A method for drawing a pseudo 3D projection map of a π orbital of a conjugated molecule and a storage medium

Abstract

The application provides a kind of conjugated molecular π orbit pseudo 3D projection drawing method and storage medium, belongs to two-dimensional projection drawing technical field.The application places drawing plane outside molecule, and with molecular plane is α angle, the geometric structure and π orbit of the plane molecule are projected simultaneously, so as to make the plane conjugated molecular π orbit projection image with pseudo 3D effect.Compared with common two-dimensional orbit section drawing and linear projection drawing, the π orbit pseudo 3D projection drawing method of conjugated molecule of the application can greatly reasonably show the p-type atomic orbital contour combined into π molecular orbital and its relative position with geometric structure (i.e. atomic coordinates), which helps people understand the core concept in molecular orbital theory-atomic orbital linear combination to form molecular orbital, and can provide further support for related teaching or scientific research activities.

Description

Technical Field

[0001] This invention relates to the field of two-dimensional projection drawing technology, specifically to a method and storage medium for drawing pseudo-3D projection drawings of the π orbitals of conjugated molecules. Background Technology

[0002] Planar conjugated molecules such as chain alkenes, benzene molecules, and their homologues of fused-ring compounds constitute a class of the most common and widely applicable delocalized π-electron structure systems. Their structural and property characteristics are a core component of chemistry teaching and scientific research. Visualizing delocalized π molecular orbitals using computer software is one of the effective ways to understand the numerous optical and chemical reactivity properties of these systems.

[0003] Current methods for visualizing delocalized π molecular orbitals include plotting contour maps of the delocalized π orbitals of planar conjugated molecules. This method assumes the plane containing the conjugated molecule is... xy Plane, take z The plane with a = a0 / 3 is the tangent (highlighted in yellow). Then, using the Hückel molecular orbital (HMO) method, the wavefunctions of each π molecular orbital are obtained on this tangent, allowing the plotting of the π orbital contour lines. z = a0 / 3 is carbon atoms 2 pz At the extreme points of the orbit. This method maintains... z The value remains unchanged, only allowing x , y The corresponding changes in function values ​​across two dimensions offer advantages such as simplicity and ease of understanding. However, this approach of reducing dimensions by taking sectional planes cannot reveal the overall contour of the orbital. It's difficult to establish a direct connection between this approach and core concepts in molecular orbital theory (such as the linear combination of atomic orbitals to molecular orbitals (LCAO-MO)). Simply stretching it into a straight line... p Atomic orbital combinations cannot adequately demonstrate the true relationship between the molecular geometry and electronic structure. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method and storage medium for drawing pseudo-3D projection images of π orbitals of conjugated molecules. This invention can simultaneously project the geometric and electronic structures of conjugated molecules, thereby producing π orbital projection images of conjugated molecules with a pseudo-3D effect.

[0005] To achieve the above-mentioned objectives, the present invention provides the following technical solution: This invention provides a method for drawing pseudo-3D projection diagrams of π orbitals in conjugated molecules, comprising the following steps: Let a certain plane containing the conjugated molecules be... xy Plane, horizontal plane and xy The angle between the planes is α Any atom in a conjugated molecule relative to xy The spatial coordinates of the plane are ( x , y μ , z Let the drawing plane be perpendicular to the horizontal plane, and denote it as the drawing plane. xz' The plane coordinates of any point in the conjugated molecule projected onto the drawing plane in reduced dimension are ( x , z' ), z' =zcos( α )+y μ sin( α ); Obtain the atomic orbital combination coefficient of each atom in the conjugated molecule's π molecular orbital. c ik The atoms of the conjugated molecule are arranged according to their position coordinates. y i The values ​​are sorted from smallest to largest, and the wavefunctions of each molecular orbital satisfy... y μ = y i wave function at : Equation (1); In equation (1), For the i-th atom in the Cartesian coordinate system, 2 p z Orbital wave function c ik is the atomic orbital combination coefficient of the i-th atom in the k-th π molecular orbital, and n is the total number of atomic orbitals; Combined with dimensionality reduction projection onto the drawing plane xz' plane coordinates ( x , z' ),get y = y μ The π molecular orbital wave function at point on the plotting plane xz' projection function : Equation (2); Through the Cartesian coordinates of each atom in the conjugated molecule ( x i , y i, z i ),according to y i The values ​​are sorted from smallest to largest, and the coordinates of each atom are projected onto the drawing plane in sequence. xz' Based on equation (2), draw a pseudo 3D projection of the π orbitals of the conjugated molecule.

