WO2011099210A1 - Dispositif d'identification d'état activé, procédé d'identification d'état activé, et programme d'identification d'état activé - Google Patents

Dispositif d'identification d'état activé, procédé d'identification d'état activé, et programme d'identification d'état activé Download PDF

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WO2011099210A1
WO2011099210A1 PCT/JP2010/070802 JP2010070802W WO2011099210A1 WO 2011099210 A1 WO2011099210 A1 WO 2011099210A1 JP 2010070802 W JP2010070802 W JP 2010070802W WO 2011099210 A1 WO2011099210 A1 WO 2011099210A1
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atom
force
force acting
eigenvalue
activation state
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PCT/JP2010/070802
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Japanese (ja)
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明賢 澤村
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住友電気工業株式会社
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    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C10/00—Computational theoretical chemistry, i.e. ICT specially adapted for theoretical aspects of quantum chemistry, molecular mechanics, molecular dynamics or the like

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  • the present invention relates to an activation state identification device, an activation state identification method, and an activation state identification program for identifying an activation state of a solid substance or the like.
  • FIG. 10 shows an example of a potential curved surface determined by the positional relationship of atoms involved in the change.
  • the activated state is the apex portion where the potential curved surface is raised like a bowl. That is, the activated state is a state that is most easily exceeded on the path from the start state to the end state in the change.
  • a path from the initial state to the activated state is searched while the position of the atom is displaced.
  • Non-Patent Document 1 proposes a method for specifying an activation state when a lattice defect or the like moves in crystalline silicon.
  • the position of the atom is slightly displaced by a fixed procedure, and the lowest order eigenvalue and eigenvector indicating the displacement direction of the atom that raises the potential most slowly are obtained from the change in force acting on the atom at that time.
  • Non-Patent Document 2 the lowest eigenvalue and eigenvector are used in the direction in which the atoms are moved, but it is the same as Non-Patent Document 1. However, as shown in FIG. Dividing the potential rise in the path into a first region that is convex downward (the lower potential side) and a second region that is not, and the calculation method for determining the position of the new atom is different in both regions It has been proposed to specify the activation state.
  • the direction for moving the atom is calculated, and the position of the new atom is iteratively calculated based on the calculated direction, thereby searching for the path where the potential increases most slowly.
  • the activation state is specified by converging the force acting on the atoms. For this reason, since the amount of computation as a whole is large and the computation time is relatively long, there is a method that can converge the force acting on the atoms more efficiently and further reduce the computation time for specifying the activation state. desirable.
  • the method proposed in Non-Patent Document 2 described above an attempt is made to improve the efficiency of convergence of the force acting on the atoms by properly using the calculation method according to the mode of potential increase.
  • the calculation time for specifying the activation state cannot be shortened.
  • Non-Patent Document 2 When a specific calculation method using the method of Non-Patent Document 2 is shown, when obtaining a new atom position based on the current atom position that is considered to be toward an activated state In the first region, the calculation is performed based on the displacement position when the atom is displaced from the current position based on the eigenvector corresponding to the lowest-order eigenvalue obtained by the following equation (a), In the two regions, calculation is performed based on the displacement position of the atoms obtained by the following formula (b).
  • the lowest order eigenvalues and eigenvectors are obtained from the change in force acting on the atom at a position slightly displaced from the current atom position in a certain procedure, and the atom is moved. It shows the direction in which the potential changes most slowly.
  • equation (a) the position of a new atom is obtained so that the potential always increases along the direction of the lowest-order eigenvector indicating the direction in which the potential is estimated to change most slowly.
  • the formula (b) in obtaining the position of a new atom, an attempt is made to move the atom so that the potential increases in the direction of the lowest-order eigenvector and decreases in the direction orthogonal to this. To do.
  • the activated state is located at the apex of the saddle shape on the potential curved surface, and in the second region, it is close to the position of the activated state and has a saddle shape.
  • a new atom position can be obtained more appropriately than in the formula (a).
  • An object is to provide an apparatus, an activation state identification method, and an activation state identification program.
  • the present inventor refers only to the lowest-order eigenvalue and eigenvector as information about the direction indicating the potential gradient when the atom is moved in the calculation for determining the position of a new atom. Focusing on this point, we conducted extensive research. As a result, when calculating the position of a new atom, if more information is referenced in addition to the lowest order eigenvalue and eigenvector, the convergence of the force acting on the atom can be improved. The present invention has been completed.
