Improved dimer method - Revision history

Csheldon at 10:52, 28 October 2024

2024-10-28T10:52:37Z

← Older revision		Revision as of 10:52, 28 October 2024
Line 1:		Line 1:
	The dimer method{{Cite\|henkelman:jpc:1999}} is a technique for the optimization of transition states. In VASP, the improved dimer method (IDM) by Heyden et al. is implemented, and a detailed presentation of the method can be found in their paper{{Cite\|heyden:jpc:2005}}.		The dimer method{{Cite\|henkelman:jpc:1999}} is a technique for the optimization of transition states. In VASP, the improved dimer method (IDM) by Heyden et al. is implemented, and a detailed presentation of the method can be found in their paper{{Cite\|heyden:jpc:2005}}.

	The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps with {{TAG\|~~FINDDIFF~~}} = 1:		The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps with {{TAG\|FINDIFF}} = 1:

	[[File:IDM.png\|800px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]		[[File:IDM.png\|800px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]

Csheldon at 10:52, 28 October 2024

2024-10-28T10:52:27Z

← Older revision		Revision as of 10:52, 28 October 2024
Line 1:		Line 1:
	The dimer method{{Cite\|henkelman:jpc:1999}} is a technique for the optimization of transition states. In VASP, the improved dimer method (IDM) by Heyden et al. is implemented, and a detailed presentation of the method can be found in their paper{{Cite\|heyden:jpc:2005}}.		The dimer method{{Cite\|henkelman:jpc:1999}} is a technique for the optimization of transition states. In VASP, the improved dimer method (IDM) by Heyden et al. is implemented, and a detailed presentation of the method can be found in their paper{{Cite\|heyden:jpc:2005}}.

	The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps:		The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps with {{TAG\|FINDDIFF}} = 1:

	[[File:IDM.png\|800px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]		[[File:IDM.png\|800px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]

Csheldon at 10:50, 28 October 2024

2024-10-28T10:50:15Z

← Older revision		Revision as of 10:50, 28 October 2024
Line 5:		Line 5:
	[[File:IDM.png\|800px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]		[[File:IDM.png\|800px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]
	<div style="clear:both;"></div>		<div style="clear:both;"></div>


	'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.		'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.

Csheldon at 10:50, 28 October 2024

2024-10-28T10:50:08Z

← Older revision		Revision as of 10:50, 28 October 2024
Line 3:		Line 3:
	The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps:		The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps:

	[[File:IDM.png\|~~700px~~\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]		[[File:IDM.png\|800px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]
			<div style="clear:both;"></div>


	'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.		'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.

Csheldon at 13:37, 25 October 2024

2024-10-25T13:37:46Z

← Older revision		Revision as of 13:37, 25 October 2024
Line 14:		Line 14:

	Rotation followed by translation is followed iteratively until convergence, i.e. the saddle point, is reached.		Rotation followed by translation is followed iteratively until convergence, i.e. the saddle point, is reached.


	The method is invoked by setting {{TAG\|IBRION}}=44 in the {{TAG\|INCAR}} file.		The method is invoked by setting {{TAG\|IBRION}}=44 in the {{TAG\|INCAR}} file.

Csheldon at 13:37, 25 October 2024

2024-10-25T13:37:27Z

← Older revision		Revision as of 13:37, 25 October 2024
Line 2:		Line 2:

	The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps:		The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps:

			[[File:IDM.png\|700px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]

	'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.		'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.
Line 13:		Line 15:
	Rotation followed by translation is followed iteratively until convergence, i.e. the saddle point, is reached.		Rotation followed by translation is followed iteratively until convergence, i.e. the saddle point, is reached.

	[[File:IDM.png\|700px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]		The method is invoked by setting {{TAG\|IBRION}}=44 in the {{TAG\|INCAR}} file.


	The method is invoked by setting {{TAG\|IBRION}}=44 in the {{TAG\|INCAR}} file.

