Atomic Electron Orbitals in VR

VR, short for Virtual Reality, is a computer simulation system. Through the simulation of the real world, VR technology created a new interactive system, integrating the latest developments in computer simulation, graphics, display, sensing, and artificial intelligence. The concept of VR was first originated in the United States in the 1950s, and the main working principle is to combine the use of computers and sensors to generate a simulating and interactive environment. It is a multi-source information fusion that interacting three-dimensional visual dynamics and physical behavior system simulation, so that the users would be immersed in the environment and feel a sense of immersion. By using equipments such as head display instruments and headphones, VR blocks the connection between the human sense and the real world, thus to create a brand-new, virtual world through the real-time rendering of the screen.^[7-11]

There are many advantages to apply VR technology to the field of education, such as^[10]：

• The characteristic of VR is to offer a sense of immersive, so people could immerse in not only a virtual space, but also have a large imaginative space with more interactions than mere thinking, so we could break the constraints of time, space and resources in the classroom when demonstrating.The traditional way of teaching often use words, pictures and sounds to demonstrate some abstract concepts or pictures that are hard to imagine, but these forms sometimes fail to provide a concrete display effects. For example, ranging from the galaxies and universe to the atoms and electrons, the traditional forms usually only provide two-dimensional images that are projections of three-dimensional objects. Therefore, students with poor spatial imaginations may find it somewhat difficult to understand. However, VR can play an important role in this regard and create real scenarios for immersive learning and understanding. For example, in this experiment, an atomic electron orbital model is constructed so that users can walk, watch, and manipulate around a huge electronic cloud in VR, as if becoming an ant-man and entering the atomic world.
• Through the use of VR devices in the classroom, students could be entertained through education. This new way of teaching and learning combines various ways of learning like game-based learning, situational learning, collaborative learning, and online education, which could effectively solve many previously unsolved education problems.
• Some experiments could have certain risk, and using VR technology could greatly reduce such risks, and at the same time, still train students on their practical experiemental abilities. However, in order to truly experience the various conditions that may occur in experiments, it is still necessary to combine the real-world experiments with those in VR.
  

Theoretic formula^[1,3-6]

• Two traversal methods：
  • By Cartesian coordinates
    
    
    
  • By Spherical coordinates
    
    
    
• Three methods to show electron density：
  • The size of spheres：For spheres from the inside to the outside, if the probability density of electron distribution are the same, then they are the same size; otherwise the radius is multiplied by the probability density.
  • The transparency of spheres：From completely opaque to completely transparent represents the probability density from maximum to minimum.
  • The color of spheres：The color of spheres range from red to blue (as shown below), indicating the probability density range from maximum to minimum
    
    
    
• Difficulty：
  • For different n, l, m models, the probability density has a normalization coefficient, so that the probability density of the models with larger diffusion range is smaller at each position, and the less obvious the observation is.
    
    Solution：
    The constant coefficient from the theoretical value is ignored when the radius is multiplied by the probability density.
    
    
  • For each n, l, m model, due to the effect of exponential relationship, the size of the sphere changes too violently from centre to edge, therefore sometimes it happens that the central sphere is so big that covers large area but spheres near the edge is still too small to observe.
    
    Solution：
    The probability density function should be alleviated by some functions with positive relationships, so that the relative relationship of size of spheres would not be changed. In this experiment, this alleviated function was chosen to be logarithmic function and root function.
    
    
• Program presentation：
  • Define the tranfer function of spherical coorinates and Cartesian coordinates
    
    
    
  • Define the probability density distribution function (shown in parst)
    
    
    
  • Program initialization
    
    where CreateMatrix() paints each sphere, n,l,m are inputs, representing n, l, m in wave function of Hydrogen atom, respectively, “dimension” choosing from 2-dimension to 3-dimension.
    
    
  • Traverse and draw every sphere, calculate probability density, modify the size, color or transparency of each sphere (pictures below show the case of modifying the size as an example)
    
    

• VR head device instruments, handles, localizer etc：Vive-VR-C
• Computer
  
  
  

Click here to look at the demo video.

Fig. 1-2：Traversing 2-dimension and 3-dimension images by Cartesian coordinates；Fig. 3-4：Traversing 2-dimension and 3-dimension images by spherical coordinates；Fig. 5：Traversing by spherical coordinates and using color to represent density of electrons.

There are concepts like atomic orbits and orbital radius in classic models, so there is no sphere (meaning no electron) outside the Bohr Radius.

In quantum model, electrons are replaced by electron cloud according to probability density, which could diffuse to the full space, so compared to classic model, the electrons that can be seen cover a larger space.

Fig. 1-2：Use Mathematica to draw theoretic 2-dimensional and 3-dimensional images; Fig. 3-4：Draw 2-dimensional and 3-dimensional images by spherical coordinates; Fig. 5：Draw spheres by spherical coordinates and use color to represent probability density.

(Under construction)

• Optimization of existing results
• Display probability density by method of patch slice
• Add manipulation interaction between user and the model
• Try to show multiple-electron atoms, covalent bonds, etc.
  

• [1] Griffith. Introduction to quantum mechanics (second edition). Beijing: Machinery Industry Press, 2006.3.
• [2] Pan Yi, Yide Xie. VR development combat. Electronics Industry Press, 2017.1.
• [3] Zhiheng Lu, YiYan Fei, Li Xuechun. The computer-aided representation of the visualization of quantum mechanics - the three-dimensional reconstruction of the electronic cloud, shell structure and covalent bonds. Physical education, 2001,30 (4).
• [4] Jianping Gong. Probability distribution of hydrogen atoms. Journal of Jinzhong University, 2015.6, 32(3).
• [5] Jinhai Li, Hengzhong Fang, Ziliang Li. Analysis of density distribution of electron clouds in hydrogen atoms. College Physics, 2004.3, 23(3).
• [6] Yu Zhang, Qixiang Tang. Comparative study on the probability density distribution of hydrogen atom and hydrogen-like atom. Journal of Wenshan college, 2017.122, 30 (6).
• [7] Mingming Zhao. The development status, application prospects and countermeasures of VR technology in China. Audiovisual, 2018(01):209-210.
• [8] Hongbo Gao. Virtual reality (VR) industry development status, problems and trends in China. Modern communication (Journal of Communication University of China), 2017,39 (02): 8-12.
• [9] Lulu Cai. Research on the current situation and development trend of VR virtual reality in China. Modern Communication, 2017(16): 197.
• [10] Jing Fang. Research on the current situation of VR education in China. Education in Times, 2016(21):200.
• [11] Jiajie Liu. VR technology development status and future trend. China new communications, 2016,18 (10): 81.
  

• Thanks for support from Professor Jinglin Lv and Hanfei Shen.
• Thanks for guidance of Professor Xinyuan Wei and Wenkai Huang.
• Thanks for help from projects of Yerong Xu.
• Thanks to software and hardware platform of VR and Steam.
• Thanks to myself tried my best to learn the language of C# and the tool of Unity.
  

Other VR Programs

VR program of Atomic Electron Orbitals in Chinese

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