Analysis device, analysis method, and analysis program

Abstract

To provide an analysis device, an analysis method, and an analysis program capable of extracting information on a molecular structure from a molecular vibration spectrum.SOLUTION: An analysis device 100 includes an acquisition unit 110 which analyzes molecular vibration spectrum of each of a plurality of organic molecules including a plurality of first organic molecules, and a second organic molecule serving as a reference for analyzing the molecule structure of each of the plurality of first organic molecules by applying a combination optimization technique using an inking pattern and acquires information on the molecular structure of each of the plurality of first organic molecules.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to an analysis apparatus, an analysis method, and an analysis program, and particularly to combinatorial optimization using an Ising model.

Background Art

[0002] Measurement data of the molecular vibration spectrum of an organic molecule is usually considered by distinguishing two regions with 1500 cm -1 as a boundary. First, the part of 600 to 1500 cm -1 is called the fingerprint region. Since the fingerprint region has a complex structure derived from angular variation and single bond stretching vibration, it is difficult to identify a functional group from each peak included in the fingerprint region. However, since each organic molecule has a unique molecular vibration spectrum in the fingerprint region, the molecular structure of each organic molecule can be identified by comparison with the molecular vibration spectrum of an organic molecule with a known molecular structure.

[0003] On the other hand, the part of 1500 to 4000 cm -1 is called the diagnostic region. The diagnostic region contains information useful for interpreting the molecular structure, such as peaks derived from double bonds such as C=O, C=C, and C=N near 1700 cm -1 , and peaks derived from C≡C triple bonds near 2200 cm -1 . On the other hand, strong absorption peaks at around 3000 cm -1 and within 200 cm -1 before and after are derived from C-H bonds, but since almost all organic molecules have C-H bonds, they are not considered important in interpreting the molecular structure.

[0004] Identification of an organic molecule is performed by combining analysis of the molecular vibration spectrum, analysis of the mass spectrum, and various analysis methods such as nuclear magnetic resonance method. Here, analysis of the mass spectrum can analyze the molecular weight and molecular formula of an organic molecule. Also, the nuclear magnetic resonance method can analyze the bonding state between carbon atoms and information on adjacent atoms.

[0005] On the other hand, techniques for solving combinatorial optimization problems using an Ising model have attracted attention. Patent Document 1 discloses a technique for searching for a stable structure of a protein using techniques such as quantum annealing.

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0007] In order to reduce the burden of performing analyses other than the analysis of the molecular vibration spectrum, it is desired to extract more information about molecular structures from the molecular vibration spectrum.

[0008] The present disclosure has been made to solve such problems. That is, an analysis device, an analysis method, and an analysis program capable of extracting information about a molecular structure from a molecular vibration spectrum are provided.

Means for Solving the Problems

[0009] The analysis device according to the present disclosure analyzes the molecular vibration spectrum of each of a plurality of organic molecules including a plurality of first organic molecules and a second organic molecule serving as a reference for analyzing the molecular structure of each of the plurality of first organic molecules, using a combinatorial optimization method using an Ising model, and includes an acquisition unit that acquires information about the molecular structure of each of the plurality of first organic molecules.

[0010] The analysis method according to the present disclosure is one in which a computer analyzes the molecular vibration spectrum of each of a plurality of organic molecules including a plurality of first organic molecules and a second organic molecule serving as a reference for analyzing the molecular structure of each of the plurality of first organic molecules, using a combinatorial optimization method using an Ising model, and acquires information about the molecular structure of each of the plurality of first organic molecules.

[0011] The analysis program according to the present disclosure causes a computer to analyze the molecular vibration spectrum of each of a plurality of organic molecules including a plurality of first organic molecules and a second organic molecule serving as a reference for analyzing the molecular structure of each of the plurality of first organic molecules, by applying a combinatorial optimization method using an Ising model, and execute a process of acquiring information regarding the molecular structure of each of the plurality of first organic molecules.

Advantages of the Invention

[0012] According to the present disclosure, information regarding the molecular structure can be extracted from the molecular vibration spectrum.

Brief Description of the Drawings

[0013]

Figure 1

Figure 2

Figure 3

Figure 4

Modes for Carrying Out the Invention

[0014] (Embodiment 1) Hereinafter, embodiments of the present invention will be described with reference to the drawings. Since the drawings are simplified, the technical scope of the embodiments should not be narrowly interpreted based on the description of these drawings. Also, the same elements are denoted by the same reference numerals, and redundant explanations are omitted.

