2.443114
300 : 3 -1.139672e-02 1.000000e+00 -2.434850 2.434677
301 : ...
302 : \endverbatim
303 :
304 : \subsection Example-LogPD Example of LogPD
305 :
306 : Use the following command line to execute a LogPD run using two MD replicas (note that only Gromacs is currently available for LogPD).
307 : Here 0/topol.tpr and 1/topol.tpr are the input files,
308 : each containing the atomic coordinates for the corresponding replica and Gromacs parameters. All the directories, 0/ and 1/, should contain the same plumed.dat.
309 :
310 : \verbatim
311 : mpirun -np 2 gmx_mpi mdrun -s topol -plumed -multidir 0 1
312 : \endverbatim
313 :
314 : This command will output files named logmfd.out in 0/, and replica.out.0 and replica.out.1 in 0/ and 1/, respectively.
315 :
316 : The output file logmfd.out records free energy and all fictitious dynamical variables at every MFD step.
317 :
318 : logmfd.out
319 :
320 : \verbatim
321 : # LogPD, replica parallel of LogMFD
322 : # number of replica : 2
323 : # CVs : phi psi
324 : # Mass for CV particles : 5000000.000000 5000000.000000
325 : # Mass for thermostat : 11923.224809
326 : # 1:iter_mfd, 2:Flog, 3:2*Ekin/gkb[K], 4:eta, 5:Veta,
327 : # 6:phi_fict(t), 7:phi_vfict(t), 8:phi_force(t),
328 : # 9:psi_fict(t), 10:psi_vfict(t), 11:psi_force(t),
329 : 0 2.000000 308.221983 0.000000 0.000000 -2.417903 0.000350 4.930899 2.451475 0.000350 -3.122024
330 : 1 1.999367 308.257404 0.000000 0.000000 -2.417552 0.000350 0.851133 2.451825 0.000350 -1.552718
331 : 2 1.999612 308.243683 0.000000 0.000000 -2.417202 0.000350 -1.588175 2.452175 0.000350 1.601274
332 : 3 1.999608 308.243922 0.000000 0.000000 -2.416852 0.000350 4.267745 2.452525 0.000350 -4.565621
333 : ...
334 : \endverbatim
335 :
336 :
337 : The output file replica.out.0 records all collective variables and the Jarzynski weight of replica No.0 at every MFD step.
338 :
339 : replica.out.0
340 :
341 : \verbatim
342 : # Replica No. 0 of 2.
343 : # 1:iter_mfd, 2:work, 3:weight,
344 : # 4:phi(q)
345 : # 5:psi(q)
346 : 0 0.000000e+00 5.000000e-01 -2.412607 2.446191
347 : 1 -4.649101e-06 4.994723e-01 -2.421403 2.451318
348 : 2 1.520985e-03 4.983996e-01 -2.420269 2.455049
349 : 3 1.588855e-03 4.983392e-01 -2.411081 2.447394
350 : ...
351 : \endverbatim
352 :
353 : The output file replica.out.1 records all collective variables and the Jarzynski weight of replica No.1 at every MFD step.
354 :
355 : replica.out.1
356 :
357 : \verbatim
358 : # Replica No. 1 of 2.
359 : # 1:iter_mfd, 2:work, 3:weight,
360 : # 4:phi(q)
361 : # 5:psi(q)
362 : 0 0.000000e+00 5.000000e-01 -2.413336 2.450516
363 : 1 -1.263077e-03 5.005277e-01 -2.412009 2.449229
364 : 2 -2.295444e-03 5.016004e-01 -2.417322 2.452512
365 : 3 -2.371507e-03 5.016608e-01 -2.414078 2.448521
366 : ...
367 : \endverbatim
368 :
369 : */
370 : //+ENDPLUMEDOC
371 :
372 : #include "bias/Bias.h"
373 : #include "core/ActionRegister.h"
374 : #include "core/Atoms.h"
375 : #include "core/PlumedMain.h"
376 :
377 : #include <iostream>
378 :
379 : using namespace std;
380 : using namespace PLMD;
381 : using namespace bias;
382 :
383 : namespace PLMD {
384 : namespace logmfd {
385 : /**
386 : \brief class for LogMFD parameters, variables and subroutines.
387 : */
388 : class LogMFD : public Bias {
389 : bool firsttime; ///< flag that indicates first MFD step or not.
390 : int step_initial; ///< initial MD step.
391 : int interval; ///< input parameter, period of MD steps when fictitious dynamical variables are evolved.
392 : double delta_t; ///< input parameter, one time step of MFD when fictitious dynamical variables are evolved.
393 : string thermostat; ///< input parameter, type of thermostat for canonical dyanamics.
394 : double kbt; ///< k_B*temperature
395 : double kbtpd; ///< k_B*temperature for PD
396 :
397 : int TAMD; ///< input parameter, perform TAMD instead of LogMFD.
398 : double alpha; ///< input parameter, alpha parameter for LogMFD.
399 : double gamma; ///< input parameter, gamma parameter for LogMFD.
400 : std::vector<double> kappa; ///< input parameter, strength of the harmonic restraining potential.
401 :
402 : std::vector<double> fict_max; ///< input parameter, maximum of each fictitous dynamical variable.