  • the present invention is an activation state specifying device that specifies the activation state of an atom by displacing the position of the atom, and an acting force that calculates a force acting on the atom from the position of the atom A calculation unit; an atomic position calculation unit that calculates a position of a new atom for converging a force acting on the atom, displaced from a current atom position, based on the force acting on the atom; and The atomic position calculation unit and the acting force calculation unit repeatedly calculate the position of the new atom and the force acting on the atom, and specify the activation state of the atom by converging the force acting on the atom.
  • a calculation control unit wherein the atomic position calculation unit solves the eigenvalue problem with respect to a minute change in force acting on the atom when the current position of the atom is slightly displaced.
  • the resulting residual is reduced
  • the position of the new atom is calculated based on a plurality of eigenvalues and a plurality of eigenvectors obtained by the unit.
  • the atomic position calculation unit calculates the position of a new atom based on a plurality of eigenvalues and a plurality of eigenvectors obtained by the eigenvalue calculation unit.
  • the position of a new atom can be calculated with reference to more information. That is, in the present invention, in addition to the lowest order eigenvectors and eigenvalues, other eigenvectors and eigenvalues other than the lowest order obtained in the process of converging the residual of the eigenvalue problem regarding the change in force acting on the atoms are also referred to.
  • the position of the new atom is calculated, the position of the new atom can be obtained so as to go in the more optimal direction toward the activated state. As a result, the convergence of the force acting on the atoms can be made more efficient, and the calculation time for specifying the activated state can be further shortened.
  • the atomic position calculation unit includes a determination unit that determines whether or not the lowest eigenvalue is positive among the plurality of eigenvalues, and when the determination result of the determination unit is not positive, It is preferable to calculate the position of the new atom based on a plurality of eigenvalues and a plurality of eigenvectors obtained by the eigenvalue calculation unit. Since the lowest eigenvalue has the property of a second derivative with respect to the potential, when the slope of the tangent surface at the position on the potential surface determined by the current atom position transitions toward the activated state, Indicates whether it is going to decrease or increase.
  • the slope is about to increase and is a region that is convex downward (low potential side) on the potential curved surface
  • the determination unit is on the potential curved surface determined by the current atom position. It is possible to determine whether or not the position is in a region protruding downward.
  • the region that is not convex downward is close to the activated state and has a saddle shape, so it is necessary to find the position of the new atom more appropriately.
  • a more optimal direction toward the activated state is obtained by calculating the position of a new atom based on a plurality of eigenvalues and a plurality of eigenvectors obtained by iterative calculation by the eigenvalue calculation unit. Find the position of the new atom so that On the other hand, in the region that protrudes downward, there is a high possibility that the path to the activated state is long compared to the region that is not so, so new atoms will be given priority in increasing the potential more quickly.
  • the efficiency can be increased by configuring the atomic position calculation unit so as to calculate the position of.
  • the atomic position calculation unit so as to calculate the position of.
  • the atomic position calculation unit obtains a displacement position, which is represented by the following equation, displaced with respect to the current atomic position based on the plurality of eigenvalues and a plurality of eigenvectors, It is preferable that the position of the new atom is calculated using this displacement position.
  • the present invention is an activation state specifying method for specifying an activation state of an atom by displacing the position of the atom, and an acting force for calculating a force acting on the atom from the position of the atom A calculation step; an atomic position calculation step for calculating a position of a new atom for converging a force acting on the atom, displaced from a current atom position, based on the force acting on the atom; By repeating the atomic position calculating step and the acting force calculating step, the position of the new atom and the force acting on the atom are repeatedly calculated, and the force acting on the atom is converged to activate the atom.
  • the atomic position calculating step solves the eigenvalue problem concerning a minute change in force acting on the atom when the current position of the atom is slightly displaced.
  • An eigenvalue calculation step of repeatedly calculating so as to reduce a residual obtained when solving a value problem and obtaining a plurality of eigenvalues and eigenvectors for a minute change in force acting on an atom, and the action force calculation step And a step of calculating the position of the new atom based on a force acting on the atom and a plurality of eigenvalues and a plurality of eigenvectors obtained by the eigenvalue calculating step.
  • the activation state specifying method having the above-described configuration, it is possible to more efficiently converge the force acting on the atoms and further reduce the calculation time for specifying the activation state.
  • the present invention is a computer-readable medium recording an activation state specifying program for causing a computer to execute an operation for specifying the activation state of an atom by displacing the position of the atom,
  • the activation state specifying program causes the computer to converge an acting force calculating step for calculating a force acting on the atom from the position of the atom, and a force acting on the atom displaced from the current atom position.
