JPH08287039A - Method for generating atomic coordinates - Google Patents

Abstract

PURPOSE: To efficiently execute coordinate data generating processing by prepar ing a surface model consisting of the repeat of surface structure to be a repeat unit by specified repeating frequency in a two-dimensional (2D) direction. CONSTITUTION: The data of respective atomic coordinates for surface structure to be a repeat unit in the 2D direction of a surface are directly inputted by a user through a keyboard 207 or a mouse 209 or inputted by a method for reading out an electronic file or the like prepared on a disk 203. Then the data of a repeat unit vector in the 2D direction corresponding to the surface structure to be the repeat unit are inputted. Then the diameter data of a circle expressing the size of a molecule projecting to the surface are inputted. Then operation for finding out minimum natural numbers (m), (n) inscribing a circle having a diameter inputted into the 2D face of the surface structure to be the repeat unit expressed by m×n input data is executed. Then the coordinates of respective atoms in surface structure constituted of repeatedly arraying (m) repeat units of surface structure in a prescribed direction and (n) repeat units of surface structure in the other prescribed direction are set up by the use of the found natural numbers (m), (n).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for generating atomic coordinates in material simulation.

[0002]

2. Description of the Related Art In a material simulation such as a molecular orbital method and a molecular dynamics method in which each atom is identified and handled, when a system in which a molecule and a surface interact like a surface adsorption phenomenon is calculated, The model is defined by specifying all the coordinates of the atomic population. In order to accurately represent the interaction between the molecule and the surface, the area in the two-dimensional plane of the atomic population that is the surface model needs to be larger than the projected area of the molecule. Furthermore, in the case of a surface having periodicity in the two-dimensional direction, if the required area in the two-dimensional surface exceeds the area in the two-dimensional surface of the repeating unit in the two-dimensional direction, 2
It is necessary to set a surface model by repeating a plurality of repeating units in the dimensional direction. A method using two-dimensional or three-dimensional image display is known as a method for efficiently generating the coordinates of an atomic population that becomes a surface model.
For example, "Journal of Computer-
Aided Molecular Design "19
For example, there are techniques described in 1995 Volume 9, page 13 to page 32.

[0003]

In the above prior art, the size of the surface model required is not automatically determined based on the size of the molecule interacting with the surface.
Therefore, the user of the same technique judges the area in the two-dimensional plane of the surface model whose coordinates have been set after a predetermined procedure, and if it is judged to be unsuitable, the coordinates of the surface model are set again. Therefore, the number of procedures in the process until the coordinate setting of the surface model atomic population is completed is not constant and the efficiency is poor.

The present invention has been made to solve the above problems.

It is an object of the present invention to facilitate the process of generating coordinate data for surface model atoms that interact with molecules.

[0006]

To achieve the above object, in an information processing terminal equipped with a display device and an input device, a system consisting of one or more molecules and a surface having a periodicity in a two-dimensional direction. In the method of generating atomic coordinates of an atomic population that is a surface model, each of the atomic coordinates of the surface structure that is a repeating unit in the two-dimensional direction of the surface and two types of vectors representing the repeating units in the two-dimensional direction of the surface And the two sides of the parallelogram represented by the two types of vectors representing the repeating unit and the angle between the two sides,
Two types of parallelograms, which have as input data a diameter of a circle representing the size of a molecule projected onto the surface and are inscribed by a circle representing the size of the molecule projected onto the surface and represent the repeating unit, In the two-dimensional direction of a parallelogram represented by two kinds of vectors representing the repeating unit for forming a parallelogram which is composed of finite repetitions of the parallelogram represented by a vector in the two-dimensional direction Is calculated, and a surface model composed of repetitions of the repetition number in the two-dimensional direction of the surface structure serving as the repetition unit is generated.

[0007]

In the input data, two vectors representing the repeating unit in the two-dimensional direction of the surface are respectively set.

[0008]

[Equation 1]

[0009]

[Equation 2]

[0010] The magnitudes of the vectors represented by these equations 1 and 2 are a and b, respectively. Further, the angle formed by the vectors represented by the equations 1 and 2 is θ.

On the other hand, let D be the diameter of a circle representing the size of the molecule.

At this time,

[0013]

(Equation 3)

And

[0015]

[Equation 4]

The minimum natural numbers m and n satisfying the above are obtained.

Next, 0 ≦ i ≦ (m−1) and 0 ≦ j ≦
For all combinations of integers i and j of (n-1)

[0018]

(Equation 5)

The vector is calculated, and the coordinate obtained by adding the vector represented by the equation 5 to each atomic coordinate of the input surface structure which is the repeating unit in the two-dimensional direction is set as the coordinate of the surface model.

[0020]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 2 is an overall configuration diagram according to an embodiment of the present invention.

