M05 Finite Temperature Simulation - Revision history

Kwkang: /* Constant Stress (N\sigmaH) Ensemble */

2011-01-20T17:26:04Z

Constant Stress (N\sigmaH) Ensemble

← Older revision		Revision as of 17:26, 20 January 2011
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	#MD++ finalcnfile = Mo-5X5X5-NPH.cn writecn eval		#MD++ finalcnfile = Mo-5X5X5-NPH.cn writecn eval
	MD++ sleep quit		MD++ sleep quit

	}}
	</pre>		</pre>

Kwkang: /* Canonical(NVT) Ensemble with Nose-Hoover Chain */

2011-01-20T17:25:40Z

Canonical(NVT) Ensemble with Nose-Hoover Chain

← Older revision		Revision as of 17:25, 20 January 2011
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	MD++ run eval		MD++ run eval
	MD++ sleep quit		MD++ sleep quit
	}}

	</pre>		</pre>

Kwkang: /* Microcanonical (NVE) Ensemble */

2011-01-20T17:24:44Z

Microcanonical (NVE) Ensemble

← Older revision		Revision as of 17:24, 20 January 2011
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	writeall = 1 DOUBLE_T = 1		writeall = 1 DOUBLE_T = 1
	randseed = 12345 srand48 #randomize random number generator		randseed = 12345 srand48 #randomize random number generator
		⚫	}}

	#*******************************************		#*******************************************
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	MD++ finalcnfile = 300K-5X5X5.cn writecn eval		MD++ finalcnfile = 300K-5X5X5.cn writecn eval
	MD++ sleep quit		MD++ sleep quit

⚫	}}
	</pre>		</pre>

Kwkang: /* Canonical(NVT) Ensemble */

2009-03-04T22:52:27Z

Canonical(NVT) Ensemble

← Older revision		Revision as of 22:52, 4 March 2009
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	{\|border="0" align="center"		{\|border="0" align="center"
	\|<math> Q = \frac{3 N k_B T_{\mathrm{OBJ}}}{\mathrm{vt2}}\times (1e+24)</math>.		\|<math> Q = \frac{3 N k_B T_{\mathrm{OBJ}}}{\mathrm{vt2}}\times (1e+24)</math>,
	\|}		\|}
	where ''N'' is number of atoms and ''k_B'' is the Boltzmann constant (8.617343e-5 eV/K).		where ''N'' is number of atoms and ''k_B'' is the Boltzmann constant (8.617343e-5 eV/K).
	<!-- For convenience, we also defined thermal mass '''NHMass''', which is exactly the Nose'-Hoover thermal mass ''Q''. -->		<!-- For convenience, we also defined thermal mass '''NHMass''', which is exactly the Nose'-Hoover thermal mass ''Q''. -->
	When '''NHMass''' is non-zero, '''vt2''' will be superceded. When ''N'' = 250 and ''T'' = 300 K (or k_B T ~ 0.026 eV), '''vt2''' = 1e28 (1/sec)<sup>2</sup> corresponds to '''NHMass''' = 1.95e-03 (eV·ps<sup>2</sup>). In comparison with other MD programs such as [http://lammps.sandia.gov LAMMPS], '''vt2''' is proportional to the square of the thermal damping frequency ω, or '''vt2'''~ω<sup>2</sup>. The proportional constant is determined by equating both units. If ω is given in the unit of 1/ps, then the equality becomes '''vt2'''= 10<sup>24</sup>ω<sup>2</sup>. In this ~~cae~~, ω = 100 (1/ps) for '''vt2'''=10<sup>28</sup> (1/sec)<sup>2</sup>.		When '''NHMass''' is non-zero, '''vt2''' will be superceded. When ''N'' = 250 and ''T'' = 300 K (or k_B T ~ 0.026 eV), '''vt2''' = 1e28 (1/sec)<sup>2</sup> corresponds to '''NHMass''' = 1.95e-03 (eV·ps<sup>2</sup>). In comparison with other MD programs such as [http://lammps.sandia.gov LAMMPS], '''vt2''' is proportional to the square of the thermal damping frequency ω, or '''vt2'''~ω<sup>2</sup>. The proportional constant is determined by equating both units. If ω is given in the unit of 1/ps, then the equality becomes '''vt2'''= 10<sup>24</sup>ω<sup>2</sup>. In this case, ω = 100 (1/ps) for '''vt2'''=10<sup>28</sup> (1/sec)<sup>2</sup>.