403 : std::vector<double> fict_min; ///< input parameter, minimum of each fictitous dynamical variable.
404 :
405 :
406 : std::vector<double> fict; ///< current values of each fictitous dynamical variable.
407 : std::vector<double> vfict; ///< current velocity of each fictitous dynamical variable.
408 : std::vector<double> mfict; ///< mass of each fictitous dynamical variable.
409 :
410 : double xeta; ///< current eta variable of thermostat.
411 : double veta; ///< current velocity of eta variable of thermostat.
412 : double meta; ///< mass of eta variable of thermostat.
413 :
414 : double phivs; ///< potential used in VS method
415 : double work; ///< current works done by fictitious dynamical variables in this replica.
416 : double weight; ///< current weight of this replica.
417 : double flog; ///< current free energy
418 : double hlog; ///< value invariant
419 :
420 : struct {
421 : std::vector<double> fict;
422 : std::vector<double> vfict;
423 : std::vector<double> ffict;
424 : double xeta;
425 : double veta;
426 : double phivs;
427 : double work;
428 : double weight;
429 : } backup;
430 :
431 : std::vector<double> ffict; ///< current force of each fictitous dynamical variable.
432 : std::vector<double> fict_ave; ///< averaged values of each collective variable.
433 :
434 : std::vector<Value*> fictValue; ///< pointers to fictitious dynamical variables
435 : std::vector<Value*> vfictValue; ///< pointers to velocity of fictitious dynamical variables
436 :
437 : public:
438 : static void registerKeywords(Keywords& keys);
439 :
440 : explicit LogMFD(const ActionOptions&);
441 : void calculate();
442 : void update();
443 : void updateNVE();
444 : void updateNVT();
445 : void updateVS();
446 : void updateWork();
447 : void calcMeanForce();
448 : double calcEkin();
449 : double calcFlog();
450 : double calcClog();
451 :
452 : private:
453 : double sgn( double x ) {
454 55 : return x>0.0 ? 1.0 : x<0.0 ? -1.0 : 0.0;
455 : }
456 : };
457 :
458 13791 : PLUMED_REGISTER_ACTION(LogMFD,"LOGMFD")
459 :
460 : /**
461 : \brief instruction of parameters for Plumed manual.
462 : */
463 7 : void LogMFD::registerKeywords(Keywords& keys) {
464 7 : Bias::registerKeywords(keys);
465 7 : keys.use("ARG");
466 14 : keys.add("compulsory","INTERVAL",
467 : "Period of MD steps (\\f$N_m\\f$) to update fictitious dynamical variables." );
468 14 : keys.add("compulsory","DELTA_T",
469 : "Time step for the fictitious dynamical variables (DELTA_T=1 often works)." );
470 14 : keys.add("compulsory","THERMOSTAT",
471 : "Type of thermostat for the fictitious dynamical variables. NVE, NVT, VS are available." );
472 14 : keys.add("optional","TEMP",
473 : "Target temperature for the fictitious dynamical variables in LogMFD/PD. "
474 : "It is recommended to set TEMP to be the same as "
475 : "the temperature of the MD system in any thermostated LogMFD/PD run. "
476 : "If not provided, it will be taken from the temperature of the MD system (Gromacs only)." );
477 :
478 14 : keys.add("optional","TAMD",
479 : "When TAMD=1, TAMD/d-AFED calculations can be performed instead of LogMFD. Otherwise, the LogMFD protocol is switched on (default)." );
480 :
481 14 : keys.add("optional","ALPHA",
482 : "Alpha parameter for LogMFD. "
483 : "If not provided or provided as 0, it will be taken as 1/gamma. "
484 : "If gamma is also not provided, Alpha is set as 4, which is a sensible value when the unit of kcal/mol is used." );
485 14 : keys.add("optional","GAMMA",
486 : "Gamma parameter for LogMFD. "
487 : "If not provided or provided as 0, it will be taken as 1/alpha. "
488 : "If alpha is also not provided, Gamma is set as 0.25, which is a sensible value when the unit of kcal/mol is used." );
489 14 : keys.add("compulsory","KAPPA",
490 : "Spring constant of the harmonic restraining potential." );
491 :
492 14 : keys.add("compulsory","FICT_MAX",
493 : "Maximum values reachable for the fictitious dynamical variables. The variables will elastically bounce back at the boundary (mirror boundary)." );
494 14 : keys.add("compulsory","FICT_MIN",
495 : "Minimum values reachable for the fictitious dynamical variables. The variables will elastically bounce back at the boundary (mirror boundary)." );
496 :
497 14 : keys.add("optional","FICT",
498 : "The initial values of the fictitious dynamical variables. "
499 : "If not provided, they are set equal to their corresponding CVs for the initial atomic configuration." );
500 14 : keys.add("optional","VFICT",
501 : "The initial velocities of the fictitious dynamical variables. "
502 : "If not provided, they will be taken as 0. "
503 : "If THERMOSTAT=VS, they are instead automatically adjusted according to TEMP. " );
504 14 : keys.add("optional","MFICT",
505 : "Masses of each fictitious dynamical variable. "
506 : "If not provided, they will be taken as 10000." );
507 :
508 14 : keys.add("optional","XETA",
509 : "The initial eta variable of the Nose-Hoover thermostat "
510 : "for the fictitious dynamical variables. "
511 : "If not provided, it will be taken as 0." );
512 14 : keys.add("optional","VETA",
513 : "The initial velocity of eta variable. "
514 : "If not provided, it will be taken as 0." );
515 14 : keys.add("optional","META",
516 : "Mass of eta variable. "
517 : "If not provided, it will be taken as \\f$N*kb*T*100*100\\f$." );
518 :
519 14 : keys.add("compulsory","FLOG",
520 : "The initial free energy value in the LogMFD/PD run."