[0006] Preferably, the characteristic is that the α The range is 0~90°.

[0007] Preferably, it is characterized in that, The expression in the Cartesian coordinate system is: Equation (3); In equation (4), ( x i , y i , z i () represents the spatial coordinates of the i-th atom; a 0 represents the Bohr radius.

[0008] Preferably, the atomic orbital combination coefficient of each atom in the conjugated molecule's π molecular orbital is calculated. c ik The method includes the following steps: Using the Hückel molecular orbital method, the secular equations are obtained through linear variational methods. Solving these equations yields the atomic orbital combination coefficients for each atom in the conjugated π molecular orbitals. c ik .

[0009] Preferably, the atomic orbital combination coefficient of each atom in the conjugated π molecular orbital is... c ik Calculated using Gaussian commercial software.

[0010] Preferably, before plotting the molecular orbital projection diagrams according to equation (2), the structure of the conjugated molecule is optimized using the Gaussian16 program to obtain the optimized Cartesian coordinates of each atom. x i , y i , z i ).

[0011] Preferably, the process of drawing the pseudo 3D projection map of the π orbitals of the conjugated molecule is performed using the contour plotting function of Excel software, based on the value of the projection function corresponding to each cell coordinate, to draw the pseudo 3D projection map of the π orbitals of the conjugated molecule.

[0012] Preferably, when drawing the pseudo-3D projection diagram of the π orbitals of conjugated molecules, select π The molecular orbital threshold is 0.1~0.2.

[0013] Preferably, the conjugated molecules include monoplanar conjugated molecules or multiplanar conjugated molecules.

[0014] The present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned method for drawing pseudo 3D projection diagrams of π orbitals of conjugated molecules.

[0015] This invention provides a method for drawing a pseudo-3D projection map of the π orbitals of conjugated molecules. This invention places the drawing plane outside the conjugated molecule and perpendicular to the plane of the conjugated molecule. α Angle, obtain the plane coordinates of any point of the conjugated molecule projected onto the drawing plane in a reduced dimension, which are ( x , z' By calculating the atomic orbital combination coefficient of each atom in the conjugated molecule's π molecular orbital, c ik And determine that the wavefunctions of each molecular orbital satisfy y μ = y i wave function at The planar coordinates of the reduced-dimensional projection onto the drawing plane are ( x , z' ),get y = y μ The projection function of the molecular orbital wavefunction at a given location onto the plotting plane. Finally, the Cartesian coordinates of each atom in the conjugated molecule are used. x i , y i , z i ),according to y i The values ​​are sorted from smallest to largest, and the coordinates of each atom are projected onto the drawing plane in sequence. xz' According to the projection function Draw a pseudo-3D projection of the π orbitals of conjugated molecules.

[0016] This invention proposes the concept and formula for creating a pseudo-3D effect two-dimensional image by dimensionality reduction projection of planar nonlinear π molecular orbitals (wave functions). The drawing plane is placed outside the molecule at an angle α to the molecular plane. Then, the geometric structure of each delocalized orbital and the π orbitals are simultaneously projected onto the molecule's plane, thus producing a pseudo-3D image of the π orbitals of a planar conjugated molecule. Compared with common two-dimensional orbital cross-sections and linear projections, this invention's method for creating pseudo-3D projections of π orbitals in conjugated molecules has significant advantages. It can greatly and reasonably display the outlines of p-type atomic orbitals that combine to form π molecular orbitals and their relative positions to the geometric structure (i.e., atomic coordinates). This helps people understand the core concept in molecular orbital theory—the linear combination of atomic orbitals tomolecular orbitals (LCAO-MO)—and can provide further support for related teaching or research activities.