[0015] FIG. 1 is a block diagram showing the configuration of the analysis device 100 according to Embodiment 1. The analysis device 100 includes an acquisition unit 110. The acquisition unit 110 analyzes the molecular vibration spectrum of each of a plurality of organic molecules including a plurality of first organic molecules and a second organic molecule serving as a reference for analyzing the molecular structure of each of the plurality of first organic molecules. Each of the plurality of organic molecules may be, for example, a chain compound having a main chain (main skeleton).

[0016] The plurality of first organic molecules are objects for analyzing the molecular structure. Specifically, the acquisition unit 110 analyzes the degree of a predetermined property of the molecular structure of each of the plurality of first organic molecules. The predetermined property is, for example, linearity or branching. The predetermined property may be a property related to the number of carbon atoms in the main chain (main-chain carbon number). The property related to the main-chain carbon number is specifically a property that the number of carbon atoms in the main chain is large or a property that the number of carbon atoms in the main chain is small. Here, the property that the number of carbon atoms in the main chain is large or small may be based on the second organic molecule. The predetermined property may be a property that can be quantified like the property related to the main-chain carbon number.

[0017] Specifically, the second organic molecule serves as a reference for analyzing the degree of a predetermined property of the molecular structure of each of the plurality of first organic molecules. The second organic molecule may be, for example, an organic molecule having a stronger predetermined property than each of the plurality of first organic molecules. Also, the second organic molecule may be an organic molecule having a weaker predetermined property than each of the plurality of first organic molecules. For example, the second organic molecule is an organic molecule having stronger linearity or weaker linearity than each of the plurality of first organic molecules. Also, for example, the second organic molecule is an organic molecule having stronger branching or weaker branching than each of the plurality of first organic molecules. Also, the second organic molecule may be an organic molecule having a larger main-chain carbon number or a smaller main-chain carbon number than each of the plurality of first organic molecules.

[0018] As described above, the acquisition unit 110 analyzes the molecular vibration spectrum of each of a plurality of organic molecules including the plurality of first organic molecules and the second organic molecule described above. Then, the acquisition unit 110 analyzes the molecular vibration spectrum of each of the plurality of organic molecules by applying a combinatorial optimization method using an Ising model, and acquires information regarding the molecular structure of each of the plurality of first organic molecules. The combinatorial optimization method using an Ising model is a method for searching for a state in which the energy of a Hamiltonian expressed by a quadratic expression of 0-1 binary variables is minimized. Here, the acquisition unit 110 may perform analysis such that the closer the molecular vibration spectra of the organic molecules are to each other, the closer the molecular structures (that is, the degree of a predetermined property) of the organic molecules become.

[0019] For example, the acquisition unit 110 can acquire a permutation in which a plurality of first organic molecules are arranged in ascending or descending order of a predetermined property, starting with the second organic molecule, using the method described above. In such a case, the acquisition unit 110 can acquire information regarding the order in which the predetermined property of each of the plurality of first organic substances increases or decreases. That is, the acquisition unit 110 can acquire information regarding the order relationship (strength-weakness relationship, magnitude relationship) between the degrees of a predetermined property of each of the plurality of first organic molecules.

[0020] Note that the plurality of first organic molecules may include an organic molecule whose molecular structure is not specified and an organic molecule whose molecular structure is specified. In such a case, it becomes possible to evaluate the degree of a predetermined property of an organic molecule whose molecular structure is not specified based on the degree of a predetermined property of an organic molecule whose molecular structure is specified.

[0021] The analysis apparatus according to Embodiment 1 analyzes a molecular vibration spectrum by applying a combinatorial optimization method using an Ising model, and acquires information regarding the molecular structure of each of a plurality of first organic molecules that are analysis targets. Therefore, the analysis apparatus according to Embodiment 1 can extract information regarding a molecular structure by analyzing a molecular vibration spectrum.

[0022] FIG. 2 is a diagram showing an example of the hardware configuration of the analysis device 100. The analysis device 100 includes a processor 1001, a memory 1002, and a storage device 1003. The storage device 1003 stores a computer program in which the processing of the analysis method according to Embodiment 1 is executed. Then, the processor 1001 causes the memory 1002 to read the computer program from the storage device 1003 and executes the computer program. Thereby, the processor 1001 realizes the function of the acquisition unit 110.