521 : "The origin of the free energy profile is adjusted by FLOG to "
522 : "realize \\f$F({\\bf X}(t)) > 0\\f$ at any \\f${\\bf X}(t)\\f$, "
523 : "resulting in enhanced barrier-crossing. "
524 : "(The value of \\f$H_{\\rm log}\\f$ is automatically "
525 : "set according to FLOG). "
526 : "In fact, \\f$F({\\bf X}(t))\\f$ is correctly "
527 : "estimated in PLUMED even when \\f$F({\\bf X}(t)) < 0\\f$ in "
528 : "the LogMFD/PD run." );
529 :
530 14 : keys.add("optional","WORK",
531 : "The initial value of the work done by fictitious dynamical "
532 : "variables in each replica. "
533 : "If not provided, it will be taken as 0.");
534 :
535 14 : keys.add("optional","TEMPPD",
536 : "Temperature of the Boltzmann factor in the Jarzynski weight in LogPD (Gromacs only). "
537 : "TEMPPD should be the same as the "
538 : "temperature of the MD system, while TEMP may be (in principle) different from it. "
539 : "If not provided, TEMPPD is set to be the same value as TEMP." );
540 :
541 7 : componentsAreNotOptional(keys);
542 14 : keys.addOutputComponent("_fict","default",
543 : "For example, the fictitious collective variable for LogMFD is specified as "
544 : "ARG=dist12 and LABEL=logmfd in LOGMFD section in Plumed input file, "
545 : "the associated fictitious dynamical variable can be specified as "
546 : "PRINT ARG=dist12,logmfd.dist12_fict FILE=COLVAR");
547 14 : keys.addOutputComponent("_vfict","default",
548 : "For example, the fictitious collective variable for LogMFD is specified as "
549 : "ARG=dist12 and LABEL=logmfd in LOGMFD section in Plumed input file, the "
550 : "velocity of the associated fictitious dynamical variable can be specified as "
551 : "PRINT ARG=dist12,logmfd.dist12_vfict FILE=COLVAR");
552 7 : }
553 :
554 :
555 : /**
556 : \brief constructor of LogMFD class
557 : \details This constructor initializes all parameters and variables,
558 : reads input file and set value of parameters and initial value of variables,
559 : and writes messages as Plumed log.
560 : */
561 3 : LogMFD::LogMFD( const ActionOptions& ao ):
562 : PLUMED_BIAS_INIT(ao),
563 3 : firsttime(true),
564 3 : step_initial(0),
565 3 : interval(10),
566 3 : delta_t(1.0),
567 6 : thermostat("NVE"),
568 3 : kbt(-1.0),
569 3 : kbtpd(-1.0),
570 3 : TAMD(0),
571 3 : alpha(0.0),
572 3 : gamma(0.0),
573 3 : kappa(getNumberOfArguments(),0.0),
574 3 : fict_max(getNumberOfArguments(),0.0),
575 3 : fict_min(getNumberOfArguments(),0.0),
576 3 : fict (getNumberOfArguments(),-999.0), // -999 means no initial values given in plumed.dat
577 3 : vfict(getNumberOfArguments(),0.0),
578 3 : mfict(getNumberOfArguments(),10000.0),
579 3 : xeta(0.0),
580 3 : veta(0.0),
581 3 : meta(0.0),
582 3 : flog(0.0),
583 3 : hlog(0.0),
584 3 : phivs(0.0),
585 3 : work(0.0),
586 3 : weight(0.0),
587 3 : ffict(getNumberOfArguments(),0.0),
588 3 : fict_ave(getNumberOfArguments(),0.0),
589 3 : fictValue(getNumberOfArguments(),NULL),
590 9 : vfictValue(getNumberOfArguments(),NULL) {
591 3 : backup.fict.resize(getNumberOfArguments(),0.0);
592 3 : backup.vfict.resize(getNumberOfArguments(),0.0);
593 3 : backup.ffict.resize(getNumberOfArguments(),0.0);
594 3 : backup.xeta = 0.0;
595 3 : backup.veta = 0.0;
596 3 : backup.phivs = 0.0;
597 3 : backup.work = 0.0;
598 3 : backup.weight = 0.0;
599 :
600 3 : parse("INTERVAL",interval);
601 3 : parse("DELTA_T",delta_t);
602 3 : parse("THERMOSTAT",thermostat);
603 3 : parse("TEMP",kbt); // read as temperature
604 3 : parse("TEMPPD",kbtpd); // read as temperature
605 :
606 3 : parse("TAMD",TAMD);
607 3 : parse("ALPHA",alpha);
608 3 : parse("GAMMA",gamma);
609 3 : parseVector("KAPPA",kappa);
610 :
611 3 : parseVector("FICT_MAX",fict_max);
612 3 : parseVector("FICT_MIN",fict_min);
613 :
614 3 : parseVector("FICT",fict);
615 3 : parseVector("VFICT",vfict);
616 3 : parseVector("MFICT",mfict);
617 :
618 3 : parse("XETA",xeta);
619 3 : parse("VETA",veta);
620 3 : parse("META",meta);
621 :
622 3 : parse("FLOG",flog);
623 :
624 : // read initial value of work for each replica of LogPD
625 3 : if( multi_sim_comm.Get_size()>1 ) {
