ABSTRACT
Solar energy is one of the most promising renewable energies. The understanding of the process of photosynthesis can provide inspiration for new mechanisms of harvesting sunlight. In this thesis the initial steps in photosynthesis, light absorption and energy delivery by antenna systems, have been researched for the lhca4 complex in the photosystem 1 (PSI). Two dierent views of light harvesting complexes in PSI have been put together: a crystal structure of the PSI, providing spatial information, and spectroscopic data providing the energies of the system and information about interaction with light. From the crystal structure data it was possible to calculate the interaction between the 15 pigments in the lhca4 complex. The interaction between the pigments, coupling, leads to delocalization of the excitation. This means that the excitation is not localized on one pigment, but is distributed between several of the 15 pigments. From the theoretical model of the spectroscopical data the pigment transition energies have been obtained. With the coupling between the pigments and their energies, a Hamiltonian has been constructed. By diagonalizing the Hamiltonian, the exciton states have been calculated, giving us insight into the delocalization and energy of the excitation. Based on this, the excitation energy landscape of the lhca4 complex is created and visualized within the crystal structure of PSI. Three dierent states for the delocalized excitation energy landscape have been calculated: a state which includes all available excited states, a state in thermodynamic equilibrium and a state which results from excitation by sunlight. These dierent states are analyzed based on the created images, with a focus on the location of the low and high energy excited states in the lhca4 complex. This leads to the conclusion that the excitation can arise with almost equal chance on every pigment after the complex is hit by sunlight and will move towards the inner side of the PSI, favoring the lhca1, lhca2 and core sides when reaching thermal equilibrium. For further research it would be interesting to include the delocalized excitation energy landscape of the other lhca complexes, to get a wider view of how the energy is transferred.
CONTENTS Abstract 2 Introduction 4 Theory 5 Photosynthesis 5 VMD molecule viewer 8
The excitation probability distribution 8
The energy probability distribution 9
Dierent states 9
Results 10
Equally distributed 10
Boltzmann equilibrium distribution 12
Light distribution 14 Conclusion 16 Discussion 16 References 18 Appendix 19 Python scripts 23
INTRODUCTION
We are living in an age where renewable energies are getting more and more important; we are running out of oil and climate change is starting to take eect on our daily lives. One of the most promising renewable energies comes directly from the sun, captured by solar panels. The understanding of the process of photosynthesis can inspire to create new mechanisms for harvesting sunlight. That is why much more research is necessary. Natural photosynthesis is more e cient than current solar panels in the process of excitation energy transfer and charge separation, as it can reach a quantum e ciency of nearly 100 percent. Photosynthesis is the process of capturing light, consisting of photons, and transferring its energy via a biochemical reaction. The main super complexes that are responsible for this process are photosystems 1 and 2 and work together. The photosystem 1 consists of a few important complexes; lhca4, lhca1, lhca2, lhca3 and the core complex. These lhca complexes are responsible for capturing light and transferring it to the core complex, which includes the reaction center. The reaction center is responsible for actually turning the energy into a usable charge separation. The chlorophylls in the lhca complexes act as light harvesting systems, also called pigments. It is not clear how the energy transfers in and between lhcas, that is why this will be researched in this paper. How does the energy within the lhca4 complex transfer, based on an image of the energy landscape of the lhca4 complex with respect to the delocalization of the excitation and energy of the pigments? In earlier research the energies of the lhca4 complex have been calculated, but no conclusions have been drawn regarding the route for the energy transfer both within the lhca4 complex and in the context of the whole PSI, neither has there been any follow up research with the calculated energies yet. Also, nobody has tried to combine the experimental and theoretical results from crystallography and spectroscopy into a uni ed picture. This is the only way to comprehend the energy transfer route in the photosystem 1.
THEORY Photosynthesis
The most common form of photosynthesis involves chlorophyll pigments and operates using light-driven electron transfer processes (Blankenship, 2014). This is the kind of photosynthesis that is done by plants and is what we are interested in. The four phases of photosynthesis are light absorption and energy delivery by antenna systems, primary electron transfer in reaction centers, energy stabilization by secondary process and synthesis and export of stable products. In this paper the focus is on the rst phase, the so-called primary process of photosynthesis. In 2014, Blankenship wrote the following in his book Molecular mechanisms of photosynthesis: for light energy to be stored by photosynthesis, it must rst be absorbed by one of the pigments associated with the photosynthetic apparatus. Photon absorption creates and excited state that eventually leads to charge separation in the reaction center. Not every pigment carries out photo chemistry; the vast majority function as antennas, collecting light and delivering energy to the reaction center where the photo chemistry takes place. The antenna system is conceptually similar to a satellite dish, collecting energy and concentrating it in a receiver, where a signal is converted into a dierent form. The excited state, after absorbing a photon, is called an excitation or an exciton; a pigment absorbs a photon and ends up in an excited state; it carries the excitation. The exciton will travel from the excited pigment to another pigment nearby that is in the ground state, exciting that pigment. Eventually, by moving between pigments in a wavelike motion, due to delocalization on the pigments, the exciton reaches the reaction center. This is where the energy is stabilized into a useful form by charge separation. This process of capturing light and transferring the light as energy to the reaction center takes place in a pigment-protein complex that is called a photosystem. In gure 1 the photosystem 1 is shown, the lhca groups are marked, they are responsible for the harvesting of light and transferring the energy to the reaction center (Blankenship, 2014). In this paper the focus will only be on the lhca4 complex since critical information is not available for the lhca2, lhca3 and lhca1 complexes to do the calculations that are necessary for calculating the delocalized energy landscape.
Figure 1. Photosystem 1.
The lhca4 consists of 15 chlorophylls. These chlorophylls have a weak dipole-dipole interaction with each other, which is called coupling. This coupling causes delocalization of the pigments (Amerongen, 2000). This delocalization of the excitation over the pigment means that it is unsure where the excitation will be, it can be partially on every pigment at the same time. An excitonic quantum state arises. To calculate the exciton, the energies and coupling have to be known. The energies of these pigments have been calculated by Novoderezhkin et al. in 2016. The coupling between two excitons is basically just a dipole dipole interaction (Amerongen, 2000). This interaction is dependent on the coordinates of the pigments as can be seen in equation 2. These coordinates are found in a molecule database called PDB, Protein Data Bank (Wwpdb.org, 2017). The code that is used in this database for the photosystem 1 is 4xk8. (Qin et al., 2017) The data in the PDB come from the crystal structure, recently obtained by X-ray
crystallography.
Figure 2. Chlorophyll A. The tail has been cut o in this picture because it does not in uence the transition dipole moment that is relevant for equation 1. The left nitrogen is Nd, the nitrogen to the right is Nb.
To understand what determines the energy transfer in the lhca4 complex, the exciton concept should be worked out. Instead of having a system with a 100 percent certainty of a pigment being excited, all the pigments have a probability of being excited and the total sum of this chance is 100 percent. This is due to the fact that the sunlight hits the super complex as a whole, not just one pigment. Since the wavelength of the sunlight is much larger than the physical size of the complex, the sunlight hits all the pigments at the same time. Thanks to this, the situation should be analyzed energetically instead of spatially. The chance of being excited now depends on the eigenenergies of the pigments and the coupling between them. It is precisely this delocalized nature of the exciton which makes it challenging to visualize it in the light harvesting complex structure.