  • An atomic position calculating step for calculating a position of a new atom based on a force acting on the atom, and repeating the atomic position calculating step and the acting force calculating step to thereby determine the position of the new atom and Performing the step of repeatedly calculating the force acting on the atom and converging the force acting on the atom to identify the activation state of the atom.
  • the activation state specifying program causes the computer to detect a minute change in force acting on the atom when the current position of the atom is slightly displaced in the atomic position calculation step.
  • An eigenvalue calculation step of obtaining a plurality of eigenvalues and eigenvectors for a minute change in force acting on an atom, so as to reduce the residual obtained when solving the eigenvalue problem, and the acting force A program for executing the step of calculating the position of the new atom based on the force applied to the atom given from the calculation step and a plurality of eigenvalues and a plurality of eigenvectors obtained by the eigenvalue calculation step It is characterized by being.
  • the computer executes the activation state identification program having the above configuration, it is possible to more efficiently converge the force acting on the atoms and shorten the calculation time for identifying the activation state.
  • the activation state identification device the activation state identification method, and the activation state identification program of the present invention, it is possible to more efficiently converge the force acting on the atoms and to reduce the calculation time for identifying the activation state. It can be shortened.
  • FIG. 1 is a block diagram showing a functional configuration of an activated state identification device according to an embodiment of the present invention.
  • This activated state identification device 1 involves the movement of atoms in a solid, such as the movement of defects in the solid or the diffusion of atoms, from the arrangement of atoms constituting a solid such as a target metal or inorganic substance.
  • a device that performs an operation for specifying an activation state for a change and is configured by a computer or the like.
  • the activation state specifying device 1 stores an input / output unit 2 including an input device such as a keyboard and a mouse and an output device such as a display and a printer, an operating system, various programs, information, and the like.
  • an input device such as a keyboard and a mouse
  • an output device such as a display and a printer
  • an operating system various programs, information, and the like.
  • a storage unit 3 composed of a hard disk or the like
  • a data processing unit 4 for performing processing for calculating an electronic state based on various data input from the input / output unit 2.
  • a program activation state identification program for performing an operation relating to identification of the activation state is stored and installed in the storage unit 3, and the program is activated by executing these programs.
  • Each functional unit for specifying the activation state that the activation state identification device 1 has is realized.
  • Each program can be provided by being carried or recorded on a computer-readable recording medium, or transmitted through a telecommunication line.
  • a computer-readable recording medium an optical medium such as a CD-ROM, a magnetic medium such as a flexible disk, or a semiconductor memory such as a flash memory or a RAM can be used.
  • the data processing unit 4 includes a potential calculation unit 5 that calculates a potential between atoms and a force acting on the atom, an atom position calculation unit 6 that calculates a position of a new atom based on the force acting on the atom,
  • the controller 6 and the controller 7 are functionally equipped with a controller 7 that performs control for causing the calculator 6 and the potential calculator 5 to repeatedly calculate the force acting on the atoms.
  • the potential calculation unit 5 gives it as a starting state set for the activated state to be specified.
  • the control unit 7 gives the position of the new atom calculated by the atomic position calculation unit 6 to the potential calculation unit 5 and also gives the force acting on the atoms calculated by the potential calculation unit 5 to the atomic position calculation unit 6.
  • These functional units have the function of repeatedly calculating the position of a new atom and the force acting on the atom.
  • the control unit 7 has a function of determining whether or not the force acting on the atoms has sufficiently converged by being smaller than a predetermined threshold, and the force acting on the atoms is sufficiently large. When it is determined that the current has converged, the position of the atom obtained by the iterative calculation and the force acting on the atom are output via the input / output unit 2.
  • the atomic position calculation unit 6 obtains a new atom position that is displaced from the current atom position. Based on the force acting on the atom obtained by the potential calculation unit 5, the atomic position calculation unit 6 It has a function of calculating the position of a new atom for converging the force acting on the atom.
  • FIG. 2 is a block diagram showing a functional configuration of the atomic position calculation unit 6.
  • the atomic position calculation unit 6 includes an eigenvalue calculation unit 6a, a determination unit 6b, and a position calculation unit 6c.
  • the eigenvalue calculation unit 6a repeatedly calculates the eigenvalue problem about the minute change of the force acting on the atom generated when the current position of the atom is slightly displaced, A plurality of eigenvalues and eigenvectors are acquired and output to the position calculation unit 6a. In addition, the eigenvalue calculation unit 6a outputs the lowest-order (smallest) eigenvalue among the acquired plurality of eigenvalues to the determination unit 6b.