626 0 : vector<double> vwork(multi_sim_comm.Get_size(),0.0);
627 0 : parseVector("WORK",vwork);
628 : // initial work of this replica
629 0 : work = vwork[multi_sim_comm.Get_rank()];
630 : } else {
631 3 : work = 0.0;
632 : }
633 :
634 3 : if( kbt>=0.0 ) {
635 3 : kbt *= plumed.getAtoms().getKBoltzmann();
636 : } else {
637 0 : kbt = plumed.getAtoms().getKbT();
638 : }
639 :
640 3 : if( kbtpd>=0.0 ) {
641 0 : kbtpd *= plumed.getAtoms().getKBoltzmann();
642 : } else {
643 3 : kbtpd = kbt;
644 : }
645 :
646 3 : if( meta == 0.0 ) {
647 2 : const double nkt = getNumberOfArguments()*kbt;
648 2 : meta = nkt*100.0*100.0;
649 : }
650 :
651 3 : if(alpha == 0.0 && gamma == 0.0) {
652 0 : alpha = 4.0;
653 0 : gamma = 1 / alpha;
654 3 : } else if(alpha != 0.0 && gamma == 0.0) {
655 3 : gamma = 1 / alpha;
656 0 : } else if(alpha == 0.0 && gamma != 0.0) {
657 0 : alpha = 1 / gamma;
658 : }
659 :
660 3 : checkRead();
661 :
662 : // output messaages to Plumed's log file
663 3 : if( multi_sim_comm.Get_size()>1 ) {
664 0 : if( TAMD ) {
665 0 : log.printf("TAMD-PD, replica parallel of TAMD, no logarithmic flattening.\n");
666 : } else {
667 0 : log.printf("LogPD, replica parallel of LogMFD.\n");
668 : }
669 0 : log.printf("number of replica : %d.\n", multi_sim_comm.Get_size() );
670 : } else {
671 3 : if( TAMD ) {
672 0 : log.printf("TAMD, no logarithmic flattening.\n");
673 : } else {
674 3 : log.printf("LogMFD, logarithmic flattening.\n");
675 : }
676 : }
677 :
678 3 : log.printf(" with harmonic force constant ");
679 6 : for(unsigned i=0; i<kappa.size(); i++) {
680 3 : log.printf(" %f",kappa[i]);
681 : }
682 3 : log.printf("\n");
683 :
684 3 : log.printf(" with interval of cv(ideal) update ");
685 3 : log.printf(" %d", interval);
686 3 : log.printf("\n");
687 :
688 3 : log.printf(" with time step of cv(ideal) update ");
689 3 : log.printf(" %f", delta_t);
690 3 : log.printf("\n");
691 :
692 3 : if( !TAMD ) {
693 3 : log.printf(" with alpha, gamma ");
694 3 : log.printf(" %f %f", alpha, gamma);
695 3 : log.printf("\n");
696 : }
697 :
698 3 : log.printf(" with Thermostat for cv(ideal) ");
699 3 : log.printf(" %s", thermostat.c_str());
700 3 : log.printf("\n");
701 :
702 3 : log.printf(" with initial free energy ");
703 3 : log.printf(" %f", flog);
704 3 : log.printf("\n");
705 :
706 3 : log.printf(" with mass of cv(ideal)");
707 6 : for(unsigned i=0; i<mfict.size(); i++) {
708 3 : log.printf(" %f", mfict[i]);
709 : }
710 3 : log.printf("\n");
711 :
712 3 : log.printf(" with initial value of cv(ideal)");
713 6 : for(unsigned i=0; i<fict.size(); i++) {
714 3 : log.printf(" %f", fict[i]);
715 : }
716 3 : log.printf("\n");
717 :
718 3 : log.printf(" with initial velocity of cv(ideal)");
719 6 : for(unsigned i=0; i<vfict.size(); i++) {
720 3 : log.printf(" %f", vfict[i]);
721 : }
722 3 : log.printf("\n");
723 :
724 3 : log.printf(" with maximum value of cv(ideal) ");
725 6 : for(unsigned i=0; i<fict_max.size(); i++) {
726 3 : log.printf(" %f",fict_max[i]);
727 : }
728 3 : log.printf("\n");
729 :
730 3 : log.printf(" with minimum value of cv(ideal) ");
731 6 : for(unsigned i=0; i<fict_min.size(); i++) {
732 3 : log.printf(" %f",fict_min[i]);
733 : }
734 3 : log.printf("\n");
735 :
736 3 : log.printf(" and kbt ");
737 3 : log.printf(" %f\n",kbt);
738 3 : log.printf(" kbt for PD %f\n",kbtpd);
739 :
740 : // setup Value* variables
741 6 : for(unsigned i=0; i<getNumberOfArguments(); i++) {
742 3 : std::string comp = getPntrToArgument(i)->getName()+"_fict";
743 3 : addComponentWithDerivatives(comp);
744 :
745 3 : if(getPntrToArgument(i)->isPeriodic()) {
746 : std::string a,b;
747 0 : getPntrToArgument(i)->getDomain(a,b);
748 0 : componentIsPeriodic(comp,a,b);
749 : } else {
750 3 : componentIsNotPeriodic(comp);
751 : }
752 3 : fictValue[i] = getPntrToComponent(comp);
753 :
754 3 : comp = getPntrToArgument(i)->getName()+"_vfict";
755 3 : addComponent(comp);
756 :
757 3 : componentIsNotPeriodic(comp);
758 3 : vfictValue[i] = getPntrToComponent(comp);
759 : }
760 3 : }
761 :
762 : /**
763 : \brief calculate forces for fictitious variables at every MD steps.