[0023] Alternatively, the acquisition unit 110 may be realized by dedicated hardware. Also, part or all of the acquisition unit 110 may be realized by general-purpose or dedicated circuitry, a processor, or the like, or a combination thereof. These may be configured by a single chip or by a plurality of chips connected via a bus. Part or all of the acquisition unit 110 may be realized by a combination of the above-described circuitry or the like and a program. Also, as the processor, a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), an FPGA (Field Programmable Gate Array), or the like can be used. Further, the analysis device 100 may include a quantum chip (not shown) that executes quantum annealing.

[0024] Also, when part or all of the acquisition unit 110 is realized by a plurality of information processing devices, circuitry, or the like, the plurality of information processing devices, circuitry, or the like may be centrally arranged or may be distributed. For example, the information processing devices, circuitry, or the like may be realized in a form in which each is connected via a communication network, such as a client-server system or a cloud computing system. Further, the function of the analysis device 100 may be provided in the form of SaaS (Software as a Service).

[0025] (Embodiment 2) Embodiment 2 is a specific example of Embodiment 1. In the following description, descriptions overlapping with Embodiment 1 are omitted. FIG. 3 is a configuration diagram showing the configuration of the analysis device 100a according to Embodiment 2. The analysis device 100a includes an acquisition unit 110a. The acquisition unit 110a is an example of the acquisition unit 110 described above. The acquisition unit 110a includes a calculation unit 111, a processing unit 112, and an optimization unit 113.

[0026] The acquisition unit 110a analyzes the molecular vibration spectrum of each of a plurality of organic molecules including a plurality of first organic molecules and a second organic molecule as a reference. The second organic molecule has a stronger predetermined property than each of the plurality of first organic molecules. Or, the second organic molecule has a weaker predetermined property than each of the plurality of first organic molecules.

[0027] The calculation unit 111 generates a similarity matrix representing the similarity (similarity evaluation value) between the molecular vibration spectra of each of the plurality of organic molecules. In other words, the similarity matrix represents the similarity of the molecular vibration spectra of each pair of organic molecules. When the number of molecular vibration spectra (the number of the plurality of organic molecules) is N, the similarity matrix is an N×N matrix. When the molecular vibration spectra are S1 to S N , the (i, j) component of the similarity matrix represents the similarity between S i and S j .

[0028] The wavenumber range of the molecular vibration spectrum may be 2800 to 3200 cm ―1 . In the analysis of the molecular vibration spectrum, strong absorption peaks in the wavenumber range of 200 cm-1 before and after 3000 cm-1 are derived from C-H bonds. Since almost all organic compounds have C-H bonds, this absorption peak has not been regarded as important in the analysis of the molecular structure. On the other hand, the analysis device 100a can acquire information regarding the molecular structure from the molecular vibration spectrum in the wavenumber range of 200 cm-1 before and after 3000 cm-1.

[0029] Here, the calculation unit 111 may calculate the similarity between the molecular vibration spectra of a plurality of organic molecules using the dynamic time warping (DTW) method. The calculation unit 111 calculates the similarity between organic molecules for N(N - 1) / 2 pairs created by taking out two different organic molecules from N organic molecules using DTW. DTW is a method for calculating the similarity between time series data, but by reading time as wavenumber (frequency), the similarity between the data of molecular vibration spectra can be evaluated. The similarity matrix is generated based on the calculation results of the similarity.

[0030] The processing unit 112 formulates a Hamiltonian H for setting an order between each of the plurality of organic molecules such that the closer the similarity between the molecular vibration spectra of the organic molecules, the closer the order between the organic molecules. In other words, the processing unit 112 determines a permutation for arranging the plurality of organic molecules such that the closer the similarity between the molecular vibration spectra of the organic molecules, the closer the order between the organic molecules. The determined permutation represents the relative similarity of each of the plurality of organic molecules. The Hamiltonian H formulated by the processing unit 112 is illustrated in Equation 1. The number of the plurality of organic molecules is N, and each of the plurality of organic molecules is pre-assigned a number from 1 to N. That is, each of the plurality of organic molecules is identified by a number from 1 to N.