Reference numeral 201 denotes a CPU (central processing unit), 202
Is a main memory for storing programs and data, 204
Is a disk controller, 206 is a keyboard controller, 208 is a mouse controller, and 210 is a bus controller.
6 is connected to a system bus 205 for transferring data of the entire system. The disk controller 204 controls the disk 203. The keyboard controller 206 is connected to the keyboard 207.
The mouse controller 208 is connected to the mouse 209. Reference numeral 211 is a display system bus for transferring display system data. The bus controller 210 is the system bus 205
And the display system bus 211 are connected. 215 is a drawing processor,
214 is VRAM, 212 is a display device controller,
Each of them is connected to the display system bus 211 via a data / address signal line 216. The display device controller 212 is connected to the display device 213.

(Embodiment 1) An embodiment of the present invention will be described below with reference to the drawings.

FIG. 3 is a diagram showing the contents of input data according to an embodiment of the present invention.

FIG. 3 is composed of silicon atoms (100)
Each atomic coordinate of the surface structure, which is a repeating unit in the two-dimensional direction of the surface, is shown. In this data, atoms up to the fourth layer are represented in the depth direction.

The input data 301 is the atom number 302 in the data, the atom number 303 representing the atom type, and the atom x.
Coordinate 304, atom y coordinate 305, atom z coordinate 306
Consists of

FIG. 4 is a diagram showing the contents of input data according to an embodiment of the present invention.

FIG. 4 is composed of silicon atoms (100)
The repeating unit vector in the two-dimensional direction corresponding to the surface structure which is the repeating unit in the two-dimensional direction of the surface is shown.

The input data 401 is the name 40 of the vector.
2, vector x component 403, vector y component 40
4, a vector z component 405, and an angle 406 formed by two vectors included in the input data 401.

FIG. 5 shows, in an embodiment of the present invention, two vectors included in the input data 401, the magnitudes a and b of each vector, and the angle 4 formed by the two vectors.
It is explanatory drawing which shows the relationship of 06. In this figure, the angle 406 formed by the two vectors is represented by θ.

FIG. 1 is a flow chart showing the processing procedure of an embodiment of the present invention.

In step 101, the user directly inputs the data using the keyboard 207 or the mouse 209 or the disk 2
Data 301 of each atomic coordinate of the surface structure, which is a repeating unit in the two-dimensional direction of the surface, is input by a method such as reading an electronic file created on 03.

The content of the data of each atomic coordinate of the surface structure which is the input repeating unit is the atom number 30 in the data.
2, atomic number 303, which indicates the type of atom, x-coordinate of atom 3,
04, the y coordinate 305 of the atom, the z coordinate 306 of the atom, etc., which are stored in the main memory 202.

In step 102, the user directly inputs the data using the keyboard 207 or the mouse 209 or the disk 2
The data 401 of the repeating unit vector in the two-dimensional direction corresponding to the surface structure serving as the repeating unit is input by a method such as reading an electronic file created on 03.

The contents of the data of the repeating unit vector in the two-dimensional direction corresponding to the input surface structure as the repeating unit are the name 402 of the vector, the x component 403 of the vector,
Vector y component 404, vector z component 405, angle 40 formed by two vectors included in input data 401
6 and is stored in the main memory 202.

In step 103, the user directly inputs the data using the keyboard 207 or the mouse 209 or the disk 2
The data of the diameter of the circle representing the size of the molecule projected on the surface is input by a method such as reading an electronic file created on 03.

The input circle diameter data is one piece of positive real number data.

In step 104, the minimum natural numbers m and n such that the circle having the diameter input in step 103 is inscribed in the two-dimensional plane of the repeating unit surface structure represented by m × n input data 301 are set. Perform the desired calculation.

This calculation is performed in the following procedure.

Here, the two repeating unit vectors input in step 102 are defined as the above equations 1 and 2. The magnitudes of the vectors represented by these equations 1 and 2 are a and b, respectively. Further, the angle formed by the vectors represented by the equations 1 and 2 is θ.

On the other hand, let D be the diameter of a circle representing the size of the molecule.

At this time, the minimum natural numbers m and n satisfying the equations 3 and 4 are obtained.

Equations 3 and 4 are necessary conditions for a circle having a diameter D to be inscribed inside a figure obtained by multiplying the number of repeating unit vectors 1 by m and the number of repeating unit vectors 2 by n.

The reason why the expressions 3 and 4 represent the above-mentioned necessary conditions will be described later.

In step 105, by using the natural numbers m and n obtained in step 104, the surface structure to be the repeating unit is repeatedly arranged in the direction of equation 1 by m pieces and in the direction of n by n pieces of the surface structure. The coordinates of each atom are set, and the process ends.

Details of the processing contents of step 105 will be described later.