764 : \details This function calculates initial values of fictitious variables
765 : and write header messages to LogMFD log files at the first MFD step,
766 : calculates restraining fources comes from difference between the fictitious variable
767 : and collective variable at every MD steps.
768 : */
769 1500 : void LogMFD::calculate() {
770 1500 : if( firsttime ) {
771 3 : firsttime = false;
772 :
773 3 : step_initial = getStep();
774 :
775 : // set initial values of fictitious variables if they were not specified.
776 6 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
777 3 : if( fict[i] != -999.0 ) {
778 3 : continue; // -999 means no initial values given in plumed.dat
779 : }
780 :
781 : // use the collective variables as the initial of the fictitious variable.
782 0 : fict[i] = getArgument(i);
783 :
784 : // average values of fictitious variables by all replica.
785 0 : if( multi_sim_comm.Get_size()>1 ) {
786 0 : multi_sim_comm.Sum(fict[i]);
787 0 : fict[i] /= multi_sim_comm.Get_size();
788 : }
789 : }
790 :
791 : // initialize accumulation value to zero
792 6 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
793 3 : fict_ave[i] = 0.0;
794 : }
795 :
796 : // calculate invariant for NVE
797 3 : if(thermostat == "NVE") {
798 : // kinetic energy
799 1 : const double ekin = calcEkin();
800 : // potential energy
801 1 : const double pot = TAMD ? flog : sgn(flog)*gamma * std::log1p( alpha*fabs(flog) );
802 : // invariant
803 1 : hlog = pot + ekin;
804 2 : } else if(thermostat == "NVT") {
805 1 : const double nkt = getNumberOfArguments()*kbt;
806 : // kinetic energy
807 1 : const double ekin = calcEkin();
808 : // bath energy
809 1 : const double ekin_bath = 0.5*veta*veta*meta + xeta*nkt;
810 : // potential energy
811 1 : const double pot = TAMD ? flog : sgn(flog)*gamma * std::log1p( alpha*fabs(flog) );
812 : // invariant
813 1 : hlog = pot + ekin + ekin_bath;
814 1 : } else if(thermostat == "VS") {
815 : // kinetic energy
816 1 : const double ekin = calcEkin();
817 1 : if( ekin == 0.0 ) { // this means VFICT is not given.
818 : // initial velocities
819 2 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
820 1 : vfict[i] = sqrt(kbt/mfict[i]);
821 : }
822 : } else {
823 0 : const double nkt = getNumberOfArguments()*kbt;
824 0 : const double svs = sqrt(nkt/ekin/2);
825 0 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
826 0 : vfict[i] *= svs; // scale velocities
827 : }
828 : }
829 : // initial VS potential
830 1 : phivs = TAMD ? flog : sgn(flog)* gamma*std::log1p( alpha*fabs(flog) );
831 :
832 : // invariant
833 1 : hlog = 0.0;
834 : }
835 :
836 3 : weight = 1.0; // for replica parallel
837 :
838 : // open LogMFD's log file
839 3 : if( multi_sim_comm.Get_rank()==0 && comm.Get_rank()==0 ) {
840 3 : FILE *outlog = std::fopen("logmfd.out", "w");
841 :
842 : // output messages to LogMFD's log file
843 3 : if( multi_sim_comm.Get_size()>1 ) {
844 : fprintf(outlog, "# LogPD, replica parallel of LogMFD\n");
845 0 : fprintf(outlog, "# number of replica : %d\n", multi_sim_comm.Get_size() );
846 : } else {
847 : fprintf(outlog, "# LogMFD\n");
848 : }
849 :
850 : fprintf(outlog, "# CVs :");
851 6 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
852 : fprintf(outlog, " %s", getPntrToArgument(i)->getName().c_str() );
853 : }
854 : fprintf(outlog, "\n");
855 :
856 : fprintf(outlog, "# Mass for CV particles :");
857 6 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
858 3 : fprintf(outlog, "%15.6f", mfict[i]);
859 : }
860 : fprintf(outlog, "\n");
861 :
862 : fprintf(outlog, "# Mass for thermostat :");
863 3 : fprintf(outlog, "%15.6f", meta);
864 : fprintf(outlog, "\n");
865 : fprintf(outlog, "# 1:iter_mfd, 2:Flog, 3:2*Ekin/gkb[K], 4:eta, 5:Veta,\n");
866 :
867 6 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
868 3 : fprintf(outlog, "# %u:%s_fict(t), %u:%s_vfict(t), %u:%s_force(t),\n",
869 : 6+i*3, getPntrToArgument(i)->getName().c_str(),
870 : 7+i*3, getPntrToArgument(i)->getName().c_str(),
871 3 : 8+i*3, getPntrToArgument(i)->getName().c_str() );
872 : }
873 3 : fclose(outlog);
874 : }
875 :
876 3 : if( comm.Get_rank()==0 ) {
877 : // the number of replica is added to file name to distingwish replica.