Now that every pigment is hit by the sunlight and just one pigment can be excited at the time, which pigment will actually get excited? Imagine a system of only two, identical, pigments that is hit by sunlight. The formula for this state is: |Ψ >= (|e1>+|e√ 2>)
2 , where |e1>and |e2>are the energy eigenstates of pigment 1 and pigment 2. Both
pigments have a 50 percent chance of being excited because they are identical in energy and share the same coupling. Now imagine having a system of 15 non identical pigments that is hit by sunlight. The description for this state is a lot more complicated than for the case with 2 pigments. The non-identical pigments do not have the same energies and have dierent couplings. To calculate the exciton exactly, the coupling has to be calculated and the energies are known, see table 1.
Pigment 601a 602a 603a 604a 605a 606b 607b 608b Energy 15400 15205 15039 15453 15750 15856 15793 15731
609a 610a 611a 612a 613a 614a 615a 15232 15345 15223 15190 15068 15190 15800 Table I. Energies of pigments in lhca4.The bold numbers are calculated by Novoderezhkin et al (2016) in their paper by reproducing spectroscopic measurements. The rest of the energies are estimated. After an analysis of how the pigments lie in the protein bath and what the actual energies are, which were already calculated, it was possible to compare the 601a,605a and 615a with the other pigments and estimate their energies. Higher energies correspond to less protein nearby and lower energies correspond to more protein nearby.
When a pigment gets excited, its electron density changes, this causes a transition dipole moment from the Nd to the Nb (see gure 2). This is described by formula 1, where N is the coordinate vector of the nitrogen atoms in the pigment. The coupling is induced by this moment, as can been seen in formula 2, where r is the distance between the magnesium atoms of two dierent pigments. In this formula, f=835000, this is the screening factor. It is a factor that is determined by the medium where the interacting particles are in, in this case this screening factor is for the protein environment of the pigments.
D = 4 Nb− Na p(Nb− Na)2 (1) J = f (|rm,n|2(Dm· Dn)− 3( Dm·rm,n |rm,n| )( Dn·rm,n |rm,n| )) 16|rm,n|3 (2)
The nitrogen and magnesium coordinates are found by loading 4xk8 (code for photosystem 1) in the Protein Data Bank (Wwpdb.org, 2017). Now the couplings and energies of the pigments are known, the excitons can be calculated. Combining the energies and the calculated coupling, it is possible to construct a Hamiltonian. The formula for the Hamiltonian is complicated if written in the standard form, consisting of T, the kinetic energy part and V, the potential energy part. The excitation relies on electrons, so an electric Hamiltonian is used. The electronic Hamiltonian is found in equation 3. ˆ H =X e P e2 2me + Ve (3)
The assumption is made that the pigments can be described as two-level systems, they can either be in the ground state or in the excited state. One can construct the electronic Hamiltonian (equation 3) in matrix form easily by writing it in the basis of the pigments. The eigenenergy states are de ned in equation 4.
ˆ H|en>= en|en > (4) ˆ H =X n |en> en< en| + X n6=m |en> Jnm< en| (5)
On the diagonal of the Hamiltonian are the eigenenergies of the pigments. The rest of the numbers in the matrix are the coupling between the pigments. On the top and left side of the matrix in equation 3, the pigments are indicated.
E e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14 e15 e1 15400 −45.18 11.56 2.76 2.30 3.26 −2.26 −4.93 1.29 −52.08 3.86 5.73 −9.78 1.02 0.34 e2 −45.18 15205 34.05 6.87 6.21 6.57 −9.26 −27.33 −10.66 8.81 17.48 −5.69 2.46 1.88 0.95 e3 11.56 34.05 15039 −5.70 −13.14 1.38 8.42 176.92 14.82 −4.35 −1.7 2.67 −7.07 −11.49 −2.24 e4 2.76 6.87 −5.70 15453 84.95 29.16 −1.05 −7.70 −5.58 −3.28 1.94 0.62 −3.62 4.75 1.80 e5 2.30 6.21 −13.14 84.95 15750 60.87 −3.31 −4.08 −3.41 −2.91 3.36 1.35 −2.28 7.50 −15.2 e6 3.26 6.57 1.38 29.16 60.87 15856 −4.54 −13.53 0.72 −3.12 3.03 0.62 −3.69 2.32 −0.97 e7 −2.26 −9.26 8.42 −1.05 −3.31 −4.54 15793 53.46 51.92 4.49 −0.61 −2.06 1.52 −1.32 24.07 e8 −4.93 −27.33 176.92 −7.7 −4.08 −13.53 53.46 15731 2.87 5.72 −2.89 −3.37 2.94 38.59 8.14 e9 1.29 −10.66 14.82 −5.58 −3.41 0.72 51.92 2.87 15232 −26.23 16.79 7.36 −2.29 2.43 7.41 e10 −52.08 8.81 −4.35 −3.28 −2.91 −3.12 4.49 5.72 −26.23 15345 134.65 −9.82 5.76 −0.51 0.72 e11 3.86 17.48 −1.70 1.94 3.36 3.03 −0.61 −2.89 16.79 134.65 15223 −2.82 2.15 1.35 0.31 e12 5.73 −5.69 2.67 0.62 1.35 0.62 −2.06 −3.37 7.36 −9.82 −2.82 15190 −79.10 −1.08 −0.80 e13 −9.78 2.46 −7.07 −3.62 −2.28 −3.69 1.52 2.94 −2.29 5.76 2.15 −79.10 15068 −0.81 −0.06 e14 1.02 1.88 −11.49 4.75 7.50 2.32 −1.32 38.59 2.43 −0.51 1.35 −1.08 −0.81 15190 −1.66 e15 0.34 0.95 −2.24 1.80 −1.52 −0.97 24.07 8.14 7.41 0.72 0.31 −0.80 −0.06 −1.66 15800 (6) This Hamiltonian can be diagonalized to nd the eigenvalues and eigenvectors, giving us the exciton states, see equation 7. The entries in this matrix are the coe cients, cn, of the pigments, where|cn|2is the chance on the nth
pigment being excited. When the coe cients are calculated, the exciton can be constructed by using the following equation:
|Ψj>=
X
n
. E Ψ1 Ψ2 Ψ3 Ψ4 Ψ5 Ψ6 Ψ7 Ψ8 Ψ9 Ψ10 Ψ11 Ψ12 Ψ13 Ψ14 Ψ15 e1 −0.01 0 0 −0 0 0.05 −0.02 0.6 −0.76 −0.01 0.13 0.08 0.03 −0.01 −0.16 e2 −0.02 0.02 0.02 −0.01 −0.01 0.19 −0.03 −0.15 0.13 0.03 0.17 0.06 0.07 −0.07 −0.94 e3 0.05 −0.11 −0.09 0.02 0.17 −0.94 0.1 0.01 −0 0 0.07 −0.04 0.02 0.1 −0.2 e4 −0.14 −0.03 0 −0.21 0 −0.01 −0.01 0.04 0.01 0.97 0.01 −0.02 0.01 0.02 0.02 e5 −0.44 −0.12 −0.02 −0.85 0.06 −0.02 0 −0.01 0 −0.25 0.01 −0 0 0.01 0 e6 −0.83 −0.26 −0.06 0.48 0.03 0 −0 −0.01 0 −0.03 0 0 −0 0 0.01 e7 0.19 −0.7 −0.23 −0.04 −0.64 −0.01 0 −0 0 0 −0.02 0.07 −0.05 −0.01 −0.02 e8 0.21 −0.49 −0.37 0.01 0.72 0.23 −0.03 −0 0 0.02 −0.02 0.01 −0.01 0.03 0.01 e9 0.02 −0.07 −0.01 0.01 −0.06 0.06 −0 0.06 0.02 −0.03 0.26 −0.8 0.52 0.04 0.03 e10 0.01 −0.01 −0 0 0 0 −0 −0.68 −0.48 0.02 0.53 0.05 −0.1 0.02 0.14 e11 −0.01 −0 0 −0 −0 −0.02 0.01 −0.37 −0.42 0.02 −0.78 −0.22 0.13 −0.01 −0.15 e12 −0 0 0 −0 −0 −0.03 −0.44 0.06 −0 −0 −0 −0.49 −0.74 −0.04 −0.09 e13 0.01 −0 −0 0 −0 −0.11 −0.89 −0.04 0.01 −0.01 −0.01 0.23 0.37 0.02 0.06 e14 0 −0.03 −0.02 −0.01 0.05 −0.1 0.01 0 −0 0.01 0.03 −0.02 0.05 −0.99 0.06 e15 0.08 −0.42 0.89 0.01 0.15 −0.01 0 0 0 −0.01 −0 0.01 −0.01 −0 0 (8) Every column represents an exciton, an example of how to interpret the matrix in equation 8 looks like this: |Ψ1 >= −0.01|e1> −0.02|e2 > +0.05|e3 > −0.14|e4> −0.44|e5 > −0.83|e6 > +0.19|e7 > +0.21|e8 > +0.02|e9 >
+0.01|e10> −0.01|e11> −0|e12> +0.01|e13> +0|e14> +0.08|e15>
The energies of the excitons are shown in table 2.