	The bigger '''vt2''' is (or the smaller '''NHMass''' is), the faster the instantaneous temperature fluctuates around the desired temperature, as shown in Fig. 3. The MD simulation also writes out variable '''HELMP''' in the property file; '''HELMP''' is the total energy of the system plus that of the thermal reservior and should be conserved. The flucutation of '''HELMP''' around its mean value is also plotted in Fig. 3.		The bigger '''vt2''' is (or the smaller '''NHMass''' is), the faster the instantaneous temperature fluctuates around the desired temperature, as shown in Fig. 3. The MD++ simulation also writes out the value of a variable '''HELMP''' in the property file; '''HELMP''' is the total energy of the system plus that of the thermal reservior, and should be conserved. The flucutation of '''HELMP''' around its mean value is also plotted in Fig. 3.

	<gallery caption="Fig.3 The Effect of Nose-Hoover Mass in NVT MD" widths="300px" heights="200px" perrow="2">		<gallery caption="Fig.3 The Effect of Nose-Hoover Mass in NVT MD" widths="300px" heights="200px" perrow="2">
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	</gallery>		</gallery>

	In the above example script, after the first MD simulation, we use the command '''multiplyvelocity''' to reverse the velocities of all atoms. This is done by setting <tt>input = -1</tt>, so that -1 is multiplied to the velocities of all atoms. We then continue the MD simulation for the same duration of time as the first one, in order to test the reversibility of the numerical (symplectic) integrator. After the second MD simulation (in the reverse direction), we save the atomic configuration into file <tt>300K-5x5x5-NVT.cn</tt>. Comparing this file with the file <tt>300K-5x5x5.cn</tt>, which contains the atomic configuration at the beginning of the (forward) simulation, reveals that the scaled coordinates of all atoms are identical in the two files within 1e-14 (close to machine precision). This demonstrates the reversibility of the chosen integrator. If on the other hand, <tt>integrator_type = Gear6</tt> is used, the discrepancy in the atomic coordinates will be on the order of 1e-6, which shows that the Gear6 integrator is not reversible.		In figure 3, you may notice that the energy and the temperature are symmetric before and after the simulation step = 2000. In the above example script, after the first MD simulation (or after the 1st 2000 steps), we use the command '''multiplyvelocity''' to reverse the velocities of all atoms. This is done by setting <tt>input = -1</tt>, so that -1 can be multiplied to the velocities of all atoms and also to ζ. We then continue the MD simulation for the same duration of time as the first one, in order to test the reversibility of the numerical (symplectic) integrator. After the second MD simulation (in the reverse direction), we save the atomic configuration into file <tt>300K-5x5x5-NVT.cn</tt>. Comparing this file with the file <tt>300K-5x5x5.cn</tt>, which contains the atomic configuration at the beginning of the (forward) simulation, reveals that the scaled coordinates of all atoms are identical in the two files within 1e-14 (close to the machine precision). This demonstrates the reversibility of the chosen integrator. If on the other hand, <tt>integrator_type = Gear6</tt> is used, the discrepancy in the atomic coordinates will be on the order of 1e-6, which shows that the Gear6 integrator is not reversible.