[0031]

Equation

[0032] The first term on the right side of Equation 1 represents the constraint that each of the organic molecules identified by ID-1 to ID-N must be assigned some order in the permutation. The second term on the right side of Equation 1 represents the constraint that some organic molecule must be assigned to each of the 1st to Nth positions in the permutation.

[0033] The third term on the right side of Equation 1 corresponds to the objective function in the combinatorial optimization problem. As described above, f(k, l) is a function that determines the strength of the correlation between the orders k and l in the permutation. Here, f(k, l) = δ k、l+1 as, d i、j is reinterpreted as the distance between vertex i and vertex j, the Hamiltonian H corresponds to the formulation of the Traveling Salesperson Problem (TSP) by the Ising model. In TSP, only the distance between a certain vertex and the vertices visited before and after it is considered, but in the Hamiltonian H, vertices other than those visited before and after may also be considered. Thereby, the analysis device 100a may be able to set a more appropriate order. The third term on the right side of Equation 1 may consider the distances (similarities) between all vertices.

[0034] As described above, f(k, l) is, for example, a Gaussian function f(k, l) = exp{-α*(k - l) 2} Here, α is a hyperparameter. α may be set to an appropriate value based on the result of actual optimization using candidate values. Using a function that rapidly decays to 0 as the difference between k and l increases, such as a Gaussian function, can stabilize the calculation by the optimization unit 113 described later. The similarity d weighted by f(k, l) ij By minimizing the sum of, molecules with similar molecular vibration spectra are arranged in adjacent orders in the permutation.

[0035] The fourth term on the right side of Equation 1 represents the constraint that the order of the organic molecules included in S peg is fixed. The fourth term on the right side of Equation 1 may be a constraint that fixes the second organic molecule at the head of the permutation.

[0036] The optimization unit 113 optimizes the Hamiltonian H formulated by the processing unit 112. Thereby, the optimization unit 113 acquires information regarding the molecular structure of each of the plurality of first organic molecules. When the predetermined property of the second organic molecule is strong, information regarding the order in which the predetermined property weakens among each of the plurality of first organic molecules may be acquired. Also, when the predetermined property of the second organic molecule is weak, information regarding the order in which the predetermined property strengthens among each of the plurality of first organic molecules may be acquired.

[0037] The optimization unit 113 may optimize the Hamiltonian H using the simulated annealing method or tabu search. The optimization unit 113 may be, for example, dedicated hardware that searches for the optimal solution of the combinatorial optimization problem using simulated annealing. Also, the optimization unit 113 may be a quantum computer that searches for the optimal solution of the combinatorial optimization problem by quantum annealing. The optimization unit 113 does not necessarily have to obtain the optimal solution using the Hamiltonian H, and it suffices to obtain the solution when the value of the Hamiltonian H decreases.

[0038] FIG. 4 is a flowchart showing the operation of the analysis device 100a according to Embodiment 2. First, the calculation unit 111 of the analysis device 100a calculates a similarity matrix representing the similarity between the molecular vibration spectra of each of a plurality of organic molecules (step S101). As described above, among the plurality of organic molecules, there is included a second organic molecule having a stronger or weaker predetermined property than the plurality of first organic molecules and serving as a reference for analysis.

[0039] Next, based on the similarity matrix created in step S101, the processing unit 112 of the analysis device 100a formulates a Hamiltonian for setting an order between each of the plurality of organic molecules such that the closer the similarity between the molecular vibration spectra of the organic molecules, the closer the order between the organic molecules (step S102). Here, the order is set based on the second organic molecule. Specifically, the order is set such that the second organic molecule comes first. In other words, a permutation for arranging the plurality of organic molecules with the second organic molecule at the head is determined.

[0040] Finally, the optimization unit 113 of the analysis device 100a optimizes the Hamiltonian formulated in step S102 (step S103). Thereby, information regarding the degree of a predetermined property of the molecular structure of each of the plurality of first organic molecules is obtained.

[0041] Next, the inventors will explain the results of verifying the above-described analysis method using the molecular vibration spectra of each of 18 isomers of octane (C8H8). The following Structural Formulas 1 to 18 show 18 isomers of octane.