878 3 : FILE *outlog2 = fopen("replica.out", "w");
879 6 : fprintf(outlog2, "# Replica No. %d of %d.\n",
880 3 : multi_sim_comm.Get_rank(), multi_sim_comm.Get_size() );
881 :
882 : fprintf(outlog2, "# 1:iter_mfd, 2:work, 3:weight,\n");
883 6 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
884 3 : fprintf(outlog2, "# %u:%s(q)\n",
885 : 4+i, getPntrToArgument(i)->getName().c_str() );
886 : }
887 3 : fclose(outlog2);
888 : }
889 :
890 : // output messages to Plumed's log file
891 : // log.printf("LOGMFD thermostat parameters Xeta Veta Meta");
892 : // log.printf(" %f %f %f", xeta, veta, meta);
893 : // log.printf("\n");
894 : // log.printf("# 1:iter_mfd, 2:Flog, 3:2*Ekin/gkb[K], 4:eta, 5:Veta,");
895 : // log.printf("# 6:X1(t), 7:V1(t), 8:F1(t), 9:X2(t), 10:V2(t), 11:F2(t), ...");
896 :
897 : } // firsttime
898 :
899 : // calculate force for fictitious variable
900 : double ene=0.0;
901 3000 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
902 : // difference between fictitious variable and collective variable.
903 1500 : const double diff = difference(i,fict[i],getArgument(i));
904 : // restraining force.
905 1500 : const double f = -kappa[i]*diff;
906 : setOutputForce(i,f);
907 :
908 : // restraining energy.
909 1500 : ene += 0.5*kappa[i]*diff*diff;
910 :
911 : // accumulate force, later it will be averaged.
912 1500 : ffict[i] += -f;
913 :
914 : // accumulate varience of collective variable, later it will be averaged.
915 1500 : fict_ave[i] += diff;
916 : }
917 :
918 : setBias(ene);
919 3000 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
920 : // correct fict so that it is inside [min:max].
921 1500 : double tmp = fict[i];
922 1500 : fict[i] = fictValue[i]->bringBackInPbc(fict[i]);
923 1500 : fictValue[i]->set(fict[i]);
924 1500 : vfictValue[i]->set(vfict[i]);
925 : }
926 1500 : } // calculate
927 :
928 : /**
929 : \brief update fictitious variables.
930 : \details This function manages evolution of fictitious variables.
931 : This function calculates mean force, updates fictitious variables by one MFD step,
932 : bounces back variables, updates free energy, and record logs.
933 : */
934 1500 : void LogMFD::update() {
935 1500 : if( (getStep()-step_initial)%interval != interval-1 ) {
936 : return;
937 : }
938 :
939 30 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
940 15 : backup.fict[i] = fict[i];
941 15 : backup.vfict[i] = vfict[i];
942 : }
943 15 : backup.xeta = xeta;
944 15 : backup.veta = veta;
945 15 : backup.phivs = phivs;
946 15 : backup.work = work;
947 15 : backup.weight = weight;
948 :
949 : // calc mean force for fictitious variables
950 15 : calcMeanForce();
951 :
952 : // record log for fictitious variables
953 15 : if( multi_sim_comm.Get_rank()==0 && comm.Get_rank()==0 ) {
954 15 : const double ekin = calcEkin();
955 15 : const double temp = 2.0*ekin/getNumberOfArguments()/plumed.getAtoms().getKBoltzmann();
956 :
957 15 : FILE *outlog = std::fopen("logmfd.out", "a");
958 15 : fprintf(outlog, "%*d", 8, (int)(getStep()-step_initial)/interval);
959 15 : fprintf(outlog, "%15.6f", flog);
960 : fprintf(outlog, "%15.6f", temp);
961 15 : fprintf(outlog, "%15.6f", xeta);
962 15 : fprintf(outlog, "%15.6f", veta);
963 30 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
964 15 : fprintf(outlog, "%15.6f", fict[i]);
965 15 : fprintf(outlog, "%15.6f", vfict[i]);
966 15 : fprintf(outlog, "%15.6f", ffict[i]);
967 : }
968 : fprintf(outlog," \n");
969 15 : fclose(outlog);
970 : }
971 :
972 : // record log for collective variables
973 15 : if( comm.Get_rank()==0 ) {
974 : // the number of replica is added to file name to distingwish replica.