	=== Canonical(NVT) Ensemble with Nose-Hoover Chain ===		=== Canonical(NVT) Ensemble with Nose-Hoover Chain ===

Kwkang: /* Canonical(NVT) Ensemble */

2009-03-04T22:27:30Z

Canonical(NVT) Ensemble

← Older revision		Revision as of 22:27, 4 March 2009
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	where ''N'' is number of atoms and ''k_B'' is the Boltzmann constant (8.617343e-5 eV/K).		where ''N'' is number of atoms and ''k_B'' is the Boltzmann constant (8.617343e-5 eV/K).
	<!-- For convenience, we also defined thermal mass '''NHMass''', which is exactly the Nose'-Hoover thermal mass ''Q''. -->		<!-- For convenience, we also defined thermal mass '''NHMass''', which is exactly the Nose'-Hoover thermal mass ''Q''. -->
	When '''NHMass''' is non-zero, '''vt2''' will be ~~ignored~~. When ''N'' = 250 and ''T'' = 300 K (or k_B T ~ 0.026 eV), '''vt2''' = 1e28 (1/sec)<sup>2</sup> corresponds to '''NHMass''' = 1.95e-03 (eV·ps<sup>2</sup>). ~~The~~ ~~bigger~~ ~~'''vt2'''~~ is ~~(or~~ ~~the~~ ~~smaller~~ '''~~NHMass~~''' is), ~~the~~ ~~faster~~ the ~~instantaneous~~ ~~temperature~~ ~~fluctuates~~ ~~around~~ ~~the~~ ~~desired~~ ~~temperature~~, ~~as shown in Fig. 3. The MD simulation also writes out variable~~ '''~~HELMP~~''' in ~~the~~ ~~property file; '''HELMP'''~~ is ~~the~~ ~~total~~ ~~energy~~ of ~~the~~ ~~system~~ ~~plus~~ ~~that~~ of the ~~thermal~~ ~~reservior~~ ~~and~~ ~~should~~ be ~~conserved.~~ ~~The flucutation of~~ '''~~HELMP~~''' ~~around~~ ~~its~~ ~~mean~~ ~~value~~ is ~~also~~ ~~plotted~~ in ~~Fig.~~ 3.		When '''NHMass''' is non-zero, '''vt2''' will be superceded. When ''N'' = 250 and ''T'' = 300 K (or k_B T ~ 0.026 eV), '''vt2''' = 1e28 (1/sec)<sup>2</sup> corresponds to '''NHMass''' = 1.95e-03 (eV·ps<sup>2</sup>). In comparison with other MD programs such as [http://lammps.sandia.gov LAMMPS], '''vt2''' is proportional to the square of the thermal damping frequency ω, or '''vt2'''~ω<sup>2</sup>. The proportional constant is determined by equating both units. If ω is given in the unit of 1/ps, then the equality becomes '''vt2'''= 10<sup>24</sup>ω<sup>2</sup>. In this cae, ω = 100 (1/ps) for '''vt2'''=10<sup>28</sup> (1/sec)<sup>2</sup>.

			The bigger '''vt2''' is (or the smaller '''NHMass''' is), the faster the instantaneous temperature fluctuates around the desired temperature, as shown in Fig. 3. The MD simulation also writes out variable '''HELMP''' in the property file; '''HELMP''' is the total energy of the system plus that of the thermal reservior and should be conserved. The flucutation of '''HELMP''' around its mean value is also plotted in Fig. 3.

	<gallery caption="Fig.3 The Effect of Nose-Hoover Mass in NVT MD" widths="300px" heights="200px" perrow="2">		<gallery caption="Fig.3 The Effect of Nose-Hoover Mass in NVT MD" widths="300px" heights="200px" perrow="2">