[0017] Furthermore, the method for drawing pseudo 3D projection maps of π orbitals of conjugated molecules provided by this invention is not only applicable to drawing pseudo 3D projection maps of π orbitals of single-plane conjugated molecules (such as butadiene and benzene rings), but also applicable to drawing pseudo 3D projection maps of π orbitals of multi-plane conjugated molecules (such as biphenyl), demonstrating good application effects and promotional value. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the dimension reduction projection coordinate transformation relationship; Figure 2 This is a schematic diagram of the plane projection of butadiene and benzene molecules; Figure 3 A flowchart for drawing projection diagrams of planar conjugated molecular π orbitals using Excel; Figure 4 A schematic diagram and pseudo-3D projection of the π molecular orbitals of butadiene; Figure 5 A schematic diagram and pseudo-3D projection of the π molecular orbitals of benzene; Figure 6 This is a schematic diagram and pseudo-3D projection of the π molecular orbital of biphenyl. Detailed Implementation

[0019] This invention provides a method for drawing pseudo-3D projection diagrams of π orbitals of conjugated molecules. In this invention, the conjugated molecules are preferably planar conjugated molecules, which preferably include monoplanar conjugated molecules and multiplanar conjugated molecules. The monoplanar conjugated molecules include, but are not limited to, one or more of butadiene, benzene, naphthalene, pyridine, furan, thiophene, and cyclopentadiene anions. The multiplanar conjugated molecules include, but are not limited to, one or more of biphenyl, bipyridine, bithiophene, trans-stilbene, and Möbius aromatic molecules.

[0020] In this invention, the method for drawing the pseudo 3D projection map of the π orbitals of the conjugated molecule includes the following steps: Let a certain plane containing the conjugated molecules be... xy Plane, horizontal plane and xy The angle between the planes is α Any point of the conjugated molecule relative to xy The spatial coordinates of the plane are ( x , y μ , z Let the drawing plane be perpendicular to the horizontal plane, and denote it as the drawing plane. xz' The plane coordinates of any point in the conjugated molecule projected onto the drawing plane in reduced dimension are ( x , z' ), z' =zcos( α )+y μ sin( α ); Obtain the atomic orbital combination coefficient of each atom in the conjugated molecule's π molecular orbital. c ik The atoms of the conjugated molecule are arranged according to their position coordinates. y i The values ​​are sorted from smallest to largest. Taking the carbon atom as an example, the molecular orbital wavefunctions satisfy... y μ = y i wave function at : Equation (1); In equation (1), For the i-th atom in the Cartesian coordinate system, 2 p z Orbital wave function c ik is the atomic orbital combination coefficient of the i-th atom in the k-th π molecular orbital, and n is the total number of atomic orbitals; The planar coordinates of the combined dimension-reduced projection onto the drawing plane are ( x , z' ),get y = y μ The projection function of the molecular orbital wavefunction at a given location onto the plotting plane. : Equation (2); Through the Cartesian coordinates of each atom in the conjugated molecule ( x i ,y i , z i ),according to y i The values ​​are sorted from smallest to largest, and the coordinates of each atom are projected onto the drawing plane in sequence. xz' Based on equation (2), draw a pseudo 3D projection of the π orbitals of the conjugated molecule.

[0021] like Figure 1 As shown, let the plane containing the conjugated molecules be... xy Plane, horizontal plane and xy The angle between the planes is α， Any point of a conjugated molecule relative to xy The spatial coordinates of the plane are ( x , y μ , z In this invention, the... α The angle is 0~90°, meaning it is applicable when there is any angle between the molecular plane and the horizontal plane. Preferably, the... α The angle is 30~60°.

[0022] This invention makes the drawing plane perpendicular to the horizontal plane, denoted as the drawing plane. xz' The plane coordinates of any point in the conjugated molecule projected onto the drawing plane in reduced dimension are ( x , z' ), combined Figure 1 It can be seen that, ( x , y μ The plane coordinates of the dimension-reduced projection onto the drawing plane are ( , 0) x y μ sin( α )),but( x , y μ , z The plane coordinates of the dimension-reduced projection onto the drawing plane are ( x , z' ), z' =zcos( α )+y μ sin( α ).