FIG. 6, FIG. 7, FIG. 8 and FIG. 9 show that in the embodiment of the present invention, the number of repeating unit vectors 1 is multiplied by m,
FIG. 9 is an explanatory diagram showing that the formulas 3 and 4 are introduced as a necessary condition for the inscribed circle of the diameter D inside the figure obtained by multiplying the number 2 of the repeating unit vectors by n. In the following description regarding these figures, a figure in which the number of repeating unit vectors 1 is multiplied by m and the number of repeating unit vectors 2 is multiplied by n is abbreviated as “m × n figure”.

FIG. 6 shows the case where the angle θ formed by the number of repeating unit vectors 1 and the number of repeating unit vectors 2 is 0 ≦ θ ≦ π / 2. At this time, the distance between the two sides of the length nb in the m × n graphic is represented by ma sin θ. Therefore, the necessary condition for the inscribed circle of the circle having the diameter D to be in the angle of the size θ is D ≦ ma sin θ. That is, the equation 3 is derived.

FIG. 7 shows the case where the angle θ formed by the number of repeating unit vectors 1 and the number of repeating unit vectors 2 is π / 2 ≦ θ ≦ π. Also in this case, as in FIG. 6, m
The distance between two sides of length nb in a × n figure is represented by ma sin θ. Therefore, Equation 3 is introduced as a necessary condition for the circle having the diameter D to be inscribed in anticipation of the angle of the size θ.

FIG. 8 shows a case where the angle θ formed by the number of repeating unit vectors 1 and the number of repeating unit vectors 2 is 0 ≦ θ ≦ π / 2. At this time, the distance between the two sides of the length na in the m × n graphic is represented by n b sin θ. Therefore, the necessary condition for inscribed inside of the circle having the diameter D in consideration of the corner portion other than the corner of the size θ is D ≦ n b sin θ. That is, the equation 4 is derived.

FIG. 9 shows the case where the angle θ formed by the number of repeating unit vectors 1 and the number of repeating unit vectors 2 is π / 2 ≦ θ ≦ π. In this case, as in FIG. 8, m
The distance between two sides of length na in a × n figure is represented by n b sin θ. Therefore, Formula 4 is derived as a necessary condition for inscribed in the corner of the circle having the diameter D other than the corner of the size θ.

FIG. 10 is a flow chart showing details of the processing procedure of step 105 in the embodiment of the present invention.

In step 1001, the value of the counter j is set to 0.

In step 1002, the value of the counter i is set to 0.

In step 1003, the vector defined by the above equation 5 is first calculated for the counters i and j at this time and the two repeating unit vectors input in step 102. Next, data obtained by adding the vector number 5 to each atomic coordinate data of the surface structure which is the repeating unit input in step 101 is set as the atomic coordinate of the surface structure.

In step 1004, it is determined whether the value of the counter i is equal to m-1. Here, m is a natural number obtained in step 104.

If i and m-1 are equal, the process proceeds to step 1006, and if i and m-1 are not equal,
Go to step 1005.

In step 1005, the value of the counter i is incremented by 1, and the process returns to step 1003.

In step 1006, it is determined whether the value of the counter j is equal to n-1. Here, n is a natural number obtained in step 104.

If j and n-1 are equal, the process is terminated, and if j and n-1 are not equal, step 1
Proceed to 007.

In step 1007, the value of the counter j is incremented by 1, and the process returns to step 1002.

(Embodiment 2) An embodiment of the present invention will be described below with reference to the drawings.

FIG. 11 is a diagram showing the contents of input data according to an embodiment of the present invention.

FIG. 11 shows atomic coordinates of B2H6 molecule and B
The input example of the constant distance d0 given to 2H6 molecules is shown.

The input data 1101 has a constant distance 110.
2, atomic number 1103, atomic number 110 in the data
4, the x coordinate 1105 of the atom, the y coordinate 1106 of the atom, and the z coordinate 1107 of the atom.

FIG. 12 is a flow chart showing the processing procedure of an embodiment of the present invention.

When carrying out claim 2 of the present invention, FIG.
After step 102, a series of processing shown in FIG. 12 is performed, and then the process proceeds to step 104.

In step 1201, the keyboard 207
Input data 1101 of a fixed distance or atomic coordinates of a molecule is input by a method such as direct input by a user using the mouse or the mouse 209 or reading an electronic file created on the disk 203.

The input data 1101 has a fixed distance of 1
102, atomic number 1103 in the data, atomic number 11
04, atom x coordinate 1105, atom y coordinate 1106,
It consists of the z-coordinate 1107 of the atom.

In step 1202, the maximum interatomic distance Rmax in the molecule represented by the input data 1101 is calculated according to the following procedure.

First, the interatomic distance Rij between the i-th atom and the j-th atom in the molecule is calculated by the coordinate (x
i, yi, zi) and the coordinates of the j-th atom (xj, y
j, zj) is defined as the following equation.