	Furthermore, the user must specify the direction of the unstable mode. The corresponding <math>3N</math> dimensional vector is defined in the {{FILE\|POSCAR}} file after the lines with atomic coordinates and a separating blank line. Note that the dimer direction is automatically normalized, i.e., the norm of the dimer axis is irrelevant. An example of a {{FILE\|POSCAR}} file for a simulation with the dimer method is given in the following:		Furthermore, the user must specify the direction of the unstable mode. The corresponding <math>3N</math> dimensional vector is defined in the {{FILE\|POSCAR}} file after the lines with atomic coordinates and a separating blank line. Note that the dimer direction is automatically normalized, i.e., the norm of the dimer axis is irrelevant. An example of a {{FILE\|POSCAR}} file for a simulation with the dimer method is given in the following:

Csheldon at 13:36, 25 October 2024

2024-10-25T13:36:51Z

← Older revision		Revision as of 13:36, 25 October 2024
Line 1:		Line 1:
	The dimer method{{Cite\|henkelman:jpc:1999}} is a technique for the optimization of transition states. In VASP, the improved dimer method (IDM) by Heyden et al. is implemented, and a detailed presentation of the method can be found in their paper{{Cite\|heyden:jpc:2005}}~~. The algorithm for IDM consists of the following cyclically repeated steps:~~		The dimer method{{Cite\|henkelman:jpc:1999}} is a technique for the optimization of transition states. In VASP, the improved dimer method (IDM) by Heyden et al. is implemented, and a detailed presentation of the method can be found in their paper{{Cite\|heyden:jpc:2005}}.
	*The curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below).
	*The dimer is rotated such that its axis is parallel with the direction of the maximal negative curvature.
	*An optimization step is taken, and the potential energy is maximized along the unstable direction, (i.e., dimer axis) while it is minimized in all other directions.

	~~[[File:IDM.png\|700px\|thumb\|left\|Figure 1.~~ The ~~IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show~~ the dimer axis ~~'''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step~~. The ~~empty circles and dashed lines indicate the structures and~~ dimer ~~axes from the previous steps. The dotted arrow in '''~~(d)~~''' represents the dimer axis on rotation by φ<sub>min</sub>~~.]]		The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps:

	The IDM procedure is shown in Figure 1 in four steps:

	'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.		'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.
Line 12:		Line 7:
	'''b)''' An additional point on the potential energy surface (PES) forward along the trial direction is defined '''q''' + δ'''u'''<sub>ξ</sub>. The first and second points together define the dimer.		'''b)''' An additional point on the potential energy surface (PES) forward along the trial direction is defined '''q''' + δ'''u'''<sub>ξ</sub>. The first and second points together define the dimer.

	'''c)''' The dimer is then rotated on the PES about '''q''' by angle φ<sub>1</sub> to '''q̃'''.		'''c)''' The dimer is then rotated on the PES about '''q''' by angle φ<sub>1</sub> to '''q̃''' such that its axis is parallel to the direction of maximal negative curvature.

			'''d)''' A new direction is defined by rotating '''u'''<sub>ξ</sub> by φ<sub>min</sub> to minimize the negative curvature of the PES λ. A search direction N̅ is defined using a minimization algorithm, then a translation (optimization step) is taken in the unstable direction of N̅ to '''q''' + εN̅, where ε is a step distance. The potential energy is is maximized along the unstable direction, (i.e., dimer axis) while it is minimized in all other directions.

	~~'''d)''' A new direction is defined~~ by ~~rotating '''u'''<sub>ξ</sub> by φ<sub>min</sub> to minimize the negative curvature of the PES λ. A search direction N̅~~ is ~~defined using a minimization algorithm~~, ~~then a translation is taken in~~ the ~~direction of N̅ to '''q''' + εN̅~~, ~~where ε~~ is ~~a step distance~~.		Rotation followed by translation is followed iteratively until convergence, i.e. the saddle point, is reached.