[0023] In this invention, the schematic diagrams of the planar projection of butadiene and benzene molecules are as follows: Figure 2 As shown.

[0024] Combining the structural characteristics of planar conjugated molecules, the 2 carbon atoms of each p z The orbital approximation is represented by a single-electron atom wavefunction, which is expressed in spherical polar coordinates as follows: Equation (4); In equation (4), r is the radial distance. It is the polar angle (the angle between the polar angle and the z-axis). It is the azimuth angle. a 0 represents the Bohr radius; The expression in the Cartesian coordinate system is: Equation (5); In equation (5), ( x i , y i , z i () represents the spatial coordinates of the i-th atom; a 0 represents the Bohr radius.

[0025] According to LCAO-MO theory, the first k indivual π Molecular orbitals can be represented by a linear combination of atomic orbital wave functions: Equation (6); In equation (6), c ik For the first k indivual π The first in the molecular orbital i The atomic orbital combination coefficient of an atom.

[0026] This invention calculates the atomic orbital combination coefficient of each atom in the π molecular orbital of the conjugated molecule. c ik Among them, the atomic orbital combination coefficient of each atom in the conjugated molecule's π molecular orbital is calculated. c ik The method preferably includes the following steps: Using the Hückel molecular orbital method (HMO), the combination coefficients are obtained by integrating the energy-average value. c i The first derivative is equal to 0, yielding the secular equations. Solving these equations yields the atomic orbital combination coefficients for each atom in the conjugated π molecular orbitals. c ik .

[0027] The Hückel molecular orbital (HMO) method is a semi-empirical quantum chemical calculation method that uses the principle of linear variational methods to solve for approximate solutions of the delocalized π orbital wavefunctions of conjugated molecules. This method assumes that π electrons move within a framework formed by the nucleus and σ bonds, approximately separating the σ and π bonds. The σ bond framework of the conjugated molecule remains unchanged, and the properties of the molecule are determined by the π electron states. The motion state of the i-th π electron is described by a function, and its Schrödinger equation is: Equation (7); In equation (7), The Hamiltonian operator represents the k-th π electron, which is the operator form corresponding to energy; Let E represent the wave function, where E is the value of the π electron in... Energy eigenvalues ​​that describe a state of motion.

[0028] Let the conjugated molecule be composed of n A conjugated system is composed of carbon atoms, with each carbon atom providing a... p The method of forming molecular orbitals by linear combination of atomic orbitals (LCAO-MO) can be used to determine the first atomic orbital. k indivual π Molecular orbitals Using the wavefunctions of each atomic orbital The linear combination is expressed as: Equation (8); In equation (8), Let be the atomic orbital wave function of the i-th atom (Equation (4)), cik be the atomic orbital combination coefficient of the i-th atom in the k-th π molecular orbital, and n be the total number of atomic orbitals.

[0029] According to the variational principle, any possible state of a molecule The corresponding average energy must be greater than or equal to the true ground state energy of the system. : Equation (9); In equation (9), Integral for the average energy value, This is the integral form of the energy average. It is the reciprocal of the normalization coefficient of the wave function.

[0030] Based on the linear variational method, the combination coefficients are obtained by integrating the energy-average value. The first derivative equals 0, yielding the secular equations: Equation (10); In equation (10), H uv Let the Coulomb integral (when u=v) represent the average energy of the electron in the i-th orbit; or let the exchange integral (when u≠v) represent the interaction energy between different orbits; E is the energy eigenvalue, c i S represents the atomic orbital combination coefficients (i=1-n). uv For the overlap integral, u / v = 1 - n.

[0031] The HMO method further assumes that the α integral of each carbon atom is the same, the β integral of each adjacent carbon atom is also the same, and the β integral and overlap integral S of non-adjacent atoms are both 0. Taking butadiene as an example, the simplified secular equations are: Equation (11); In equation (11), , For the first k indivual π The energy of the molecular orbital. The α integral / β integral is a known value. E k The energy of the molecular orbitals after combination (unknown) is determined by solving the above system of equations. x Then, substitute x Worth getting the corresponding E k .