Chemical Formula

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[0042] Molecular vibration spectra have not been measured for all 18 isomers of octane. Therefore, the inventor performed quantum chemical calculations on 18 isomers of octane to determine the optimized structure, calculated the vibration frequencies for that structure, calculated the reference vibration frequencies and absorption intensities, and obtained the molecular vibration spectra. Then, based on the obtained molecular vibration spectra, the inventor calculated the similarity matrix described above. Here, the inventor calculated the similarity matrix using the vibration frequencies and absorption intensities in the range of 2800 - 3200 cm-1 corresponding to the stretching vibrations of C-H bonds.

[0043] First, the inventor analyzed the organic molecules shown in Structural Formulas 2 to 18 with reference to the organic molecule shown in Structural Formula 1 to verify whether information regarding the strength of a predetermined property could be obtained. That is, the organic molecule shown in Structural Formula 1 corresponds to the second organic molecule described above. The organic molecules shown in Structural Formulas 2 to 18 correspond to the plurality of first organic molecules described above.

[0044] The organic molecule shown in Structural Formula 1 is normal octane. Normal octane has a main chain (carbon chain) that is not branched and has 8 main chain carbon atoms. The organic molecule shown in Structural Formula 1 has more main chain carbon atoms than the organic molecules shown in Structural Formulas 2 to 17. Also, the organic molecule shown in Structural Formula 1 is more linear than the organic molecules shown in Structural Formulas 2 to 17. Therefore, according to the analysis method of Embodiment 2, information regarding the order in which the number of main chain carbon atoms decreases or the order in which the linearity weakens among the organic molecules shown in Structural Formulas 2 to 17 should be obtained.

[0045] The inventor generated the Hamiltonian H such that the organic molecule shown in Structural Formula 1 was at the beginning, and determined the permutation for arranging 18 isomers by optimizing the Hamiltonian H. As a result of optimizing the Hamiltonian H, the permutation (Structural Formula 1) → (Structural Formula 10) → (Structural Formula 14) → (Structural Formula 11) → (Structural Formula 16) → (Structural Formula 4) → (Structural Formula 13) → (Structural Formula 12) → (Structural Formula 17) → (Structural Formula 18) → (Structural Formula 9) → (Structural Formula 7) → (Structural Formula 3) → (Structural Formula 5) → (Structural Formula 8) → (Structural Formula 2) → (Structural Formula 6) → (Structural Formula 15) was obtained. Focusing on the number of carbon atoms in the main chain of each isomer in this permutation, the number of main-chain carbon atoms is: 8 → 7 → 7 → 7 → 5 → 6 → 6 → 6 → 6 → 5 → 6 → 6 → 5 → 5 → 6 → 5 → 5 → 4. The permutation obtained by optimizing the Hamiltonian shows an order in which the number of carbon atoms in the main chain decreases as a whole while arranging molecules with the same number of carbon atoms in the main chain locally. It can also be said that the obtained permutation shows an order in which the linearity of the main chain becomes weaker.

[0046] In addition, the inventor also verified the case where the isomer shown in Structural Formula 15 was at the beginning. That is, the inventor analyzed the isomer shown in Structural Formula 15 as the second organic molecule. The isomer shown in Structural Formula 15 has 4 carbon atoms in the main chain, which is the smallest number of carbon atoms in the main chain among the 18 isomers. When the Hamiltonian H for setting the order of the 18 isomers was optimized, a permutation in which the above permutation was reversed and the number of main-chain carbon atoms increased was obtained. Also, the isomer shown in Structural Formula 15 is the most branched organic molecule among the 18 isomers, and it can be said that a permutation showing an order in which the branching becomes weaker was obtained.

[0047] In the analysis of the normal molecular vibration spectrum, it was difficult to obtain information on the structure of the entire organic molecule. However, according to the analysis method according to Embodiment 2, information on the structure of the entire organic molecule (e.g., the number of main-chain carbon atoms) is extracted from the spectral region related to the stretching vibration of the C-H bond.

[0048] Thus, by applying the combinatorial optimization method using the Ising model, it becomes possible to extract information on the molecular structure from the molecular vibration spectrum. In the analysis of the molecular structure, additional analysis and evaluation are performed in addition to the analysis of the molecular vibration spectrum. However, according to the analysis apparatus according to Embodiment 2, the burden of analysis and evaluation other than the molecular vibration spectrum can be reduced.