Exciton Ψ1 Ψ2 Ψ3 Ψ4 Ψ5 Ψ6 Ψ7 Ψ8 Ψ9 Ψ10 Ψ11 Ψ12 Ψ13 Ψ14 Ψ15
Energy 15898 15849 15791 15736 15730 14984 15029 15470 15378 15430 15122 15240 15223 15190 15205 Table II. The energies of the excitons
VMD molecule viewer
VMD stands for visual molecular dynamics. It is designed for visualization, analysis and modeling of biological systems (Ks.uiuc.edu, 2017). It has a wide variety of options that will be used for presenting the nal image of the delocalized energy landscape. To create an image that gives an easy interpretation of the delocalization and energy in one, a lot of thought was necessary on how to construct this without neglecting some basic laws of physics. PDB (protein data base) has an open database with all sorts molecules which are free to open and edit and VMD is able to load these les. For this research the 4xk8 (Qin et al., 2017) super complex has been used from the PDB. 4xk8 is experimentally researched (Qin et al., 2017). It contains all the x,y and z coordinates of every single atom in the super complex. With the help of VMD the excitation probability and energy probability will be visualized. Namely, VMD is also able to read .dx les. These dx les load a grid into VMD and VMD turns it into volumes or colours. These dx les are created by a python le that writes a grid, which VMD interprets as densities. This grid is constructed by multiplying the excitation probability or the energy probability by a Gaussian function for every grid point (see the python scripts in the appendix). On most of the grid points this function goes to zero, but not on the grid points nearby the pigments, here do blobs arise, centered on the pigments. A blob is from now on a spherical representation of the excitation probability, coloured by the energy probability.
The excitation probability distribution
The rst important thing to do is to create blobs centered on the pigments, that symbolize the excitation probability and scale with the|cn
n and j count the excitons. The rst problem that arises is that there is not one exciton in this system, but 15. This is a problem because 15 dierent excitons do not give a clear view of the total delocalized energy landscape and it would also take 15 images to show. So, somehow these 15 excitons must be combined in one image. The rst idea was to scale the blobs only by the coe cients of the pigments: Pm
P
n|c n
m|2· blob(counting the coe cients on 1 pigment,
m, for all 15 excitons, n, repeating this for every pigment). Unfortunately it turns out that Pm
P
n|c n
m|2 = 1 by
de nition. A dierent approach is necessary. Instead of assuming that any state is just as probable as every other state, the Boltzmann factor is included to scale every pigment by its coe cient and the probability, based on the Boltzmann distribution in thermal equilibrium. This equilibrium is reached because the energy transfer in the lhca4 complex is faster than the energy transfer from the lhca4 to the core or to the other lhca complexes. As a result, the excitation reaches temporarily a thermal equilibrium in the lhca4 complex, before being transferred further. The distribution shows that lower energy states are always more probable than higher energy states, assuming they have the same temperature. In this equation the factor kT = 204 cm−1, corresponding with room temperature.
Excitationprobability = 15 X m=1 15 X n=1 |cnm| 2 e−En/kT P je−Ej/kT (9)
The state based on what happens when sunlight hits the complex is also calculated. It tells what pigments are most probable to be excited at the beginning of the excitation transfer process. To do this, rstly the transition dipole moments of the excitons, ˜Dn have to be calculated: ˜Dn =Pmc
n
mDm In this formula, Dm are the same transition
dipole as in equation 1. Because the sunlight spectrum is broad, it can be considered at in the region of the lhca4 absorption. The probability of the exciton n to be excited is then given by the square of its transition dipole moment,
˜ D2 n. Lightexcitationprobability = 15 X m=1 15 X n=1 |cn m| 2 ( ˜Dn)2 P j( ˜Dj)2 (10)
The energy probability distribution
The energy density is calculated in a similar way to the excitation probability. It is the chance of a pigment being excited, times the energy of the exciton. This way the energy is scaled by the chance of the pigment having that actual energy. Energyprobability = 15 X m=1 15 X n=1 En|cnm| 2 e−En/kT P je−Ej/kT (11)
The light density is calculated in a similar way to the light probability and energy probability.
Lightenergyprobability = 15 X m=1 15 X n=1 En|cnm| 2 ( ˜Dn)2 P j( ˜Dj)2
We created blobs for the excitation probability and energy probability, which represents volumes. VMD has the option to scale the colours by the volume data that is loaded into the molecule. This way the colour of the blobs is scaled by the size of the blob, but then including the energy as an extra scaling.
Dierent states
Without including the Boltzmann factor, the state of the complex is based upon the assumption that every pigment has the same probability to be excited. This translates into every blob having the same size, but dierent colours, re ecting dierent energies. The Boltzmann-state shows what the lhca4 looks like in thermal equilibrium. This is the state that occurs a few picoseconds after the sunlight hits the complex. The energy transfer within the complex is then nished, the distribution is at its nal state before jumping to another complex. This is very interesting because it tells us where the excitation will probably end up. The light-excitation-state shows the possibility and energy of the pigments getting hit by a photon.
RESULTS
Equally distributed
Figure 4. Back view of the equally distributed energy landscape.
In these gures the energy landscape of equal distribution of excitation can be seen. All the pigments have the same probability to be excited, only the energies dier. This gives a view of how the energy is distributed in the lhca4 complex. In the center of the complex the blobs are blue, meaning that it has a high energy. It is interesting to see that the energy is the lowest, red, nearby the lhca2 and lhca1 complex. This representation shows all the available excitation states in the lhca4, they span the whole complex.
Boltzmann equilibrium distribution
Figure 6. Back view of the Boltzmann equilibrium distribution landscape.
In these gures a Boltzmann equilibrium distribution can be seen. The pictures represent where the energy and excitation will ow to, a few picoseconds after the complex is hit by sunlight. The center of the complex is blue(high energy) and has a small probability of being excited. On the other hand, the outer pigments are red and have a larger probability of being excited. It is interesting to notice that these red pigments are close to the lhca2 and lhca1 complex, suggesting the excitation will probably move towards these complexes. It is also interesting that the pigments are red nearby pigments that are in the core of the photosystem. It is perhaps possible, though this is a speculation, that the excitation can directly jump from the lhca4 to the core, instead of following the lhca2 or lhca1 route. The latter route is currently thought to be the route the exciton would take.