[0032] In this invention, the atomic orbital combination coefficient of each atom in the conjugated molecular π molecular orbital is... c ik It can also be calculated using Gaussian commercial software.

[0033] Obtain the atomic orbital combination coefficients of each atom in the π molecular orbitals of the conjugated molecule. c ik Subsequently, this invention arranges the carbon atoms of the conjugated molecule according to their position coordinates. y i The values ​​are sorted from smallest to largest, and the wavefunctions of each molecular orbital satisfy... y μ = y i wave function at : Equation (1); In equation (1), For the i-th atom in the Cartesian coordinate system, 2 p z Orbital wave function c ik Let be the atomic orbital combination coefficient of the i-th atom in the k-th π molecular orbital, and n be the total number of atomic orbitals.

[0034] The expression in the Cartesian coordinate system is: Equation (3); In equation (4), (x i ,y i ,z i () represents the spatial coordinates of the i-th atom; a 0 represents the Bohr radius.

[0035] The planar coordinates of the combined dimension-reduced projection onto the drawing plane are ( x , z' ),get y = y μ The projection function of the molecular orbital wavefunction at a given location onto the plotting plane. : Equation (2); Through the Cartesian coordinates of each atom in the conjugated molecule ( x i , y i , z i ),according to y i The values ​​are sorted from smallest to largest, and the coordinates of each atom are projected onto the drawing plane in sequence. xz' A pseudo-3D projection diagram of the π orbitals of the conjugated molecule is drawn according to equation (2). In this invention, the Cartesian coordinates of each atom in the conjugated molecule are ( x i , y i , z i That is, any point of the conjugated molecule relative to... xy The spatial coordinates of the plane are ( x , y μ , z ).

[0036] In this invention, before drawing the molecular orbital projection diagrams according to equation (2), it is preferable to further optimize the structure of the conjugated molecules using the Gaussian16 program to obtain the optimized Cartesian coordinates of each atom. x i , y i , z iThis invention preferably uses the Gaussian16 program to optimize the structure of conjugated molecules at the B3LYP / 6-31G(d) level. Through this structural optimization, this invention can provide a reasonable molecular geometry.

[0037] The present invention preferably utilizes the visualization processing function of data processing tools to perform the drawing. Furthermore, the present invention preferably uses the contour plotting function of Excel software to draw a pseudo-3D projection map of the π orbitals of conjugated molecules based on the value of the projection function corresponding to the coordinates of each cell. The basic principle of using Excel software to draw molecular orbital projection contour maps is as follows: each cell in Excel is regarded as an evenly divided grid point on the drawing plane, and the value of the point corresponding to each cell is calculated by editing the Excel formula, that is, the value calculated by formula (2). π The value of the projection of the molecular orbital onto the drawing plane at that cell position, and then according to... Figure 3 The process shown uses Excel's contour plotting function to draw the projection map.

[0038] Taking butadiene as an example, its position coordinates in the projection plane x The range is from -2.20 Å to 2.20 Å. y The range is -1.06 Å to 1.06 Å. Taking a grid interval of 0.02 Å, the coordinates of the point in the two-dimensional plane corresponding to the cell in the ROW() row and COLUMN() column are ( x , z ') can be expressed as (-2.22+0.02 COLUMN(), 1.08-0.02 Substituting into the projection function (2), any... y = y μ Contour map of projection functions on a plane.

[0039] To avoid occlusion between atomic orbitals, a selection must be made when drawing the projection diagram. π Molecular orbital thresholding. The choice of threshold directly affects the image rendering effect. If the selected threshold is too large, the drawn image will... π Molecular orbital images are small and cannot accurately reflect the spatial distribution characteristics of orbitals; if the selected threshold is too small, then... y μ Smaller atomic orbitals will affect y μLarger orbital images have excessive occlusion. When plotting using Excel, the IF() function can be used to skip points on each plane where the wavefunction value is less than a threshold. Here, the threshold is preferably 0.1~0.2, more preferably 0.15. Combining the syntax rules of the IF() function (IF(condition, output if condition is met, output if condition is not met)), ... Absolute value of ABS ( Cells with a value less than 0.15 are assigned a value of 0; otherwise, they are assigned a value of 0. The actual calculated value is displayed. The IF function expression is: Equation (12).