Kwkang: /* Canonical(NVT) Ensemble */

2009-03-04T20:33:39Z

Canonical(NVT) Ensemble

← Older revision		Revision as of 20:33, 4 March 2009
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	for MD simulations of N particles in 3-dimensions. We can use three different implementations of the Nose-Hoover thermostat in conjunction with the velocity Verlet integrator. When <tt>implementation_type = 0</tt>, an implicit integrator is used. When <tt>implementation_type = 1</tt>, an explicit integrator based on Stormer-Verlet method is used. When <tt>implementation_type = 2</tt>, an explicit integrator baed on Liouville formulation is used.		for MD simulations of N particles in 3-dimensions. We can use three different implementations of the Nose-Hoover thermostat in conjunction with the velocity Verlet integrator. When <tt>implementation_type = 0</tt>, an implicit integrator is used. When <tt>implementation_type = 1</tt>, an explicit integrator based on Stormer-Verlet method is used. When <tt>implementation_type = 2</tt>, an explicit integrator baed on Liouville formulation is used.

	The Nose-Hoover thermal mass <math>Q</math> in the above equation of motion is specified through the MD++ variable '''vt2''' by the following relationship		The MD++ variable '''NHMass''', in the unit of eV·ps<sup>2</sup>, corresponds to the Nose-Hoover thermal mass <math>Q</math> in the above equation of motion. The thermal mass <math>Q</math> can also be specified through the MD++ variable '''vt2''' , in the unit of (1/sec)<sup>2</sup>, by the following relationship

	{\|border="0" align="center"		{\|border="0" align="center"
	\|<math> Q = \frac{3 N k_B T_{\mathrm{OBJ}}}{\mathrm{vt2}}\times (1e+24)</math>.		\|<math> Q = \frac{3 N k_B T_{\mathrm{OBJ}}}{\mathrm{vt2}}\times (1e+24)</math>.
	\|}		\|}
			where ''N'' is number of atoms and ''k_B'' is the Boltzmann constant (8.617343e-5 eV/K).
⚫	where ''N'' is number of atoms and ''k_B'' is the Boltzmann constant (8.617343e-5 eV/K). For convenience, we also defined thermal mass '''NHMass''', which is exactly the Nose'-Hoover thermal mass ''Q''. (When '''NHMass''' is non-zero, '''vt2''' will be ignored.) When ''N'' = 250 and ''T'' = 300 K (or k_B T ~ 0.026 eV), '''vt2''' = 1e28 corresponds to '''NHMass''' = 1.95e-03. The bigger '''vt2''' is (or the smaller '''NHMass''' is), the faster the instantaneous temperature fluctuates around the desired temperature, as shown in Fig. 3. The MD simulation also writes out variable '''HELMP''' in the property file; '''HELMP''' is the total energy of the system plus that of the thermal reservior and should be conserved. The flucutation of '''HELMP''' around its mean value is also plotted in Fig. 3.
			<!-- For convenience, we also defined thermal mass '''NHMass''', which is exactly the Nose'-Hoover thermal mass ''Q''. -->
		⚫	When '''NHMass''' is non-zero, '''vt2''' will be ignored. When ''N'' = 250 and ''T'' = 300 K (or k_B T ~ 0.026 eV), '''vt2''' = 1e28 (1/sec)<sup>2</sup> corresponds to '''NHMass''' = 1.95e-03 (eV·ps<sup>2</sup>). The bigger '''vt2''' is (or the smaller '''NHMass''' is), the faster the instantaneous temperature fluctuates around the desired temperature, as shown in Fig. 3. The MD simulation also writes out variable '''HELMP''' in the property file; '''HELMP''' is the total energy of the system plus that of the thermal reservior and should be conserved. The flucutation of '''HELMP''' around its mean value is also plotted in Fig. 3.