  • the eigenvalue calculation unit 6a repeatedly performs the calculation so that the residual obtained when solving the eigenvalue problem is reduced, and repeats the calculation until the residual is reduced to such a degree that the residual is considered to have converged.
  • the eigenvalue calculation unit 6a obtains a direction (displacement vector) for minutely displacing the atom position from the residual obtained each time the eigenvalue problem is calculated. Further, the position of the atom is slightly displaced from the current position based on this direction, and each time the position is displaced, the approximate eigenvalue and approximate eigenvector at that time are calculated.
  • the approximate eigenvalue and approximate eigenvector at the time when the residual converges are output as a plurality of eigenvalues and eigenvectors as the operation result.
  • the eigenvalue is information indicating the potential gradient when the current position of the atom is slightly displaced, and indicates that the smaller the potential is, the smaller the potential is.
  • the corresponding eigenvector is a unit vector indicating the direction of displacement of the atom when the position is slightly displaced. Therefore, the lowest order eigenvector corresponding to the smallest lowest order eigenvalue among the plurality of eigenvectors obtained as a result of the calculation indicates the moving direction of the atom that changes the potential most slowly.
  • the determination unit 6b determines whether or not the lowest-order eigenvalue output from the eigenvalue calculation unit 6a is positive.
  • the position calculation unit 6c calculates the position of a new atom based on the force acting on the current atom and a plurality of eigenvalues and eigenvectors given from the eigenvalue calculation unit 6a.
  • the position calculation unit 6c calculates a displacement position obtained by displacing the atom from the current position based on the eigenvalue or eigenvector, and calculates a position of a new atom using the displacement position. Thereby, the position of the atom can be displaced along the optimum path toward the activated state.
  • the position calculation unit 6c has a function of changing the calculation method for calculating the position of a new atom according to the determination result of the determination unit 6b.
  • the data processing unit 4 includes a first counter 8 for counting the number of iterations when the force acting on the atoms is iteratively calculated by the atomic position calculation unit 6 and the potential calculation unit 5, and an eigenvalue by the eigenvalue calculation unit 6a.
  • a second counter 9 is functionally provided for counting the number of iterations when the problem is iteratively calculated.
  • FIG. 3 is a flowchart showing the overall operation of the activation state identification device 1 of the present embodiment.
  • the control unit 7 of the data processing unit 4 first sets the count value j of the first counter 8 to “ 0 "is set (step S101).
  • the initial position x (0) is a column vector representing the position in the initial state of the atom related to the change related to the activated state that the apparatus 1 is trying to identify.
  • the starting state is an atom position set as an initial state of the change related to the activation state to be specified, and an appropriate atom position is determined in advance as the starting state.
  • the initial position x (0) is represented as a column vector indicating the positions of the plurality of atoms.
  • FIG. 4 is an example of a display for accepting an input of the initial position x (0) in step S102.
  • the data processing unit 4 displays an input field 40 for inputting numerical information on the display of the input / output unit 2.
  • the input field 40 is provided so that, for example, a three-dimensional coordinate value of each atom related to the change can be input.
  • the operator of the device 1 moves the cursor to the input field 40 to be input with a mouse or the like and then operates the keyboard or the like to input numerical information related to the three-dimensional coordinate value.
  • the input / output unit 2 accepts the numerical information input in the input field 40 as the initial position x (0) indicating the position of the atom. Further, FIG.
  • FIG. 4 shows a mode in which information regarding the initial position x (0) is input, but other information (threshold value j th , threshold value f th , threshold value i th , threshold value r th , minute displacement parameter) described later.
  • ⁇ and displacement parameter ⁇ a similar input screen is prepared and accepted.
  • the control unit 7 gives the potential calculation unit 5 the initial position x (0) and the force f ( acting on the atom at the initial position x (0) . j) is calculated (step S103).
  • the potential calculation unit 5 obtains the potential between the atoms involved in the change based on the given initial position x (0) and information such as the solid material to be calculated and the physical properties of the atoms. Further, the potential calculation unit 5 obtains a force f (j) acting on the atoms based on this potential (hereinafter also simply referred to as force f (j) ).
  • the initial position x (0), the atom position x (j) , and the force f (j) acting on the atoms are column vectors unless otherwise specified.
  • step S103 information on the solid substance to be calculated and information on the physical properties of the atoms used in the calculation of the potential calculation unit 5 are received via the input / output unit 2 and stored in the storage unit 3 in advance.