[0072]

(Equation 6)

By the definition of the equation 6, Rij = Rji. In addition, Rii = 0. Therefore, if the number of atoms in the molecule is N, the inter-atomic distance Rij that does not become 0 is N (N-1) / 2, that is, there is a finite number. Therefore, the maximum value is found from this finite number of interatomic distances, and Rmax
And

As a calculation method for finding the maximum value from a finite number of numerical data, for example, the method shown on pages 48 to 56 of "FORTRAN77 introductory revised edition" (edited by Shoji Ura, Baifukan, 1990) is used.

In step 1203, step 1202
The sum of Rmax obtained in step S1 and d0 input in step 1201 is calculated and assigned to D, and the process ends.

[0076]

As described above, according to the present invention, it is possible to easily and efficiently generate the coordinates of the surface model atomic population having the area in the two-dimensional plane required according to the size of the interacting molecule. Can be

[0077]

[Brief description of drawings]

FIG. 1 is a flowchart showing a processing procedure according to an embodiment of the present invention.

FIG. 2 is an overall configuration diagram according to an embodiment of the present invention.

FIG. 3 is a diagram showing the contents of input data according to an embodiment of the present invention.

FIG. 4 is a diagram showing the contents of input data according to an embodiment of the present invention.

FIG. 5 shows input data 401 according to an embodiment of the present invention.
2 is an explanatory diagram showing a relationship between two vectors included in the vector, magnitudes a and b of each vector, and an angle 406 formed by the two vectors.

FIG. 6 is a diagram showing the number of necessary conditions for an inscribed circle of the diameter D inside a figure obtained by multiplying the number of repeating unit vectors 1 by m and the number of repeating unit vectors 2 by n in an embodiment of the present invention. Explanatory drawing which shows that 3 is guide | induced.

FIG. 7 is a diagram showing the number of necessary conditions for an inscribed circle of the diameter D inside a figure obtained by multiplying the number of repeating unit vectors by 1 and the number of repeating unit vectors by n in an embodiment of the present invention. Explanatory drawing which shows that 3 is guide | induced.

FIG. 8 is a diagram showing the number of necessary conditions for an inscribed circle of the diameter D inside a figure obtained by multiplying the number of repeating unit vectors 1 by m and the number of repeating unit vectors 2 by n in one embodiment of the present invention. Explanatory drawing which shows that 4 is guide | induced.

FIG. 9 is a diagram showing the number of necessary conditions for the inscribed circle of the diameter D inside a figure obtained by multiplying the number of repeating unit vectors by 1 and the number of repeating unit vectors by n in an embodiment of the present invention. Explanatory drawing which shows that 4 is guide | induced.

FIG. 10 is a flow chart of step 105 in an embodiment of the present invention.
5 is a flowchart showing details of the processing procedure of FIG.

FIG. 11 is a diagram showing the contents of input data according to an embodiment of the present invention.

FIG. 12 is a flowchart showing a processing procedure according to an embodiment of the present invention.

[Explanation of symbols]

101 ... Processing step for inputting each atomic coordinate data of the surface structure which is a repeating unit, 102 ... Processing step for inputting repeating unit vector data, 103 ... Processing for inputting diameter data of a circle representing the size of a molecule Step, 104
An arithmetic processing step for obtaining minimum natural numbers m and n such that a circle is inscribed in m × n repeating units.

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Ryotaro Irie 1-280, Higashi Koigokubo, Kokubunji, Tokyo Metropolitan Research Center, Hitachi, Ltd.

Claims (2)

[Claims] 1. An information processing terminal equipped with a display device and an input device, wherein atomic coordinates of an atomic population of a surface model of a system consisting of one or more molecules and a surface having a periodicity in a two-dimensional direction are generated. A method comprising the steps of:
Each atomic coordinate of the surface structure that becomes a repeating unit in the dimensional direction,
Input the coordinates of two kinds of vectors representing the repeating unit in the two-dimensional direction of the surface, the angle formed by the two kinds of vectors representing the repeating unit, and the diameter of the circle representing the size of the molecule projected on the surface. A finite repetition in a two-dimensional direction of a parallelogram which is a parallelogram in which a circle representing the size of a molecule projected on the surface is inscribed as data and which is represented by two kinds of vectors representing the repeating unit. Of the parallelogram represented by two kinds of vectors representing the repeating unit for forming the parallelogram as shown in FIG. A method of generating atomic coordinates, characterized in that a surface model consisting of repetitions of the number of repetitions is generated. 2. The method for generating atomic coordinates according to claim 1, wherein the atomic coordinates of the one or more molecules and a fixed distance are used as input data, and the interatomic distance in the one or more molecules. 2. The atomic coordinate generation method according to claim 1, wherein the sum of the maximum value of the above and the constant distance is used as the diameter of a circle representing the size of the molecule projected on the surface.