Light distribution
Figure 8. Back view of the light-excited distribution landscape.
In these gures the light-excitation distribution can be seen. The pictures represent where the energy and excitation will arise at the moment the complex is hit by sunlight. Most of the blobs are red and the probability of being excited does not dier a lot per pigment. It looks a lot like the gures of the equal distribution, except the colours have changed because a dierent energy scale is used. The low energy states are not signi cantly more likely to be excited than high energy states and vice versa. This means that the sunlight does not favour certain pigments a lot more than the others. When compared with the Boltzmann state, it can be seen that the excitation moves towards the center of the PSI complex, favouring the parts that are nearby the core, lhca1 and lhca2 complexes. This process is exactly what was expected, since the exciton does not want to be trapped at the outer side of the photosystem , meaning that it will never reach the core. The dierence between the Boltzmann equilibrium state and the light excitation state can be seen in the gures 9-13 in the appendix.
CONCLUSION
Two views of light-harvesting complexes in photosystem 1 have been combined: the crystal structure of the PSI, containing spatial information of the pigments, and the spectroscopic data, providing the energies of the system and information on interaction with light. Based on this recently available information, the excitation and energy distribution within the lhca4 light-harvesting complex of PSI have been calculated. Three dierent states have been analyzed: the state where every pigment has the same probability to be excited, the state in thermal (Boltzmann) equilibrium and the state that is excited by light. We found that the excitation can arise almost with equal chance on every pigment after the complex is hit by sunlight and will move towards the inner side of the photosystem, favoring the lhca1, lhca2 and core sides before reaching thermal equilibrium.
DISCUSSION
This paper is based on theoretically calculated energies byNovoderezhkin et al (2016), obtained by tting spectro-scopic data. This has been combined with the experimentally calculated crystal structure, provides the paper with a rm connection to experimental observations. On the other hand, our work depends and relies on this research. Concerning the uniqueness of the theoretical simulations, Novoderezhkin et al (2016) provides several energy sets which reasonably well describe the experiments. The dierences between the energy values are relatively small and in our calculation would not result in big changes.
We have used the average energies from Novoderezhkin et al (2016)´s research, but in reality the energies uctuate due to natural disorder of the PSI. If we did not use the average energy, but the uctuating energies and summed over these, the results might change a little. It is di cult to estimate how much this would dier and might be interesting to research. However, we believe that this eect will be small, at least in the Boltzmann equilibrium. That is because the low-energy states are located at strongly coupled pigments (see Table 8) and it has been shown previously that strong excitonic coupling stabilizes excitonic states (Ramanan et al., 2015).
Also the hypothetical case of zero coupling has been calculated; instead of using the couplings that have been calculated with equation 2, the couplings are zero. The assumption was that the energy landscape would dier signi cantly from the case with non-zero couplings, but that result has not been found. The zero coupling state diers non signi cantly from the coupled Boltzmann equilibrium distribution state. This means that the coupling appears to have only minor in uence on the excitation probability and the energy distribution when the system is in thermal equilibrium. This result is intriguing, since the current view on this process is that the coupling should signi cantly change the excitation probability and the energy distribution when the system is in thermal equilibrium. Further investigation in this direction is of interest.
The focus has been on only the lhca4 complex, completely neglecting the eects of the other lhca complexes, even though the pigments of other complexes are sometimes nearby lhca4 pigments and thus creating an extra coupling. Though the coupling does not in uence the energy landscape at all, so it is unsure if including the other lhca couplings would make any dierence. Though, if the energies of the neighboring lhca pigments and core pigments are known, a more exact analyses of the exciton route can be made.
In our conclusion we claim that the energy will probably jump from the lhca4 complex to one of the lhca1 or lhca2 complexes, or to the core. These conclusions might be somewhat premature since the actual values of the energies of these complexes are not known. It is simply not known whether the neighboring side of the lhca complexes have a higher or lower energy than the lhca4 complex. We do know that every lhca has similar structure and thus energy landscape, this would mean that the lhca2 also has low energy at the outer left side (front view) of the complex. This would mean, though, that it also has a really high energy in the center of the complex, what would imply that the energy, somehow, passes this high energy barrier to reach the reaction center if it takes this route. It would be necessary to create the energy landscape of every lhca group to exactly understand what is happening in the lhca-belt of photosystem 1.
Some energies were not calculated but estimated by analyzing the environment of the pigments. This estimation is not precise, but will give a indication of the actual energies. The results would be more precise if these energies were calculated in a way that is done in the research of Novoderezhkin et al (2016).
In this paper a really direct approach has been made to write formulas for the excitation and energy. This interpretation is pretty simple and straightforward, it is possible that a more complex approach can give other results. It might be interesting to research the energy landscape in the future by constructing the formulas in another way.
In the bigger scheme of things, it is interesting to understand what is really happening in the lhca4 in context of the whole PSI. The excitation can start almost anywhere in the lhca4, and it also has a wide variety of options to end up in thermal equilibrium as it can go either to the core, lhca1 or lhca2. The fact that the photosystem is build in such way that every option is left open, instead of having one golden route that optimizes the excitation route, tells
us a lot about the complexity of nature. These photosystems have evolved over billion of years to become what they are now. They probably are not the fastest or most e cient in some speci c situations, but overall they will do their job in a robust way. Even when a few pigments are malfunctioning, the excitation can still nd a route by hopping to other pigments. This is perhaps the most important realization when trying to create solar panels; there is no golden formula that optimizes the energy transfer, it must be just as prepared for harsh situations as for the ideal situation.
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[3] Croce, R. and van Amerongen, H. (2013). Light-harvesting in photosystem I. Photosynthesis Research, 116(2-3), pp.153-166.(Croce and van Amerongen, 2013)
[4] Novoderezhkin, V. and van Grondelle, R. (2010). Physical origins and models of energy transfer in photosynthetic light-harvesting. Physical Chemistry Chemical Physics, 12(27), p.7352.(Novoderezhkin and van Grondelle, 2010)
[5] Novoderezhkin, V., Croce, R., Wahadoszamen, M., Polukhina, I., Romero, E. and van Grondelle, R. (2016). Mixing of exciton and charge-transfer states in light-harvesting complex Lhca4. Phys. Chem. Chem. Phys., 18(28), pp.19368-19377.(Novoderezhkin et al., 2016)
[6] Ramanan, C., Gruber, J., Malý, P., Negretti, M., Novoderezhkin, V., Krüger, T., Man£al, T., Croce, R. and van Grondelle, R. (2015). The Role of Exciton Delocalization in the Major Photosynthetic Light-Harvesting Antenna of Plants. Biophysical Journal, 108(5), pp.1047-1056.(Ramanan et al., 2015)
[7] Ks.uiuc.edu. (2017). VMD - Visual Molecular Dynamics. [online] Available at: http://www.ks.uiuc.edu/Research/vmd/ [Accessed 5 Jul. 2017].
APPENDIX
In the following gures, the dierence between the Boltzmann equilibrium distribution and the light excitation distribution can be seen. In gure 9 and 10 the arrival of the energy can be seen. This is the overall excitation that has been moved when comparing the two states. In gures 11 and 12 it is the overall excitation that dissapeared to reach the Boltzmann equilibrium, when comparing the two states.