  • step S101 the initial position x (0) may be received and stored in the storage unit 3.
  • the potential calculation unit 5 is given the initial position x (0) or a new atom position x (j + 1) from the atom position calculation unit 6 as described later, the information stored in the storage unit 3 is stored. And the potential and force f (j) are obtained.
  • control unit 7 determines whether or not the counter value j of the first counter 8 is “0” (step S104). If the counter value j is not “0”, the control unit 7 proceeds to step S105, where the magnitude
  • the threshold value f th is set to a value that allows the magnitude
  • the control unit 7 when the control unit 7 repeatedly calculates a new atom position x (j + 1) and a corresponding force f (j) as described later, the magnitude of the force f (j)
  • the counter value j of the first counter 8 is equal to or greater than the threshold value j even if the counter value j does not satisfy the determination regarding convergence. This is for the purpose of forcibly terminating the processing when the threshold value j th or more is reached and preventing the calculation from being repeated unnecessarily.
  • step S105 the control unit 7 determines that the magnitude
  • the current force f (j) and the current atom position x (j) are given to the atom position calculation unit 6, and a new atom position for converging the magnitude of force
  • the calculation of x (j + 1) is performed by the atomic position calculation unit 6 (step S106). The contents of step S106 will be described in detail later. If the control unit 7 determines in step S104 that the counter value j is “0”, the control unit 7 proceeds to step S106. This is to prevent the processing from being terminated without performing the calculation of the activation state at the stage where the initial position x (0) is given.
  • step S106 after causing the atom position calculation unit 6 to calculate the new atom position x (j + 1) , the control unit 7 adds “1” to the counter value j of the first counter (step S107). ), The process returns to step S103. And the control part 7 calculates
  • step S105 the control unit 7 determines that the magnitude
  • control unit 7 sends the new atom position x (j) and the corresponding force f (j) to the atomic position calculation unit 6 and the potential calculation unit 5 in the magnitude of the force f (j) .
  • Steps S103 to S107 are repeated until it is determined that
  • the counter value j of the first counter indicates the number of iterations of the iterative calculation in steps S103 to S107.
  • of the force f (j) is “0” is an activated state that exists from the start state to the end state in the change.
  • the control unit 7 specifies a state that is considered to have converged when the magnitude
  • the control unit 7 determines the position x (j) of the atom from the initial position x (0) until it is specified as the activation state, and the corresponding force f (j). Is output.
  • FIG. 5 is a flowchart showing an aspect when the atomic position calculation unit 6 calculates a new atom position x (j + 1) in step S106.
  • the atom position calculation unit 6 moves the atom from the current position x (j).
  • the eigenvalue and eigenvector of the minute change u of the force at the position (minute displacement position x * (i, j) ) when it is slightly displaced are calculated (step S201).
  • FIG. 6 is a flowchart showing an aspect of processing for calculating eigenvalues and eigenvectors of the minute force change u in step S201.
  • the eigenvalue calculation unit 6a normalizes the current force f (j) to a unit vector, thereby slightly displacing the atom from the current position x (j) .
  • the initial value of the displacement vector t (i) necessary for this is calculated (step S302).
  • the eigenvalue calculation unit 6a performs the minute displacement of the atom position based on the displacement vector t (i) and the current atom position x (j) .
  • a minute displacement position x * (i, j) is obtained (step S303).
  • the minute displacement parameter ⁇ is a parameter for determining how much to be displaced according to the displacement vector t (i) and is set in advance.
  • the eigenvalue calculation unit 6a acquires the force calculation unit 5 by calculating the force f * (i, j) acting on the atom at the minute displacement position x * (i, j) obtained in step S303 (step S304). ).
  • the eigenvalue calculation unit 6a After acquiring the force f * (i, j) acting on the atom, the eigenvalue calculation unit 6a, as shown in the following formula (3), the atom at the minute displacement position x * (i, j) obtained in step S304.
  • a small change u (i) of the force is calculated (step S305).
  • the eigenvalue calculation unit 6a calculates the approximate eigenvalue ⁇ ⁇ (i) , the approximate eigenvector ⁇ ⁇ (i) , and the residual vector r ⁇ (i) for the minute change u (i) obtained in step S305. This is performed (step S306).
  • “ ⁇ ” attached to each value is a code for distinguishing each of a plurality of solutions obtained by solving the eigenvalue problem described below.
  • the (approximate) eigenvector and residual vector are assigned the same number as “ ⁇ ” assigned to the corresponding (approximate) eigenvalue.