	<gallery caption="Fig.3 The Effect of Nose-Hoover Mass in NVT MD" widths="300px" heights="200px" perrow="2">		<gallery caption="Fig.3 The Effect of Nose-Hoover Mass in NVT MD" widths="300px" heights="200px" perrow="2">

Caiwei at 04:40, 14 April 2008

2008-04-14T04:40:38Z

← Older revision		Revision as of 04:40, 14 April 2008
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	</DIV>		</DIV>
	<P ALIGN="CENTER">[First written, [ Jan 19 ]], [[2007]]</P>		<P ALIGN="CENTER">[First written, [ Jan 19 ]], [[2007]]</P>
	<P ALIGN="CENTER">[Last Modified, [ ~~Mar~~ 03 ]], [[2008]]</P>		<P ALIGN="CENTER">[Last Modified, [ Apr 13 ]], [[2008]]</P>
	<P>		<P>
	<BR><HR>		<BR><HR>

Caiwei: /* Constant Stress (N $\sigma$ H) Ensemble */

2008-04-14T04:39:46Z

Constant Stress (N<math>\sigma</math>H) Ensemble

Show changes

Caiwei: /* Canonical(NVT) Ensemble with Nose-Hoover Chain */

2008-04-14T04:04:52Z

Canonical(NVT) Ensemble with Nose-Hoover Chain

@@ Line 215: / Line 215: @@
 === Canonical(NVT) Ensemble with Nose-Hoover Chain ===
 ----
-Martyna ''et al''<ref>G. J. Martyna, M. L. Klein and M. Tuckerman, "Nose-Hoover chains: The canonical ensemble via continuous dynamics", J. Chem. Phys. '''97''' 2635--2643</ref> modified the original Nose-Hoover thermostat such that a chain of thermostats is added instead of one thermostat. The purpose of this chain method is to increase the size of the phase space and help the system to be ergodic even when the system is stiff or its dynamics is not ergodic. To implement the Nose-Hoover chain integrator, we refered another paper of Martyna's.<ref>G. J. Martyna, "Explicit reversible integrators for extended systems dynamics", Molecular Physics '''87''' 1117-1157 (1996)</ref>
+Martyna ''et al''<ref>G. J. Martyna, M. L. Klein and M. Tuckerman, "Nose-Hoover chains: The canonical ensemble via continuous dynamics", J. Chem. Phys. '''97''' 2635--2643</ref> modified the original Nose-Hoover thermostat so that a chain of thermostats are used instead of just one thermostat. The purpose of this chain method is to increase the size of the phase space and help the system to be ergodic when the system is stiff or is not ergodic.  Our implementation of the Nose-Hoover chain method in MD++ follows another paper of Martyna.<ref>G. J. Martyna, "Explicit reversible integrators for extended systems dynamics", Molecular Physics '''87''' 1117-1157 (1996)</ref>  The following example script, <tt>Mo_NVTC.tcl</tt>, demonstrates how to use the Nose-Hoover chain method in MD++.
 <pre>
@@ Line 226: / Line 224: @@
 # Definition of procedures
 #*******************************************
 #--------------------------------------------
 proc setup_md { } { MD++ {
@@ Line 274: / Line 264: @@
 </pre>
 === Constant Stress (N<math>\sigma</math>H) Ensemble ===

Caiwei: /* Canonical(NVT) Ensemble */

2008-04-14T03:28:34Z

Canonical(NVT) Ensemble

← Older revision		Revision as of 03:28, 14 April 2008
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	MD++ sleep quit		MD++ sleep quit
	</pre>		</pre>
	Instead of creating a perfect crystal as the initial condition, this script uses the command '''readcn''' to read the file <tt>300K_5X5X5.cn</tt> created at the end of the previous simulation (NVE ensemble simulation). Note that in this case, the new simulation must use the same time step as the previous simulation that created the .cn file. This is because in MD++ the velocity information are stored as scaled velocity time the time step. If you really need to change the time step in the new simulation (not recommended), you will need to rescale your velocity using the MD++ command '''~~scalevelocity~~'''.		Instead of creating a perfect crystal as the initial condition, this script uses the command '''readcn''' to read the file <tt>300K_5X5X5.cn</tt> created at the end of the previous simulation (NVE ensemble simulation). Note that in this case, the new simulation must use the same time step as the previous simulation that created the .cn file. This is because in MD++ the velocity information are stored as scaled velocity time the time step. If you really need to change the time step in the new simulation (not recommended), you will need to rescale your velocity using the MD++ command '''multiplyvelocity'''.