PYTHON SCRIPTS
import numpy as np import math
import operator
from numpy import l i n a l g as LA
#wat i s h e t middelpunt van de r e c h t h o e k ? x0 = 0 y0 = −25 z0 = 195 #wat i s de g r o o t t e van de r e c h t h o e k ? xrechthoek=70 yrechthoek=85 zrechthoek=90 np . s e t _ p r i n t o p t i o n s ( p r e c i s i o n =2, suppress=True ) w, v = LA. e i g ( np . array ( [ [15400 , −45.18 , 1 1 . 5 6 , 2 . 7 6 , 2 . 3 , 3 . 2 6 , −2.26 , −4.93 , 1 . 2 9 , −52.08 , 3 . 8 6 , 5 . 7 3 , −9.78 , 1 . 0 2 , 0 . 3 4 ] , [ −45.18 , 15205 , 3 4 . 0 5 , 6 . 8 7 , 6 . 2 1 , 6 . 5 7 , −9.26 , −27.33 , −10.66 , 8 . 8 1 , 1 7 . 4 8 , −5.69 , 2 . 4 6 , 1 . 8 8 , 0 . 9 5 ] , [ 1 1 . 5 6 , 34 . 0 5 , 15039 , −5.7 , −13.14 , 1 . 3 8 , 8 . 4 2 , 176.92 , 1 4 . 8 2 , −4.35 , −1.7 , 2 . 6 7 , −7.07 , −11.49 , −2.24] , [ 2 . 7 6 , 6 . 8 7 , −5.7 , 15453 , 84 .9 5 , 2 9 . 16 , −1.05 , −7.7 , −5.58 , −3.28 , 1 . 9 4 , 0 . 6 2 , −3.62 , 4 . 7 5 , 1 . 8 ] , [ 2 . 3 , 6 . 2 1 , −13.14 , 84 .9 5 , 15750 , 6 0 . 8 7 , −3.31 , −4.08 , −3.41 , −2.91 , 3 . 3 6 , 1 . 3 5 , −2.28 , 7 . 5 , −1.52] , [ 3 . 2 6 , 6 . 5 7 , 1 . 3 8 , 2 9 . 16 , 6 0 . 87 , 15856 , −4.54 , −13.53 , 0 . 7 2 , −3.12 , 3 . 0 3 , 0 . 6 2 , −3.69 , 2 . 3 2 , −0.97] , [ −2.26 , −9.26 , 8 . 4 2 , −1.05 , −3.31 , −4.54 , 15793 , 5 3 .4 6 , 5 1 .9 2 , 4 . 4 9 , −0.61 , −2.06 , 1 . 5 2 , −1.32 , 2 4 . 0 7 ] , [ −4.93 , −27.33 , 176.92 , −7.7 , −4.08 , −13.53 , 53 .4 6 , 15731 , 2 . 8 7 , 5 . 7 2 , −2.89 , −3.37 , 2 . 9 4 , 38 .5 9 , 8 . 1 4 ] , [ 1 . 2 9 , −10.66 , 1 4 . 8 2 , −5.58 , −3.41 , 0 . 7 2 , 5 1 .9 2 , 2 . 8 7 , 15232 , −26.23 , 1 6 . 7 9 , 7 . 3 6 , −2.29 , 2 . 4 3 , 7 . 4 1 ] , [ −52.08 , 8 . 8 1 , −4.35 , −3.28 , −2.91 , −3.12 , 4 . 4 9 , 5 . 7 2 , −26.23 , 15345 , 134.65 , −9.82 , 5 . 7 6 , −0.51 , 0 . 7 2 ] , [ 3 . 8 6 , 1 7. 48 , −1.7 , 1 . 9 4 , 3 . 3 6 , 3 . 0 3 , −0.61 , −2.89 , 1 6 . 7 9 , 134.65 , 15223 , −2.82 , 2 . 1 5 , 1 . 3 5 , 0 . 3 1 ] , [ 5 . 7 3 , −5.69 , 2 . 6 7 , 0 . 6 2 , 1 . 3 5 , 0 . 6 2 , −2.06 , −3.37 , 7 . 3 6 , −9.82 , −2.82 , 15190 , −79.1 , −1.08 , −0.8] , [ −9.78 , 2 . 4 6 , −7.07 , −3.62 , −2.28 , −3.69 , 1 . 5 2 , 2 . 9 4 , −2.29 , 5 . 7 6 , 2 . 1 5 , −79.1 , 15068 , −0.81 , −0.06] , [ 1 . 0 2 , 1 . 8 8 , −11.49 , 4 . 7 5 , 7 . 5 , 2 . 3 2 , −1.32 , 3 8 . 5 9 , 2 . 4 3 , −0.51 , 1 . 3 5 , −1.08 , −0.81 , 15190 , −1.66] , [ 0 . 3 4 , 0 . 9 5 , −2.24 , 1 . 8 , −1.52 , −0.97 , 2 4 . 0 7 , 8 . 1 4 , 7 . 4 1 , 0 . 7 2 , 0 . 3 1 , −0.8 , −0.06 , −1.66 , 1 5 8 0 0 ] ] ) ) matrix=np . array ( v ) m=matrix . transpose ( ) #nu z i j n de c o e f f i c i e n t s h o r i z o n t a a l !