  • the eigenvalue calculation unit 6a generates matrices A and B from the minute change u (i) and the displacement vector t (i) .
  • the matrix A is an i-row / i-column matrix composed of components a kl (1 ⁇ k ⁇ i, 1 ⁇ l ⁇ i).
  • the matrix A B is a matrix of i rows and i columns composed of components b kl (1 ⁇ k ⁇ i, 1 ⁇ l ⁇ i).
  • the eigenvalue computing unit 6a finds a plurality of approximate eigenvalues ⁇ ⁇ (i) and a plurality of approximate eigenvectors ⁇ ⁇ (i) by solving the eigenvalue problem expressed by the following equation (6).
  • the plurality of approximate eigenvalues ⁇ ⁇ (i) and the plurality of approximate eigenvectors ⁇ ⁇ (i) obtained by the eigenvalue calculation unit 6a solving the above equation (6) are expressed by the following equations (7) and (8). Shown in
  • the eigenvalue calculation unit 6a obtains a plurality of residual vectors r ⁇ (i) from the results of the above formulas (7) and (8) by performing a calculation based on the following formula (9).
  • the eigenvalue calculation unit 6a determines the magnitude of the residual vector r 1 (i) corresponding to the lowest-order approximate eigenvalue ⁇ 1 (i) , which is the smallest value among the plurality of residual vectors r ⁇ (i)
  • the threshold value r th is set to a value at which the magnitude
  • the eigenvalue calculation unit 6a repeatedly calculates the residual vector r ⁇ (i) and the like as described later, the residual vector r 1 (i) corresponding to the lowest-order approximate eigenvalue ⁇ 1 (i). It can be determined whether or not
  • the threshold value i th is set to prevent the calculation of the residual vector r ⁇ (i) and the like from being unnecessarily repeated. For example, the magnitude of the residual vector r 1 (i)
  • step S307 the magnitude
  • the eigenvalue calculation unit 6a adds “1” to the counter value i of the second counter 9 (step S309), and returns to step S303. Then, the eigenvalue calculation unit 6a performs the processing of steps S303 to S306 again based on the displacement vector t (i) obtained as a new displacement vector in step S308, so that a plurality of approximate eigenvalues ⁇ ⁇ (i ) , A plurality of approximate eigenvectors ⁇ ⁇ (i) and a plurality of residual vectors r ⁇ (i) are obtained.
  • step S307 the eigenvalue calculation unit 6a determines that the magnitude
  • a plurality of approximate eigenvalues ⁇ ⁇ (i) and a plurality of approximate eigenvectors v ⁇ (i) is acquired as a plurality of eigenvalues ⁇ ⁇ (j) and a plurality of eigenvectors ⁇ ⁇ (j) , respectively, as calculation results (step S310), and the process in step S201 of the flowchart in FIG. Finish.
  • the eigenvalue calculation unit 6a determines whether the magnitude
  • the eigenvalue calculation unit 6a calculates the displacement vector t (i) based on the residual vector r 1 (i) corresponding to the lowest-order approximate eigenvalue ⁇ ⁇ (i) obtained every time iterative calculation is performed as described above.
  • the position of the atom is slightly displaced from the current position based on the displacement vector t (i) .
  • a plurality of approximate eigenvalues ⁇ ⁇ (i) and a plurality of approximate eigenvectors ⁇ ⁇ (i) for the minute change u (i) of the force at that time are calculated.
  • the eigenvalues lambda alpha for the power of minimal change u (i) (i) is an information indicating the gradient of the potential when the position of the current atom x (j) is finely displaced The smaller the value, the more slowly the potential changes.
  • the corresponding eigenvector ⁇ ⁇ (i) is a unit vector indicating the moving direction of the atom when the position is slightly displaced. Accordingly, the eigenvector ⁇ 1 (j) corresponding to the smallest lowest-order eigenvalue ⁇ 1 (j) among the plurality of eigenvalues ⁇ ⁇ (j) obtained by the eigenvalue calculation unit 6a changes the potential with the slowest gradient. The moving direction of the atoms to be moved is shown.
  • step S310 When the eigenvalue calculation unit 6a finishes the calculation process of the eigenvalue ⁇ ⁇ (j) and eigenvector ⁇ ⁇ (j) for the minute change u (i) by proceeding to step S310, the process returns to the flowchart in FIG. The process proceeds to step S202.
  • step S202 the determination unit 6b of the atomic position calculation unit 6 has the smallest lowest eigenvalue ⁇ 1 (j) among the plurality of eigenvalues ⁇ ⁇ (j) obtained by the eigenvalue calculation unit 6a. It is determined whether or not (step S202).