	Setting '''ensemble_type = "NVT"''' activates Nose-Hoover thermostat, which ~~basically~~ adds ~~an additional~~ variable (<math>\zeta</math>) to the ~~system~~ ~~such~~ ~~that~~ ~~the~~ ~~temperature~~ is ~~controlled by~~ the ~~feedback routine virtually mimicking~~ heat ~~transfer~~ to the heat reservoir,		Setting '''ensemble_type = "NVT"''' activates the Nose-Hoover thermostat, which adds a variable (<math>\zeta</math>) to the equation of motion. This variable mimicks the heat deposited to the heat reservoir. The coupled equation of motion is
	{\|border="0" align="center"		{\|border="0" align="center"
	\|<math> \begin{array}{rcl} \ddot\mathbf{r}_i &=& -\frac{1}{m_i}\frac{\partial U(\{\mathbf{r}_i\})}{\partial \mathbf{r}_i} - \zeta \dot\mathbf{r}_i \\ \dot\zeta &=& \frac{3N k_B}{Q} ( T_{\mathrm{inst}} - T_{\mathrm{OBJ}} ) \end{array}</math>.		\|<math> \begin{array}{rcl} \ddot\mathbf{r}_i &=& -\frac{1}{m_i}\frac{\partial U(\{\mathbf{r}_i\})}{\partial \mathbf{r}_i} - \zeta \dot\mathbf{r}_i \\ \dot\zeta &=& \frac{3N k_B}{Q} ( T_{\mathrm{inst}} - T_{\mathrm{OBJ}} ) \end{array}</math>.
	\|}		\|}
			for MD simulations of N particles in 3-dimensions. We can use three different implementations of the Nose-Hoover thermostat in conjunction with the velocity Verlet integrator. When <tt>implementation_type = 0</tt>, an implicit integrator is used. When <tt>implementation_type = 1</tt>, an explicit integrator based on Stormer-Verlet method is used. When <tt>implementation_type = 2</tt>, an explicit integrator baed on Liouville formulation is used.
	when the degree of freedom is 3''N''.

	In MD++, Nose-Hoover thermostat are implemented in three diﬀerent way, each of which uses different integrator deﬁned through '''implementation_type'''. If it is zero, the implicit integrator will be chosen. If it is one, the explicit integrator based on Sto¨rmer-Verlet method will work. If it is two, another explicit integrator based on Liouville formulation will be activated.
			The Nose-Hoover thermal mass <math>Q</math> in the above equation of motion is specified through the MD++ variable '''vt2''' by the following relationship

	Thermal coeﬃcient '''vt2''' is related with thermal mass ''Q'' of Nose´-Hoover thermostat as
	{\|border="0" align="center"		{\|border="0" align="center"
	\|<math> Q = \frac{3 N k_B T_{\mathrm{OBJ}}}{\mathrm{vt2}}\times (1e+24)</math>.		\|<math> Q = \frac{3 N k_B T_{\mathrm{OBJ}}}{\mathrm{vt2}}\times (1e+24)</math>.
	\|}		\|}
	where ''N'' is number of atoms and ''k_B'' is the Boltzmann constant (8.617343e-5 eV/K). For convenience, we also defined thermal mass '''NHMass''', which is exactly Nose'-Hoover thermal mass ''Q''. When ''N'' = 250 and ''T'' = 300 K (or k_B T ~ 0.026 eV), '''vt2''' = 1e28 corresponds to '''NHMass''' = 1.95e-03. The bigger '''vt2''' is (or the smaller '''NHMass''' is), the faster the ~~response~~ of the system is to ~~control~~ the ~~temperature~~.		where ''N'' is number of atoms and ''k_B'' is the Boltzmann constant (8.617343e-5 eV/K). For convenience, we also defined thermal mass '''NHMass''', which is exactly the Nose'-Hoover thermal mass ''Q''. (When '''NHMass''' is non-zero, '''vt2''' will be ignored.) When ''N'' = 250 and ''T'' = 300 K (or k_B T ~ 0.026 eV), '''vt2''' = 1e28 corresponds to '''NHMass''' = 1.95e-03. The bigger '''vt2''' is (or the smaller '''NHMass''' is), the faster the instantaneous temperature fluctuates around the desired temperature, as shown in Fig. 3. The MD simulation also writes out variable '''HELMP''' in the property file; '''HELMP''' is the total energy of the system plus that of the thermal reservior and should be conserved. The flucutation of '''HELMP''' around its mean value is also plotted in Fig. 3.
	The eﬀect of '''vt2''' on Helmholtz free energy and temperature ﬂuctuation is shown in Fig. 3.