[0040] Before plotting the pseudo-3D projection of the π orbitals of conjugated molecules, this invention preferably sets the colors. As a specific embodiment of this invention, the color setting method is as follows: the cell with the smallest wavefunction value (-1.6900) is set to blue (RGB values ​​0, 0, 255), and the cell with the largest wavefunction value (1.6900) is set to red (RGB values ​​255, 0, 0), with a color step size of 0.0325. From -1.6900 to 0.0000, the B value of RGB remains constant at 255. For each step increase, R and G are each increased by 5. When the wavefunction value range is -0.0325 to 0.0000, the RGB values ​​are 255, 255, 255, i.e., white. From 1.6900 to 0.0000, the R value of RGB remains constant at 255. For each step decrease, the G and B values ​​are each increased by 5. When the wavefunction value ranges from 0.0000 to 0.0325, the RGB value is 255, 255, 255, which is white. This color setting method allows for the generation of a projection image of the π molecular orbital and avoids points in the image that do not conform to the projection range.

[0041] The present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it implements the above-described method for drawing pseudo 3D projection diagrams of π orbitals of conjugated molecules.

[0042] The following detailed description, in conjunction with embodiments, illustrates the method for drawing pseudo-3D projection diagrams of π orbitals of conjugated molecules and the storage medium provided by the present invention. However, these descriptions should not be construed as limiting the scope of protection of the present invention.

[0043] Example 1 Pseudo 3D projection of butadiene's π orbitals: Let the plane containing the conjugated molecule butadiene be... xy Plane, horizontal plane and xy The included angle between the planes is α = 30°.

[0044] The structure of the conjugated molecule was optimized using the Gaussian16 program. π Molecular orbitals Ψ Taking 1 as an example, the optimized Cartesian coordinates of each carbon atom are (1.55, -0.50, 0.00), (0.74, 0.56, 0.00), (-0.74, 0.56, 0.00), and (-1.55, -0.50, 0.00), respectively. The planar coordinates of the reduced-dimensional projection onto the drawing plane are (1.55, -0.25), (0.74, 0.28), (-0.74, 0.28), and (-1.55, -0.25), respectively.

[0045] Based on the HMO method, the atomic orbital combination coefficients in each π molecular orbital are calculated. The combination coefficient matrix of the wavefunctions of each π molecular orbital in butadiene is as follows: Substituting the obtained combination coefficients and formula (5) into formula (6), we obtain the wave function expressions for each π molecular orbital.

[0046] Equation (5); Equation (6); Finally, a pseudo-3D projection diagram of the π orbitals of the conjugated molecule is drawn according to equation (2): Equation (2).

[0047] A schematic diagram and pseudo-3D projection of the π molecular orbitals of butadiene are shown below. Figure 4 As shown, Figure 4 In the image, (a) shows a schematic diagram of the LCAO-MO orbit and its wave function expression, and (b) shows a pseudo-3D projection plot drawn using Excel.

[0048] It can be seen intuitively that butadiene π Molecular orbitals Ψ 1– Ψ The number of nodal faces for the 4-membered molecule are 0, 1, 2, and 3. Regarding orbital energies, they follow the general rule that the more nodal faces, the higher the molecular orbital energy. (Butadiene molecule...) π The track projection map presents a pseudo-3D effect, offering a better sense of depth and providing a more intuitive display. π Distribution characteristics of molecular orbitals in three-dimensional space.

[0049] Example 2 Pseudo 3D projection of benzene's π orbitals: Let the plane containing the conjugated benzene molecule be denoted as . xy Plane, horizontal plane and xy The included angle between the planes is α = 30°.