975 15 : FILE *outlog2 = fopen("replica.out", "a");
976 15 : fprintf(outlog2, "%*d", 8, (int)(getStep()-step_initial)/interval);
977 15 : fprintf(outlog2, "%16.6e ", work);
978 15 : fprintf(outlog2, "%16.6e ", weight);
979 30 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
980 15 : fprintf(outlog2, "%15.6f", fict_ave[i]);
981 : }
982 : fprintf(outlog2," \n");
983 15 : fclose(outlog2);
984 : }
985 :
986 : // update fictitious variables
987 15 : if(thermostat == "NVE") {
988 5 : updateNVE();
989 10 : } else if(thermostat == "NVT") {
990 5 : updateNVT();
991 5 : } else if(thermostat == "VS") {
992 5 : updateVS();
993 : }
994 :
995 : // update work done by fictitious dynamical variables
996 15 : updateWork();
997 :
998 : // check boundary
999 : bool reject = false;
1000 30 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1001 15 : if( fict[i] < fict_min[i] || fict_max[i] < fict[i] ) {
1002 : reject = true;
1003 0 : backup.vfict[i] *= -1.0;
1004 : }
1005 : }
1006 15 : if( reject ) {
1007 0 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1008 0 : fict[i] = backup.fict[i];
1009 0 : vfict[i] = backup.vfict[i];
1010 : }
1011 0 : xeta = backup.xeta;
1012 0 : veta = backup.veta;
1013 0 : phivs = backup.phivs;
1014 0 : work = backup.work;
1015 0 : weight = backup.weight;
1016 : }
1017 :
1018 : // update free energy
1019 15 : flog = calcFlog();
1020 :
1021 : // reset mean force
1022 30 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1023 15 : ffict[i] = 0.0;
1024 15 : fict_ave[i] = 0.0;
1025 : }
1026 :
1027 : } // update
1028 :
1029 : /**
1030 : \brief update fictitious variables by NVE mechanics.
1031 : \details This function updates ficitious variables by one NVE-MFD step using mean forces
1032 : and flattening coefficient and free energy.
1033 : */
1034 5 : void LogMFD::updateNVE() {
1035 5 : const double dt = delta_t;
1036 :
1037 : // get latest free energy and flattening coefficient
1038 5 : flog = calcFlog();
1039 5 : const double clog = calcClog();
1040 :
1041 : // update all ficitious variables by one MFD step
1042 10 : for( unsigned i=0; i<getNumberOfArguments(); ++i ) {
1043 : // update velocity (full step)
1044 5 : vfict[i]+=clog*ffict[i]*dt/mfict[i];
1045 : // update position (full step)
1046 : fict[i]+=vfict[i]*dt;
1047 : }
1048 5 : } // updateNVE
1049 :
1050 : /**
1051 : \brief update fictitious variables by NVT mechanics.
1052 : \details This function updates ficitious variables by one NVT-MFD step using mean forces
1053 : and flattening coefficient and free energy.
1054 : */
1055 5 : void LogMFD::updateNVT() {
1056 5 : const double dt = delta_t;
1057 5 : const double nkt = getNumberOfArguments()*kbt;
1058 :
1059 : // backup vfict
1060 10 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1061 5 : backup.vfict[i] = vfict[i];
1062 : }
1063 :
1064 : const int niter=5;
1065 30 : for(unsigned j=0; j<niter; ++j) {
1066 : // get latest free energy and flattening coefficient
1067 25 : flog = calcFlog();
1068 25 : const double clog = calcClog();
1069 :
1070 : // restore vfict from backup.vfict
1071 50 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1072 25 : vfict[i] = backup.vfict[i];
1073 : }
1074 :
1075 : // evolve vfict from backup.vfict by dt/2
1076 50 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1077 25 : vfict[i] *= exp(-0.25*dt*veta);
1078 25 : vfict[i] += 0.5*dt*clog*ffict[i]/mfict[i];
1079 25 : vfict[i] *= exp(-0.25*dt*veta);
1080 : }
1081 : }
1082 :
1083 : // get latest free energy and flattening coefficient
1084 5 : flog = calcFlog();
1085 5 : const double clog = calcClog();
1086 :
1087 : // evolve vfict by dt/2, and evolve fict by dt
1088 10 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1089 5 : vfict[i] *= exp(-0.25*dt*veta);
1090 5 : vfict[i] += 0.5*dt*clog*ffict[i]/mfict[i];
1091 5 : vfict[i] *= exp(-0.25*dt*veta);
1092 5 : fict[i] += dt*vfict[i];
1093 : }
1094 :
1095 : // evolve xeta and veta by dt
1096 5 : xeta += 0.5*dt*veta;
1097 5 : const double ekin = calcEkin();
1098 5 : veta += dt*(2.0*ekin-nkt)/meta;
1099 5 : xeta += 0.5*dt*veta;
1100 5 : } // updateNVT
1101 :
1102 : /**
1103 : \brief update fictitious variables by VS mechanics.
1104 : \details This function updates ficitious variables by one VS-MFD step using mean forces
1105 : and flattening coefficient and free energy.