  • the lowest-order eigenvalue ⁇ 1 (j) has a property as a second derivative with respect to the potential when the current position x (j) of the atom is slightly displaced. Therefore, the lowest-order eigenvalue ⁇ 1 (j) decreases when the slope of the tangent surface at the position on the potential surface determined by the current atom position x (j) transitions from the initial state toward the activated state. Indicates whether it is going to increase or increase.
  • FIG. 7 is a graph schematically showing a potential change in a cross section along a line connecting the starting state and the activated state on the potential curved surface.
  • the potential change (increase) in the path from the initial state to the activated state is divided into a first region that is convex downward (a lower potential side) and a second region that is not. Can be divided.
  • the manner of increasing the potential is convex upward (the higher potential side).
  • the slope of the tangent (tangent surface) at each position in the first region tends to increase from the initial state toward the activated state.
  • the lowest-order eigenvalue ⁇ 1 (j) having a property as a second derivative is positive.
  • the second region is convex downward, the lowest-order eigenvalue ⁇ 1 (j) is negative.
  • the determination unit 6b determines whether the lowest eigenvalue ⁇ 1 (j) is positive, so that the position on the potential curved surface determined by the current atom position x (j) is It can be determined whether the first region is a downwardly convex region or the second region that is not.
  • step S202 when it is determined in step S202 that the lowest-order eigenvalue ⁇ 1 (j) is positive, the position calculation unit 6c of the atomic position calculation unit 6 is represented by the following equation (11). Based on the current atom position x (j) , the current force f (j) , and the lowest eigenvector ⁇ 1 (j) , the displacement position x ** ( j) is obtained (step S203).
  • step S202 if it is determined in step S202 that the lowest-order eigenvalue ⁇ 1 (j) is not positive, the position calculation unit 6c, as shown in the following formula (12), the current atom position x (j) , Based on the current force f (j) , a plurality of eigenvalues ⁇ ⁇ (j) and a plurality of eigenvectors ⁇ ⁇ (j) , a displacement position x ** (j) when the position of the atom is displaced is obtained (step S204).
  • the displacement parameter ⁇ is a parameter for relatively determining how much the current atom position x (j) is displaced, and is set in advance.
  • “ ⁇ ” is the maximum eigenvalue of the plurality of eigenvalues ⁇ ⁇ (j) .
  • step S205 When determining the step S202 and the displacement position x ** in step S203 (j), atomic position calculating unit 6, the force f ** acting on atoms in the displaced position x ** (j) a (j), the potential The calculation unit 5 is caused to calculate (step S205).
  • the atomic position calculation unit 6 is configured to output the displacement position x ** (j) , force f ** (j) , current atom position x (j) , current force.
  • a new atom position x (j + 1) is calculated based on f (j) (step S206), and the process returns to step S106 in the flowchart of FIG.
  • the subsequent processing is as described above, and the control unit 7 repeats the processing of steps S103 to S107 in FIG. 3 to repeat the calculation for obtaining the atom position x (j) and force f (j) .
  • the state is considered to have converged.
  • the position x (j) of the atom from the initial position x (0) until it is identified as the activated state and the corresponding force f (j) are output.
  • the atomic position calculation unit 6 Since the new atom position x (j + 1) is calculated based on the plurality of eigenvalues ⁇ ⁇ (j) and the plurality of eigenvectors ⁇ ⁇ (j) obtained by 6a, more than the above conventional example.
  • the position of a new atom can be calculated with reference to the information.
  • the residual of the eigenvalue problem with respect to the minute change u (i) of the force acting on the atoms is obtained in the process of convergence.
  • the position x (j + 1) of the new atom is calculated with reference to the other eigenvalues ⁇ ⁇ (j) and eigenvectors ⁇ ⁇ (j) other than the lowest order, which is more optimal for the activated state.
  • a new atom position x (j + 1) can be obtained so as to go in any direction.
  • the calculation method for obtaining the displacement position with respect to the current position of the atom is selected according to the determination result of the determination unit 6b. Force to converge. That is, in the second region, since it is close to the activated state and has a bowl shape, it is necessary to determine the position of a new atom more appropriately.
  • the above formula ( 12) a new atom position x (j + 1) is determined based on a plurality of eigenvalues ⁇ ⁇ (j) and a plurality of eigenvectors ⁇ ⁇ (j) obtained by iterative calculation by the eigenvalue calculation unit 6a.