e x c i t o n s =[v1 , v2 , v3 , v4 , v5 , v6 , v7 , v8 , v9 , v10 , v11 , v12 , v13 , v14 , v15 ]=[m[ 0 ] ,m[ 1 ] ,m[ 2 ] ,m[ 3 ] ,m [ 4 ] ,m[ 5 ] ,m[ 6 ] ,m[ 7 ] ,m[ 8 ] ,m[ 9 ] ,m[ 1 0 ] ,m[ 1 1 ] ,m[ 1 2 ] ,m[ 1 3 ] ,m[ 1 4 ] ] #CLA a601 = [ [ 2 0 . 4 3 1 , 18.837 , 236.758 ] , [ 1 8 . 9 1 2 , 19.838 , 2 3 5 . 7 5 8 ] , [ 2 1 . 4 4 8 , 18.620 , 235.000 ] , [ 2 2 . 0 2 1 , 18.248 ,237.931 ] , [ 1 9 . 7 1 3 , 19.396 , 238.583 ] ] a602 = [ [ 2 9 . 9 1 0 , 12.038 , 231.085 ] , [ 2 9 . 5 2 7 , 10.005 , 231.225 ] , [ 3 1 . 0 4 8 , 11.695 , 229.425 ] , [ 2 9 . 8 2 6 , 14.076 ,230.791 ] , [ 2 8 . 4 4 5 , 12.488 , 232.431 ] ] a603 = [ [ 3 6 . 7 8 1 , 13.826 , 221.572 ] , [ 3 5 . 3 6 6 , 12.306 , 221.466 ] , [ 3 5 . 2 7 6 , 15.191 , 221.803 ] , [ 3 8 . 1 8 3 , 15.249 ,221.053 ] , [ 3 8 . 2 5 2 , 12.611 , 220.855 ] ] a604 = [ [ 5 0 . 5 7 0 , 26.287 , 225.916 ] , [ 5 1 . 5 3 2 , 26.428 ,224.083 ] , [ 4 9 . 8 5 2 , 24.452 , 225.378 ] , [ 5 0 . 0 7 6 , 26.075 ,227.906 ] , [ 5 1 . 5 7 5 , 27.890 , 226.675 ] ] a608 = [ [ 4 4 . 1 7 7 , 8 . 8 54 , 220.971 ] , [ 4 3 . 0 9 4 , 7 . 0 8 3 , 220.885 ] , [ 4 5 . 4 3 1 , 8. 1 3 9 , 219.527 ] , [ 4 4 . 8 5 9 , 10.797 , 220.825 ] , [ 42.733 , 9 .7 8 1 , 222.068 ] ] a609 = [ [ 4 4 . 5 6 7 , 13.401 , 237.595 ] , [ 4 4 . 6 5 9 , 12.448 , 239.434 ] , [ 4 3 . 4 0 9 , 14.862 , 238.434 ] , [ 4 4 . 9 5 6 , 14.474 , 235.880 ] , [ 4 6 . 0 6 8 , 12.251 , 236.828 ] ] a610 = [ [ 2 9 . 7 5 8 , 21.907 , 243.215 ] , [ 3 0 . 5 4 0 , 20.874 , 244.838 ] , [ 2 8 . 3 2 5 , 22.708 , 244.430 ] , [ 2 9 . 3 8 1 , 23.201 , 241.652 ] , [ 3 1 . 3 7 6 , 21.485 , 242.047 ] ] a611 = [ [ 3 8 . 8 9 9 , 23.585 , 239.802 ] , [ 4 0 . 1 2 3 , 22.575 , 241.143 ] , [ 4 0 . 5 5 7 , 24.149 , 238.748 ] , [ 3 7 . 6 5 7 , 24.948 , 238.874 ] , [ 3 7 . 2 9 3 , 2 3 . 4 7 8 , 241.051 ] ] a612 = [ [ 2 9 . 2 8 3 , 30.852 , 226.594 ] , [ 2 9 . 1 8 2 , 32.780 , 227.360 ] , [ 2 9 . 6 1 2 , 30.128 , 228.476 ] , [ 2 8 . 9 3 1 , 2 8 . 9 9 7 , 225.768 ] , [ 2 8 . 4 9 6 , 3 1 . 4 3 3 , 224.805 ] ] a613 = [ [ 2 6 . 3 8 7 , 36.644 , 233.403 ] , [ 2 4 . 3 9 9 , 37.087 , 233.010 ] , [ 2 6 . 5 2 9 , 38.317 , 234.573 ] , [ 2 8 . 1 6 3 , 3 5 . 8 3 6 , 234.066 ] , [ 2 6 . 2 1 8 , 34.782 , 232.589 ] ] a614 = [ [ 4 8 . 0 1 9 , 3 . 2 10 , 213.347 ] , [ 4 9 . 5 0 7 , 2 . 9 0 5 , 211.931 ] , [ 4 7 . 4 9 4 , 4 . 9 4 6 , 212.407 ] , [ 4 6 . 3 0 1 , 3 .1 2 2 , 214.485 ] , [ 4 8 . 1 9 7 , 1 .3 1 0 , 214.068 ] ] #CLB b605 = [ [ 5 2 . 8 2 5 , 20.456 , 219.914 ] , [ 5 3 . 7 6 3 , 19.086 , 221.028 ] , [ 5 1 . 0 1 4 , 19.639 , 220.407 ] , [ 5 1 . 9 4 9 , 22.136 , 219.094 ] , [ 5 4 . 5 0 3 , 21.585 , 219.619 ] ] b606 = [ [ 4 5 . 6 5 1 , 23.940 , 215.055 ] , [ 4 4 . 2 5 0 , 25.207 ,214.402 ] , [ 4 4 . 2 5 4 , 22.923 , 216.149 ] , [ 4 7 . 1 0 0 ,22.499 ,215.366 ] , [ 4 7 . 1 2 0 , 2 4 . 6 9 2 , 213.855 ] ] b607 = [ [ 5 0 . 4 5 8 , 7 . 6 13 , 229.243 ] , [ 5 0 . 4 4 4 , 9.611 ,229.216 ] , [ 5 2 . 4 4 8 , 7.606 ,228.769 ] , [ 5 0 . 4 6 8 , 5 .5 9 9 , 229.707 ] , [ 4 8 . 6 0 3 , 7 .4 6 2 , 230.084 ] ] b615 = [ [ 6 0 . 9 7 2 , 4 . 0 1 2 , 231.907 ] , [ 6 2 . 5 4 0 , 5 .1 1 3 , 232.478 ] , [ 6 1 . 3 9 8 , 4 .3 77 , 229.939 ] , [ 5 9 . 1 2 6 , 3 . 1 8 8 , 231.467 ] , [ 6 0 . 2 5 1 , 3 .7 9 3 , 233.806 ] ]
Atoms=[a601 , a602 , a603 , a604 , b605 , b606 , b607 , a608 , a609 , a610 , a611 , a612 , a613 , a614 , b615 ] f o r i i n range ( 0 , 1 5 ) : Molecuul=Atoms [ i ] Mg=Molecuul [ 0 ] Mgx=Mg[ 0 ] Mgy=Mg[ 1 ] Mgz=Mg[ 2 ] d e f mgx(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] xn=Mg[ 0 ] r e t u r n xn d e f mgy(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] yn=Mg[ 1 ] r e t u r n yn d e f mgz(n) :
Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] zn=Mg[ 2 ] r e t u r n zn d e f nax (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] xn=na [ 0 ] r e t u r n xn d e f nay (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] yn=na [ 1 ] r e t u r n yn d e f naz (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] zn=na [ 2 ] r e t u r n zn d e f nbx (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] xn=nb [ 0 ] r e t u r n xn d e f nby (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] yn=nb [ 1 ] r e t u r n yn d e f nbz (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] zn=nb [ 2 ] r e t u r n zn d e f ncx (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] xn=nc [ 0 ] r e t u r n xn d e f ncy (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] yn=nc [ 1 ] r e t u r n yn d e f ncz (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] zn=nc [ 2 ] r e t u r n zn d e f ndx (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] xn=nd [ 0 ] r e t u r n xn