[0049] Note that the present invention is not limited to the above-described embodiments, and can be appropriately modified without departing from the gist thereof.

Description of Reference Numerals

[0050] 100, 100a Analysis apparatus 110, 110a Acquisition unit 111 Calculation unit 112 Processing unit 113 Optimization unit 1001 Processor 1002 Memory 1003 Storage device

Claims

1. For each of a plurality of organic molecules including a plurality of first organic molecules and a second organic molecule serving as a reference for analyzing the molecular structure of each of the plurality of first organic molecules, analyze the molecular vibration spectrum by applying a combinatorial optimization method using an Ising model, and obtain information regarding the molecular structure of each of the plurality of first organic molecules, an acquisition unit comprising wherein the acquisition unit generates a similarity matrix representing the similarity between the molecular vibration spectra of each of the plurality of organic molecules, by optimizing a Hamiltonian for setting an order between each of the plurality of organic molecules such that the closer the order of the organic molecules to each other as the similarity between the molecular vibration spectra of each of the organic molecules to each other is greater, obtains information regarding the molecular structure of each of the plurality of first organic molecules, wherein the second organic molecule is an organic molecule serving as a reference for analyzing the degree of a predetermined property of the molecular structure of each of the plurality of first organic molecules, wherein the information regarding the molecular structure is information indicating an order relationship between the degrees of the predetermined property of each of the plurality of organic molecules, wherein the predetermined property is a property related to linearity, branching, or the number of main-chain carbon atoms, an analysis device.

2. wherein the acquisition unit optimizes the Hamiltonian using an annealing method or a tabu search, the analysis device according to claim 1.

3. wherein the acquisition unit calculates the similarity between the molecular vibration spectra of each of the plurality of organic molecules using a dynamic time warping method and generates the similarity matrix based on the calculation result, the analysis device according to claim 1 or 2.

4. The wavenumber range of the molecular vibration spectrum of each of the plurality of organic molecules is 2,800 to 3,200 cm ―１ The analysis apparatus according to any one of claims 1 to 3, wherein the analysis apparatus is as described above.

5. A computer analyzes the molecular vibration spectrum of each of a plurality of organic molecules including a plurality of first organic molecules and a second organic molecule serving as a reference for analyzing the molecular structure of each of the plurality of first organic molecules by applying a combinatorial optimization method using an Ising model, and obtains information regarding the molecular structure of each of the plurality of first organic molecules, including wherein the obtaining generates a similarity matrix representing the similarity between the molecular vibration spectra of each of the plurality of organic molecules, by optimizing a Hamiltonian for setting an order between each of the plurality of organic molecules such that the closer the order of the organic molecules to each other as the similarity between the molecular vibration spectra of each of the organic molecules to each other is greater, obtains information regarding the molecular structure of each of the plurality of first organic molecules, The second organic molecule is an organic molecule serving as a reference for analyzing the degree of a predetermined property of the molecular structure of each of the plurality of first organic molecules. The information regarding the molecular structure is information indicating an order relationship among the degrees of the predetermined property of each of the plurality of organic molecules. The predetermined property is a property related to linearity, branching, or the number of main-chain carbon atoms. Analysis method. Claim 6 On a computer, Analyze the molecular vibration spectrum of each of a plurality of organic molecules including a plurality of first organic molecules and a second organic molecule serving as a reference for analyzing the molecular structure of each of the plurality of first organic molecules, by applying a combinatorial optimization method using an Ising model, and execute a process of obtaining information regarding the molecular structure of each of the plurality of first organic molecules. The process of obtaining Generate a similarity matrix representing the similarity between the molecular vibration spectra of each of the plurality of organic molecules. Obtain information regarding the molecular structure of each of the plurality of first organic molecules by optimizing a Hamiltonian for setting an order between each of the plurality of organic molecules such that the closer the order between the organic molecules, the greater the similarity between the molecular vibration spectra of each of the organic molecules. The second organic molecule is an organic molecule serving as a reference for analyzing the degree of a predetermined property of the molecular structure of each of the plurality of first organic molecules. The information regarding the molecular structure is information indicating an order relationship among the degrees of the predetermined property of each of the plurality of organic molecules. The predetermined property is a property related to linearity, branching, or the number of main-chain carbon atoms. Analysis program.

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