	~~Rotation followed by translation~~ is ~~followed iteratively until convergence, i~~.e. the ~~saddle point, is reached~~		[[File:IDM.png\|700px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]

Csheldon at 13:33, 25 October 2024

2024-10-25T13:33:03Z

← Older revision		Revision as of 13:33, 25 October 2024
Line 7:		Line 7:

	The IDM procedure is shown in Figure 1 in four steps:		The IDM procedure is shown in Figure 1 in four steps:

	'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.		'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.

	'''b)''' An additional point on the potential energy surface (PES) forward along the trial direction is defined '''q''' + δ'''u'''<sub>ξ</sub>. The first and second points together define the dimer.		'''b)''' An additional point on the potential energy surface (PES) forward along the trial direction is defined '''q''' + δ'''u'''<sub>ξ</sub>. The first and second points together define the dimer.

	'''c)''' The dimer is then rotated on the PES about '''q''' by angle φ<sub>1</sub> to '''q̃'''.		'''c)''' The dimer is then rotated on the PES about '''q''' by angle φ<sub>1</sub> to '''q̃'''.

	'''d)''' A new direction is defined by rotating '''u'''<sub>ξ</sub> by φ<sub>min</sub> to minimize the negative curvature of the PES λ. A search direction N̅ is defined using a minimization algorithm, then a translation is taken in the direction of N̅ to '''q''' + εN̅, where ε is a step distance.		'''d)''' A new direction is defined by rotating '''u'''<sub>ξ</sub> by φ<sub>min</sub> to minimize the negative curvature of the PES λ. A search direction N̅ is defined using a minimization algorithm, then a translation is taken in the direction of N̅ to '''q''' + εN̅, where ε is a step distance.

Csheldon at 13:32, 25 October 2024

2024-10-25T13:32:41Z

← Older revision		Revision as of 13:32, 25 October 2024
Line 1:		Line 1:
	The dimer method{{Cite\|henkelman:jpc:1999}} is a technique for the optimization of transition states. In VASP, the improved dimer method (IDM) by Heyden et al. is implemented, and a detailed presentation of the method can be found in their paper{{Cite\|heyden:jpc:2005}}. The algorithm for IDM consists of the following cyclically repeated steps:		The dimer method{{Cite\|henkelman:jpc:1999}} is a technique for the optimization of transition states. In VASP, the improved dimer method (IDM) by Heyden et al. is implemented, and a detailed presentation of the method can be found in their paper{{Cite\|heyden:jpc:2005}}. The algorithm for IDM consists of the following cyclically repeated steps:
	*The curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below).		*The curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below).
	*The dimer is rotated such that its axis is parallel with the direction of the maximal negative curvature.		*The dimer is rotated such that its axis is parallel with the direction of the maximal negative curvature.
	*An optimization step is taken, and the potential energy is maximized along the unstable direction, (i.e., dimer axis) while it is minimized in all other directions.		*An optimization step is taken, and the potential energy is maximized along the unstable direction, (i.e., dimer axis) while it is minimized in all other directions.

	[[File:IDM.png\|700px\|thumb\|left\|The IDM procedure is ~~given~~ in four steps: '''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''. '''b)''' An additional point on the potential energy surface (PES) forward along the trial direction is defined '''q''' + δ'''u'''<sub>ξ</sub>. The first and second points together define the dimer. '''c)''' The dimer is then rotated on the PES about '''q''' by angle φ<sub>1</sub> to '''q̃'''. '''d)''' A new direction is defined by rotating '''u'''<sub>ξ</sub> by φ<sub>min</sub> to minimize the negative curvature of the PES λ. A search direction N̅ is defined using a minimization algorithm, then a translation is taken in the direction of N̅ to '''q''' + εN̅, where ε is a step distance. Rotation followed by translation is followed iteratively until convergence, i.e. the saddle point, is reached]]		[[File:IDM.png\|700px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]

			The IDM procedure is shown in Figure 1 in four steps:
			'''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''.
			'''b)''' An additional point on the potential energy surface (PES) forward along the trial direction is defined '''q''' + δ'''u'''<sub>ξ</sub>. The first and second points together define the dimer.
			'''c)''' The dimer is then rotated on the PES about '''q''' by angle φ<sub>1</sub> to '''q̃'''.
			'''d)''' A new direction is defined by rotating '''u'''<sub>ξ</sub> by φ<sub>min</sub> to minimize the negative curvature of the PES λ. A search direction N̅ is defined using a minimization algorithm, then a translation is taken in the direction of N̅ to '''q''' + εN̅, where ε is a step distance.