d e f ndy (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] yn=nd [ 1 ] r e t u r n yn d e f ndz (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] zn=nd [ 2 ] r e t u r n zn d e f blob (x , y , z , n) : #A = 1 alpha = 20
r e t u r n np . exp ( −((x−mgx(n) ) **2 + (y−mgy(n) ) **2 + ( z−mgz(n) ) **2) /(2* alpha ) ) d e f blobna (x , y , z , n) :
alpha=20
r e t u r n np . exp ( −((x−nax (n) ) **2 + (y−nay (n) ) **2 + ( z−naz (n) ) **2) /(2* alpha ) ) d e f blobnb (x , y , z , n) :
alpha=20
r e t u r n np . exp ( −((x−nbx (n) ) **2 + (y−nby (n) ) **2 + ( z−nbz (n) ) **2) /(2* alpha ) ) d e f blobnc (x , y , z , n) :
alpha=20
r e t u r n np . exp ( −((x−ncx (n) ) **2 + (y−ncy (n) ) **2 + ( z−ncz (n) ) **2) /(2* alpha ) ) d e f blobnd (x , y , z , n) :
alpha=20
r e t u r n np . exp ( −((x−ndx (n) ) **2 + (y−ndy (n) ) **2 + ( z−ndz (n) ) **2) /(2* alpha ) )
f 1=open ( 'C: \ Users \ Gebruiker \Desktop\ Studie \ S c r i p t i e \ excitationFINAL . dx ' , 'w ' ) #c r e a t i n g t h e f i l e t h a t w i l l be l o a d e d by VMD
f 1 . write ( '# Data c a l c u l a t e d by Tomas f u n c t i o n \n ' )
f 1 . write ( " o b j e c t 1 c l a s s g r i d p o s i t i o n s counts %s %s %s \n" %(xrechthoek , yrechthoek , zrechthoek ) )
f 1 . write ( " o r i g i n %s %s %s \n" %(x0 , y0 , z0 ) ) f 1 . write ( ' d e l t a 1 0 0\n ' )
f 1 . write ( ' d e l t a 0 1 0\n ' ) f 1 . write ( ' d e l t a 0 0 1\n ' )
f 1 . write ( " o b j e c t 2 c l a s s g r i d c o n n e c t i o n s counts %s %s %s \n"%(xrechthoek , yrechthoek , zrechthoek ) )
f 1 . write ( " o b j e c t 3 c l a s s array type double rank 0 items %s data f o l l o w s \n\n"%( xrechthoek * yrechthoek * zrechthoek ) )
KbT=204 e n e r g i e s=w #b o l t z m a n f u n c t i o n d e f boltzman ( i ) : r e t u r n np . exp(−( e n e r g i e s [ i ]−min ( e n e r g i e s ) ) /(KbT) ) totdens=0 t o t c o e f f =0 b o l t z c o n s t a n t=0
#summing a l l t h e boltzman f o r i i n range ( 0 , 1 5 ) : b o l t z c o n s t a n t+=boltzman ( i ) #b o l t z m a n c o e f f i c i e n t c r e a t i n g d e f t o t c o e f f ( ) : E c o e f f i c i e n t =[] f o r n i n range ( 0 ,1 5 ) : t o t c o e f f =0 f o r i i n range ( 0 ,1 5 ) : t o t c o e f f+=boltzman ( i ) / b o l t z c o n s t a n t * e x c i t o n s [ i ] [ n ]**2 E c o e f f i c i e n t . append ( t o t c o e f f ) r e t u r n E c o e f f i c i e n t b o l t z c o e f f i c i e n t=t o t c o e f f ( ) #c r e a t i n g a square , m u l t i p l y i n g t h e b l o b s with t h e b o l t z c o e f f i c i e n t . f o r x i i n range (1 , xrechthoek +1) : f o r y i i n range (1 , yrechthoek +1) : f o r z i i n range (1 , zrechthoek +1) : totdens=0 f o r n i n range ( 0 , 1 5) :
totdens=totdens+b o l t z c o e f f i c i e n t [ n ] * ( blobna ( x i+x0 , y i+y0 , z i+z0 , n)+ blobnb ( x i+x0 , y i+y0 , z i+z0 , n)+blobnc ( x i+x0 , y i+y0 , z i+z0 , n)+blobnd ( x i +x0 , y i+y0 , z i+z0 , n) )
f 1 . wri te ( s t r ( totdens )+' ' ) i f z i % 3 == 0 :
f 1 . wri te ( ' \n ' )
f 1 . write ( ' \ nobject " d e n s i t y ( element N) [A^−3]" c l a s s f i e l d ' ) f 1 . c l o s e ( )
Listing 1. Boltzmann equilibrium excitation probability
import numpy as np import math
import operator
from numpy import l i n a l g as LA
#wat i s h e t middelpunt van de r e c h t h o e k ? x0 = 0 y0 = −25 z0 = 195 #wat i s de g r o o t t e van de r e c h t h o e k ? xrechthoek=70 yrechthoek=85 zrechthoek=90 np . s e t _ p r i n t o p t i o n s ( p r e c i s i o n =2, suppress=True ) w, v = LA. e i g ( np . array ( [ [15400 , −45.18 , 1 1 . 5 6 , 2 . 7 6 , 2 . 3 , 3 . 2 6 , −2.26 , −4.93 , 1 . 2 9 , −52.08 , 3 . 8 6 , 5 . 7 3 ,
−9.78 , 1 . 0 2 , 0 . 3 4 ] , [ −45.18 , 15205 , 3 4 . 05 , 6 . 8 7 , 6 . 2 1 , 6 . 5 7 , −9.26 , −27.33 , −10.66 , 8 . 8 1 , 1 7 .4 8 , −5.69 , 2 . 4 6 , 1 . 8 8 , 0 . 9 5 ] , [ 1 1 . 5 6 , 34 . 0 5 , 15039 , −5.7 , −13.14 , 1 . 3 8 , 8 . 4 2 , 176.92 , 1 4 . 8 2 , −4.35 , −1.7 , 2 . 6 7 , −7.07 , −11.49 , −2.24] , [ 2 . 7 6 , 6 . 8 7 , −5.7 , 15453 , 8 4 .9 5 , 2 9 . 1 6 , −1.05 , −7.7 , −5.58 , −3.28 , 1 . 9 4 , 0 . 6 2 , −3.62 , 4 . 7 5 , 1 . 8 ] , [ 2 . 3 , 6 . 2 1 , −13.14 , 8 4 .9 5 , 15750 , 6 0. 8 7 , −3.31 , −4.08 , −3.41 , −2.91 , 3 . 3 6 , 1 . 3 5 , −2.28 , 7 . 5 , −1.52] , [ 3 . 2 6 , 6 . 5 7 , 1 . 3 8 , 2 9 . 1 6 , 6 0 . 8 7 , 15856 , −4.54 , −13.53 , 0 . 7 2 , −3.12 , 3 . 0 3 , 0 . 6 2 , −3.69 , 2 . 3 2 , −0.97] , [ −2.26 , −9.26 , 8 . 