1106 : */
1107 5 : void LogMFD::updateVS() {
1108 5 : const double dt = delta_t;
1109 5 : const double nkt = getNumberOfArguments()*kbt;
1110 :
1111 : // get latest free energy and flattening coefficient
1112 5 : flog = calcFlog();
1113 5 : const double clog = calcClog();
1114 :
1115 10 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1116 : // update velocity (full step)
1117 5 : vfict[i] += clog*ffict[i]*dt/mfict[i];
1118 : }
1119 :
1120 5 : const double ekin = calcEkin();
1121 5 : const double svs = sqrt(nkt/ekin/2);
1122 :
1123 10 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1124 : // update position (full step)
1125 5 : vfict[i] *= svs;
1126 5 : fict[i] += vfict[i]*dt;
1127 : }
1128 :
1129 : // evolve VS potential
1130 5 : phivs += nkt*std::log(svs);
1131 5 : } // updateVS
1132 :
1133 : /**
1134 : \brief update work done by fictious variables.
1135 : \details This function updates work done by ficitious variables.
1136 : */
1137 15 : void LogMFD::updateWork() {
1138 : // accumulate work, it was initialized as 0.0
1139 30 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1140 15 : work -= backup.ffict[i] * vfict[i] * delta_t;
1141 : }
1142 15 : } // updateWork
1143 :
1144 : /**
1145 : \brief calculate mean force for fictitious variables.
1146 : \details This function calculates mean forces by averaging forces accumulated during one MFD step,
1147 : update work variables done by fictitious variables by one MFD step,
1148 : calculate weight variable of this replica for LogPD.
1149 : */
1150 15 : void LogMFD::calcMeanForce() {
1151 : // cale temporal mean force for each CV
1152 30 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1153 15 : ffict[i] /= interval;
1154 : // backup force of replica
1155 15 : backup.ffict[i] = ffict[i];
1156 : // average of diff (getArgument(i)-fict[i])
1157 15 : fict_ave[i] /= interval;
1158 : // average of getArgument(i)
1159 15 : fict_ave[i] += fict[i];
1160 :
1161 : // correct fict_ave so that it is inside [min:max].
1162 15 : fict_ave[i] = fictValue[i]->bringBackInPbc(fict_ave[i]);
1163 : }
1164 :
1165 : // for replica parallel
1166 15 : if( multi_sim_comm.Get_size()>1 ) {
1167 : // find the minimum work among all replicas
1168 0 : double work_min = work;
1169 0 : multi_sim_comm.Min(work_min);
1170 :
1171 : // weight of this replica.
1172 : // here, work is reduced by work_min to avoid all exp(-work/kbt)s disconverge
1173 0 : if( kbtpd == 0.0 ) {
1174 0 : weight = work==work_min ? 1.0 : 0.0;
1175 : } else {
1176 0 : weight = exp(-(work-work_min)/kbtpd);
1177 : }
1178 :
1179 : // normalize the weight
1180 0 : double sum_weight = weight;
1181 0 : multi_sim_comm.Sum(sum_weight);
1182 0 : weight /= sum_weight;
1183 :
1184 : // weighting force of this replica
1185 0 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1186 0 : ffict[i] *= weight;
1187 : }
1188 :
1189 : // averaged mean forces of all replica.
1190 0 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1191 0 : multi_sim_comm.Sum(ffict[i]);
1192 : }
1193 : // now, mean force is obtained.
1194 : }
1195 15 : } // calcMeanForce
1196 :
1197 : /**
1198 : \brief calculate kinetic energy of fictitious variables.
1199 : \retval kinetic energy.
1200 : \details This function calculates sum of kinetic energy of all fictitious variables.
1201 : */
1202 83 : double LogMFD::calcEkin() {
1203 : double ekin=0.0;
1204 166 : for(unsigned i=0; i<getNumberOfArguments(); ++i) {
1205 83 : ekin += mfict[i]*vfict[i]*vfict[i]*0.5;
1206 : }
1207 83 : return ekin;
1208 : } // calcEkin
1209 :
1210 : /**
1211 : \brief calculate free energy of fictitious variables.
1212 : \retval free energy.
1213 : \details This function calculates free energy by using invariant of canonical mechanics.
1214 : */
1215 55 : double LogMFD::calcFlog() {
1216 55 : const double nkt = getNumberOfArguments()*kbt;
1217 55 : const double ekin = calcEkin();
1218 : double pot;
1219 :
1220 55 : if (thermostat == "NVE") {
1221 10 : pot = hlog - ekin;
1222 45 : } else if (thermostat == "NVT") {
1223 35 : const double ekin_bath = 0.5*veta*veta*meta+xeta*nkt;
1224 35 : pot = hlog - ekin - ekin_bath;
1225 10 : } else if (thermostat == "VS") {
1226 10 : pot = phivs;
1227 : } else {
1228 : pot = 0.0; // never occurs
1229 : }
1230 :
1231 110 : return TAMD ? pot : sgn(pot)*expm1(fabs(pot)/gamma)/alpha;
1232 : } // calcFlog
1233 :
1234 : /**
1235 : \brief calculate coefficient for flattening.
1236 : \retval flattering coefficient.
1237 : \details This function returns 1.0 for TAMD, flattening coefficient for LogMFD.
1238 : */
1239 40 : double LogMFD::calcClog() {
1240 40 : return TAMD ? 1.0 : alpha*gamma/(alpha*fabs(flog)+1.0);
1241 : } // calcClog
1242 :
1243 : } // logmfd
1244 : } // PLMD
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