[0050] The structure of the conjugated molecule was optimized using the Gaussian16 program. π Molecular orbitals Ψ Taking 1 as an example, the optimized Cartesian coordinates of each carbon atom are (-1.40, 0.00, 0.00), (-0.70, -1.21, 0.00), (0.70, -1.21, 0.00), (1.40, 0.00, 0.00), (0.70, 1.21, 0.00), and (-0.70, 1.21, 0.00). The planar coordinates projected onto the drawing plane after dimensionality reduction are (-1.40, 0.00), (-0.70, -0.60), (0.70, -0.60), (1.40, 0.00), (0.70, 0.60), and (-0.70, 0.60).

[0051] Based on the HMO method, the atomic orbital combination coefficients in each π molecular orbital are calculated. The combination coefficient matrix of the wavefunctions of each π molecular orbital in the benzene molecule is as follows: Substituting the obtained combination coefficients and formula (5) into formula (6), we obtain the wave function expressions for each π molecular orbital.

[0052] Equation (5); Equation (6); Finally, a pseudo-3D projection diagram of the π orbitals of the conjugated molecule is drawn according to equation (2): Equation (2).

[0053] A schematic diagram and pseudo-3D projection of the π molecular orbitals of benzene are shown below. Figure 5 As shown, Figure 5 In the image, (a) shows a schematic diagram of the LCAO-MO orbit and its wave function expression, and (b) shows a pseudo-3D projection plot drawn using Excel.

[0054] It can be seen intuitively that benzene π Molecular orbitals Ψ 1– Ψ The nodal numbers for 6 are 0, 1, 1, 2, 2, and 3. Regarding orbital energy, Ψ 2 and Ψ 3. Degeneracy Ψ 4 and Ψ 5. The degeneracy is such that the number of nodal planes of the degenerate orbitals is equal, which conforms to the general rule that the more nodal planes there are, the higher the molecular orbital energy. πThe pseudo-3D effect of the orbital projection diagram provides a stronger sense of depth and more intuitively demonstrates the contribution of atomic orbitals to molecular orbitals, helping students deepen their understanding of the LCAO-MO method.

[0055] Example 3 Pseudo 3D projection of the π orbitals of biphenyl: Let the plane containing the conjugated benzene molecule be denoted as . xy Plane, horizontal plane and xy The included angle between the planes is α = 30°.

[0056] The structure of the conjugated molecule was optimized using the Gaussian16 program. π Molecular orbitals Ψ Taking 1 as an example, the optimized Cartesian coordinates of each carbon atom are (2.86, 1.14, -0.396), (1.47, 1.14, -0.397), (0.743, 0.00, 0.00), (1.47, -1.14, 0.397), (2.86, -1.14, 0.396), (3.56, 0.00, 0.00), (-2.86, -1.14, -0.396), (-1.47, -1.14, -0.397), (-0.743, 0.00, 0.00), (-1.47, 1.14, 0.397), (-2.86, 1.14, 0.396), (-3.56, 0.00, The coordinates of the reduced-dimensional projection onto the drawing plane are (2.86, 0.227), (1.47, 0.226), (0.743, 0.00), (1.47, -0.226), (2.86, -0.227), (3.56, 0.00), (-2.86, -0.913), (-1.47, -0.914), (-0.743, 0.00), (-1.47, 0.914), (-2.86, 0.913), and (-3.56, 0.00).

[0057] Based on the HMO method, the atomic orbital combination coefficients in each π molecular orbital are calculated. The combination coefficient matrix of the wavefunctions of each π molecular orbital in the biphenyl molecule is as follows: Substituting the obtained combination coefficients and formula (5) into formula (6), we obtain the wave function expressions for each π molecular orbital.

[0058] Equation (5); Equation (6); Finally, a pseudo-3D projection diagram of the π orbitals of the conjugated molecule is drawn according to equation (2): Equation (2).