  • a new atom position x (j + 1) is obtained so as to be directed in a more optimal direction toward the activated state.
  • the first region there is a high possibility that the path to the activated state is longer than in the second region, so priority is given to increasing the potential more quickly using the above formula (11).
  • Calculate the position of a new atom In Equation (11), a new atom position x (j + 1) is obtained so that the potential always changes (rises) along the direction of the lowest-order eigenvector ⁇ 1 (j) .
  • the force acting on the atoms can be converged more efficiently, and the activation state can be changed.
  • the calculation time for specifying can be further shortened.
  • step S204 in FIG. 5 is performed using the formula (b) shown in the conventional example, and the other calculations are performed in the same manner as in the present embodiment.
  • the calculation from the same starting state to the activated state is performed for the same target substance by the method according to the present embodiment and the conventional method, and passes through the second region in FIG. 7 at that time. iterations of operation of the force f (j) taken to, i.e., evaluated by comparing the number of iterations of the calculation of the force f (j) taken to reach the activation state after leaving the first region did.
  • the target substance that is the calculation target of the activated state was Zn-doped InP that functions as a p-type semiconductor.
  • the threshold value j th is 1000
  • the threshold value f th is 0.001 Ry / Bohr
  • the threshold value i th is 5
  • the threshold value r th is 0.1
  • the minute displacement parameter ⁇ was set to 0.01 Bohr.
  • the displacement parameter ⁇ was automatically adjusted so that x ** (j) ⁇ x (j) was 0.1 Bohr.
  • FIG. 8 is a diagram showing the atomic arrangement (position of atoms) of the target substance from the initial state to the activated state.
  • (A) is the initial state set in this verification
  • (b) is the diagram.
  • the state immediately after exiting from the first region in FIG. 7, (c) shows the position of the atom in the activated state specified in this verification.
  • Zn is present in the form of replacing In.
  • Zn present in the form of replacing In in FIG. 8 (a) has moved to the gap between the crystal lattices of In and P, and accompanying it is accompanied by Zn.
  • P is also displaced from the lattice position.
  • Zn and P are slightly moved, though not significantly different from FIG. 8B.
  • FIG. 9 is a graph comparing the number of iterations of operations according to the method according to the present embodiment and the conventional method.
  • the vertical axis indicates the magnitude of the force acting on the atoms
  • the horizontal axis indicates the number of repetitions from the first region to the activation state.
  • the method according to the present embodiment can reduce the number of iterations compared to the conventional method.

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Abstract

Le dispositif d'identification d'état activé (1) présenté est pourvu d'une unité de calcul de potentiel (5) pour calculer une force agissant sur un atome à partir de sa position atomique ; d'une unité de calcul de position atomique (6) pour calculer une nouvelle position atomique pour amener une force agissant sur l'atome qui s'est déplacé de la position atomique actuelle à converger ; et d'une unité de commande (7) pour amener l'unité de calcul de position atomique (6) et l'unité de calcul de potentiel (5) à calculer de manière itérative la nouvelle position atomique et la force agissant sur l'atome, et à identifier l'état activé de l'atome en amenant la force agissant sur l'atome à converger. L'unité de calcul de position atomique (6) calcule la nouvelle position atomique sur la base d'une pluralité de valeurs propres et d'une pluralité de vecteurs propres concernant une variation mineure de la force agissant sur l'atome lorsque la position atomique actuelle a été déplacée d'un degré mineur.
PCT/JP2010/070802 2010-02-10 2010-11-22 Dispositif d'identification d'état activé, procédé d'identification d'état activé, et programme d'identification d'état activé WO2011099210A1 (fr)

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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH10240780A (ja) * 1997-02-24 1998-09-11 Hitachi Ltd 分子設計支援装置および固有値求解方法
WO2007097224A1 (fr) * 2006-02-22 2007-08-30 Osaka University Procede d'estimation d'etat quantique, dispositif d'estimation d'etat quantique et programme informatique

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH10240780A (ja) * 1997-02-24 1998-09-11 Hitachi Ltd 分子設計支援装置および固有値求解方法
WO2007097224A1 (fr) * 2006-02-22 2007-08-30 Osaka University Procede d'estimation d'etat quantique, dispositif d'estimation d'etat quantique et programme informatique

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
AKITAKA SAWAMURA: "Davidson-ho ni yoru Kasseika Jotai Tansaku no Kosokuka, Abstracts of the Japan Institute of Metals", THE JAPAN INSTITUTE OF METALS, vol. 2010, 28 March 2010 (2010-03-28), pages 307 *

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