	<gallery caption="Fig.3 The Effect of Nose-Hoover Mass in NVT MD" widths="300px" heights="200px" perrow="2">		<gallery caption="Fig.3 The Effect of Nose-Hoover Mass in NVT MD" widths="300px" heights="200px" perrow="2">
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	</gallery>		</gallery>

			In the above example script, after the first MD simulation, we use the command '''multiplyvelocity''' to reverse the velocities of all atoms. This is done by setting <tt>input = -1</tt>, so that -1 is multiplied to the velocities of all atoms. We then continue the MD simulation for the same duration of time as the first one, in order to test the reversibility of the numerical (symplectic) integrator. After the second MD simulation (in the reverse direction), we save the atomic configuration into file <tt>300K-5x5x5-NVT.cn</tt>. Comparing this file with the file <tt>300K-5x5x5.cn</tt>, which contains the atomic configuration at the beginning of the (forward) simulation, reveals that the scaled coordinates of all atoms are identical in the two files within 1e-14 (close to machine precision). This demonstrates the reversibility of the chosen integrator. If on the other hand, <tt>integrator_type = Gear6</tt> is used, the discrepancy in the atomic coordinates will be on the order of 1e-6, which shows that the Gear6 integrator is not reversible.
	'''HELMP''' in the '''output_fmt''' is Helmholtz free energy which is the conserved quantity in NVT MD.

	'''multiplyvelocity''' multiplies the number speciﬁed by the preceding input to all velocity components of all atoms. With '''input=-1''', the MD++ command '''multiplyvelocity''' reverses the velocity direction of all the atoms and they are expected to be at the initial position after the reverse run. This is done to test the reversibility of the symplectic integrator. Comparing two configuration files '''300K-5X5X5.cn''' and '''300K-5X5X5-NVT.cn''' reveals that the numbers become different after 10^(-14) digit. If we consider the total step is 4000, the difference at each step would be ''O''(10^(-17)), which corresponds to the machine precision. On the other hand, if you test '''integrator_type = Gear6''', the numbers become different only after 10^(-6) digit. We can say the symplectic integrator is indeed reversible.

	=== Canonical(NVT) Ensemble with Nose-Hoover Chain ===		=== Canonical(NVT) Ensemble with Nose-Hoover Chain ===

M05 Finite Temperature Simulation - Revision history

Kwkang: /* Constant Stress (N\sigmaH) Ensemble */

Kwkang: /* Canonical(NVT) Ensemble with Nose-Hoover Chain */

Kwkang: /* Microcanonical (NVE) Ensemble */

Kwkang: /* Canonical(NVT) Ensemble */

Kwkang: /* Canonical(NVT) Ensemble */

Kwkang: /* Canonical(NVT) Ensemble */

Caiwei at 04:40, 14 April 2008

Caiwei: /* Constant Stress (N\sigmaH) Ensemble */

Caiwei: /* Canonical(NVT) Ensemble with Nose-Hoover Chain */

Caiwei: /* Canonical(NVT) Ensemble */

Caiwei: /* Constant Stress (N $\sigma$ H) Ensemble */