[0059] Schematic diagram and pseudo-3D projection of the π molecular orbitals of biphenyl are shown below. Figure 6 As shown, Figure 6 In the image, (a) shows a schematic diagram of the LCAO-MO orbit and its wavefunction expression, and (b) shows a pseudo-3D projection plot drawn using Excel. Regarding orbital energy, Ψ 4 and Ψ 5. Degeneracy Ψ 8 and Ψ 9. Degeneracy. π The pseudo-3D effect of the orbital projection diagram has a stronger sense of three-dimensionality. It not only intuitively shows the spatial distribution of molecular orbitals, but also shows the dihedral angle between the two benzene rings in the biphenyl molecule.

[0060] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for drawing a pseudo-3D projection diagram of the π orbitals of a conjugated molecule, characterized in that, Includes the following steps: set up The plane containing the conjugated molecules is xy Plane, horizontal plane and xy The angle between the planes is α Any atom in a conjugated molecule relative to xy The spatial coordinates of the plane are ( x , y μ , z Let the drawing plane be perpendicular to the horizontal plane, and denote it as the drawing plane. xz' The plane coordinates of any point in the conjugated molecule projected onto the drawing plane in reduced dimension are ( x , z' ), z' =zcos( α )+y μ sin( α ); Obtain the atomic orbital combination coefficients of each atom in the π molecular orbitals of the conjugated molecule. c ik The atoms of the conjugated molecule are arranged according to their position coordinates. y i The values ​​are sorted from smallest to largest, and the wavefunctions of each molecular orbital satisfy... y μ = y i wave function at : Equation (1); In equation (1), For the i-th atom in the Cartesian coordinate system, 2 p z Orbital wave function, c ik is the atomic orbital combination coefficient of the i-th atom in the k-th π molecular orbital, and n is the total number of atomic orbitals; Combined with dimensionality reduction projection onto the drawing plane xz' plane coordinates ( x , z' ),get y = y μ The π molecular orbital wavefunction at the location is on the plotting plane xz' projection function : Equation (2); Through the Cartesian coordinates of each atom in the conjugated molecule ( x i , y i , z i ),according to y i The values ​​are sorted from smallest to largest, and the coordinates of each atom are projected onto the drawing plane in sequence. xz' Based on equation (2), draw a pseudo 3D projection of the π orbitals of the conjugated molecule.

2. The drawing method according to claim 1, characterized in that, The α The range is 0~90°.

3. The drawing method according to claim 1, characterized in that, The expression in the Cartesian coordinate system is: Equation (3); In equation (4), ( x i , y i , z i () represents the spatial coordinates of the i-th atom; a 0 represents the Bohr radius.

4. The drawing method according to claim 1, characterized in that, Calculate the atomic orbital combination coefficient of each atom in the conjugated molecule's π molecular orbital. c ik The method includes the following steps: Using the Hückel molecular orbital method, the secular equations are obtained through linear variational methods. Solving these equations yields the atomic orbital combination coefficients for each atom in the conjugated π molecular orbitals. c ik .

5. The drawing method according to claim 1, characterized in that, The atomic orbital combination coefficient of each atom in the conjugated molecular π molecular orbital c ik Calculated using Gaussian commercial software.

6. The drawing method according to claim 1, characterized in that, Before plotting the molecular orbital projections according to equation (2), the structure of the conjugated molecule is optimized using the Gaussian16 program to obtain the optimized Cartesian coordinates of each atom. x i , y i , z i ).

7. The drawing method according to claim 1, characterized in that, The method of drawing the pseudo 3D projection map of the π orbitals of the conjugated molecule is to use the contour plotting function of Excel software, based on the value of the projection function corresponding to each cell coordinate, to draw the pseudo 3D projection map of the π orbitals of the conjugated molecule.

8. The drawing method according to claim 1 or 7, characterized in that, When drawing the pseudo 3D projection diagram of the π orbitals of conjugated molecules, select π The molecular orbital threshold is 0.1~0.

2.

9. The drawing method according to claim 1, characterized in that, The conjugated molecules include monoplanar conjugated molecules or multiplanar conjugated molecules.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the method for drawing pseudo-3D projection diagrams of the π orbitals of conjugated molecules as described in any one of claims 1 to 9.

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