			Rotation followed by translation is followed iteratively until convergence, i.e. the saddle point, is reached

Csheldon at 13:29, 25 October 2024

2024-10-25T13:29:59Z

← Older revision		Revision as of 13:29, 25 October 2024
Line 4:		Line 4:
	*An optimization step is taken, and the potential energy is maximized along the unstable direction, (i.e., dimer axis) while it is minimized in all other directions.		*An optimization step is taken, and the potential energy is maximized along the unstable direction, (i.e., dimer axis) while it is minimized in all other directions.

	[[File:IDM.png\|700px\|thumb\|left\|The IDM procedure is given in four steps: '''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''. '''b)''' An additional point on the potential energy surface (PES) forward along the trial direction is defined '''q''' + δ'''u'''<sub>ξ</sub>. The first and second points together define the dimer. '''c)''' The dimer is then rotated on the PES about '''q''' by angle φ<sub>1</sub> to '''q̃'''. '''d)''' A new direction is defined by rotating '''u'''<sub>ξ</sub> by φ<sub>min</sub> to minimize the negative curvature of the PES λ. A search direction N̅ is defined using a minimization algorithm, then a translation is taken in the direction of N̅ to '''q''' + ε N̅, where ε is a step distance. Rotation followed by translation is followed iteratively until convergence, i.e. the saddle point, is reached]]		[[File:IDM.png\|700px\|thumb\|left\|The IDM procedure is given in four steps: '''a)''' An initial direction '''u'''<sub>ξ</sub> is taken from the most negative vibrational mode of the trial structure. The trial structure is the first point '''q'''. '''b)''' An additional point on the potential energy surface (PES) forward along the trial direction is defined '''q''' + δ'''u'''<sub>ξ</sub>. The first and second points together define the dimer. '''c)''' The dimer is then rotated on the PES about '''q''' by angle φ<sub>1</sub> to '''q̃'''. '''d)''' A new direction is defined by rotating '''u'''<sub>ξ</sub> by φ<sub>min</sub> to minimize the negative curvature of the PES λ. A search direction N̅ is defined using a minimization algorithm, then a translation is taken in the direction of N̅ to '''q''' + εN̅, where ε is a step distance. Rotation followed by translation is followed iteratively until convergence, i.e. the saddle point, is reached]]

← Older revision		Revision as of 10:52, 28 October 2024
Line 1:		Line 1:
	The dimer method{{Cite\|henkelman:jpc:1999}} is a technique for the optimization of transition states. In VASP, the improved dimer method (IDM) by Heyden et al. is implemented, and a detailed presentation of the method can be found in their paper{{Cite\|heyden:jpc:2005}}.		The dimer method{{Cite\|henkelman:jpc:1999}} is a technique for the optimization of transition states. In VASP, the improved dimer method (IDM) by Heyden et al. is implemented, and a detailed presentation of the method can be found in their paper{{Cite\|heyden:jpc:2005}}.

	The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps with {{TAG\|~~FINDDIFF~~}} = 1:		The initial curvature along the dimer axis is computed using finite differences. The initial dimer direction must be provided (see below). The IDM procedure shown in Figure 1 is described in four steps with {{TAG\|FINDIFF}} = 1:

	[[File:IDM.png\|800px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]		[[File:IDM.png\|800px\|thumb\|left\|Figure 1. The IDM is relaxed on the potential energy surface (PES) in four ionic steps. Solid arrows show the dimer axis '''u'''<sub>ξ</sub> and solid circles the structure for which the forces are calculated in the step. The empty circles and dashed lines indicate the structures and dimer axes from the previous steps. The dotted arrow in '''(d)''' represents the dimer axis on rotation by φ<sub>min</sub>.]]