4 2 , −1.05 , −3.31 , −4.54 , 15793 , 5 3 . 4 6 , 5 1 . 9 2 , 4 . 4 9 , −0.61 , −2.06 , 1 . 5 2 , −1.32 , 2 4 . 0 7 ] , [ −4.93 , −27.33 , 176.92 , −7.7 , −4.08 , −13.53 , 5 3 .4 6 , 15731 , 2 . 8 7 , 5 . 7 2 , −2.89 , −3.37 , 2 . 9 4 , 38 .5 9 , 8 . 1 4 ] , [ 1 . 2 9 , −10.66 , 1 4 . 8 2 , −5.58 , −3.41 , 0 . 7 2 , 5 1.9 2 , 2 . 8 7 , 15232 , −26.23 , 1 6 .7 9 , 7 . 3 6 , −2.29 , 2 . 4 3 , 7 . 4 1 ] , [ −52.08 , 8 . 8 1 , −4.35 , −3.28 , −2.91 , −3.12 , 4 . 4 9 , 5 . 7 2 , −26.23 , 15345 , 134.65 , −9.82 , 5 . 7 6 , −0.51 , 0 . 7 2 ] , [ 3 . 8 6 , 1 7. 48 , −1.7 , 1 . 9 4 , 3 . 3 6 , 3 . 0 3 , −0.61 , −2.89 , 1 6 . 7 9 , 134.65 , 15223 , −2.82 , 2 . 1 5 , 1 . 3 5 , 0 . 3 1 ] , [ 5 . 7 3 , −5.69 , 2 . 6 7 , 0 . 6 2 , 1 . 3 5 , 0 . 6 2 , −2.06 , −3.37 , 7 . 3 6 , −9.82 , −2.82 , 15190 , −79.1 , −1.08 , −0.8] , [ −9.78 , 2 . 4 6 , −7.07 , −3.62 , −2.28 , −3.69 , 1 . 5 2 , 2 . 9 4 , −2.29 , 5 . 7 6 , 2 . 1 5 , −79.1 , 15068 , −0.81 , −0.06] , [ 1 . 0 2 , 1 . 8 8 , −11.49 , 4 . 7 5 , 7 . 5 , 2 . 3 2 , −1.32 , 3 8 . 5 9 , 2 . 4 3 , −0.51 , 1 . 3 5 , −1.08 , −0.81 , 15190 , −1.66] , [ 0 . 3 4 , 0 . 9 5 , −2.24 , 1 . 8 , −1.52 , −0.97 , 2 4. 0 7 , 8 . 1 4 , 7 . 4 1 , 0 . 7 2 , 0 . 3 1 , −0.8 , −0.06 , −1.66 , 1 5 8 0 0 ] ] ) ) matrix=np . array ( v ) m=matrix . transpose ( ) #nu z i j n de c o e f f i c i e n t s h o r i z o n t a a l ! e x c i t o n s =[v1 , v2 , v3 , v4 , v5 , v6 , v7 , v8 , v9 , v10 , v11 , v12 , v13 , v14 , v15 ]=[m[ 0 ] ,m[ 1 ] ,m[ 2 ] ,m[ 3 ] ,m [ 4 ] ,m[ 5 ] ,m[ 6 ] ,m[ 7 ] ,m[ 8 ] ,m[ 9 ] ,m[ 1 0 ] ,m[ 1 1 ] ,m[ 1 2 ] ,m[ 1 3 ] ,m[ 1 4 ] ] e n e r g i e s=w #CLA a601 = [ [ 2 0 . 4 3 1 , 18.837 , 236.758 ] , [ 1 8 . 9 1 2 , 19.838 , 2 3 5 . 7 5 8 ] , [ 2 1 . 4 4 8 , 18.620 , 235.000 ] , [ 2 2 . 0 2 1 , 18.248 ,237.931 ] , [ 1 9 . 7 1 3 , 19.396 , 238.583 ] ] a602 = [ [ 2 9 . 9 1 0 , 12.038 , 231.085 ] , [ 2 9 . 5 2 7 , 10.005 , 231.225 ] , [ 3 1 . 0 4 8 , 11.695 , 229.425 ] , [ 2 9 . 8 2 6 , 14.076 ,230.791 ] , [ 2 8 . 4 4 5 , 12.488 , 232.431 ] ] a603 = [ [ 3 6 . 7 8 1 , 13.826 , 221.572 ] , [ 3 5 . 3 6 6 , 12.306 , 221.466 ] , [ 3 5 . 2 7 6 , 15.191 , 221.803 ] , [ 3 8 . 1 8 3 , 15.249 ,221.053 ] , [ 3 8 . 2 5 2 , 12.611 , 220.855 ] ] a604 = [ [ 5 0 . 5 7 0 , 26.287 , 225.916 ] , [ 5 1 . 5 3 2 , 26.428 ,224.083 ] , [ 4 9 . 8 5 2 , 24.452 , 225.378 ] , [ 5 0 . 0 7 6 , 26.075 ,227.906 ] , [ 5 1 . 5 7 5 , 27.890 , 226.675 ] ] a608 = [ [ 4 4 . 1 7 7 , 8 . 8 54 , 220.971 ] , [ 4 3 . 0 9 4 , 7 . 08 3 , 220.885 ] , [ 4 5 . 4 3 1 , 8 . 1 3 9 , 219.527 ] , [ 4 4 . 8 5 9 , 10.797 , 220.825 ] , [ 42.733 , 9 .7 8 1 , 222.068 ] ] a609 = [ [ 4 4 . 5 6 7 , 13.401 , 237.595 ] , [ 4 4 . 6 5 9 , 12.448 , 239.434 ] , [ 4 3 . 4 0 9 , 14.862 , 238.434 ] , [ 4 4 . 9 5 6 , 14.474 , 235.880 ] , [ 4 6 . 0 6 8 , 12.251 , 236.828 ] ] a610 = [ [ 2 9 . 7 5 8 , 21.907 , 243.215 ] , [ 3 0 . 5 4 0 , 20.874 , 244.838 ] , [ 2 8 . 3 2 5 , 22.708 , 244.430 ] , [ 2 9 . 3 8 1 , 23.201 , 241.652 ] , [ 3 1 . 3 7 6 , 21.485 , 242.047 ] ] a611 = [ [ 3 8 . 8 9 9 , 23.585 , 239.802 ] , [ 4 0 . 1 2 3 , 22.575 , 241.143 ] , [ 4 0 . 5 5 7 , 24.149 , 238.748 ] , [ 3 7 . 6 5 7 , 24.948 , 238.874 ] , [ 3 7 . 2 9 3 , 2 3 . 4 7 8 , 241.051 ] ] a612 = [ [ 2 9 . 2 8 3 , 30.852 , 226.594 ] , [ 2 9 . 1 8 2 , 32.780 , 227.360 ] , [ 2 9 . 6 1 2 , 30.128 , 228.476 ] , [ 2 8 . 9 3 1 , 2 8 . 9 9 7 , 225.768 ] , [ 2 8 . 4 9 6 , 3 1 . 4 3 3 , 224.805 ] ] a613 = [ [ 2 6 . 3 8 7 , 36.644 , 233.403 ] , [ 2 4 . 3 9 9 , 37.087 , 233.010 ] , [ 2 6 . 5 2 9 , 38.317 , 234.573 ] , [ 2 8 . 1 6 3 , 3 5 . 8 3 6 , 234.066 ] , [ 2 6 . 2 1 8 , 34.782 , 232.589 ] ]
a614 = [ [ 4 8 . 0 1 9 , 3 . 2 10 , 213.347 ] , [ 4 9 . 5 0 7 , 2 . 9 0 5 , 211.931 ] , [ 4 7 . 4 9 4 , 4 . 9 4 6 , 212.407 ] , [ 4 6 . 3 0 1 , 3 . 1 22 , 214.485 ] , [ 4 8 . 1 9 7 , 1 .3 1 0 , 214.068 ] ] #CLB b605 = [ [ 5 2 . 8 2 5 , 20.456 , 219.914 ] , [ 5 3 . 7 6 3 , 19.086 , 221.028 ] , [ 5 1 . 0 1 4 , 19.639 , 220.407 ] , [ 5 1 . 9 4 9 , 22.136 , 219.094 ] , [ 5 4 . 5 0 3 , 21.585 , 219.619 ] ] b606 = [ [ 4 5 . 6 5 1 , 23.940 , 215.055 ] , [ 4 4 . 2 5 0 , 25.207 ,214.402 ] , [ 4 4 . 2 5 4 , 22.923 , 216.149 ] , [ 4 7 . 1 0 0 ,22.499 ,215.366 ] , [ 4 7 . 1 2 0 , 2 4 . 6 9 2 , 213.855 ] ] b607 = [ [ 5 0 . 4 5 8 , 7 . 6 1 3 , 229.243 ] , [ 5 0 . 4 4 4 , 9.611 ,229.216 ] , [ 5 2 . 4 4 8 , 7.606 ,228.769 ] , [ 5 0 . 4 6 8 , 5 .59 9 , 229.707 ] , [ 4 8 . 6 0 3 , 7 .4 6 2 , 230.084 ] ] b615 = [ [ 6 0 . 9 7 2 , 4 . 0 1 2 , 231.907 ] , [ 6 2 . 5 4 0 , 5 .1 1 3 , 232.478 ] , [ 6 1 . 3 9 8 , 4 .3 77 , 229.939 ] , [ 5 9 . 1 2 6 , 3 .1 8 8 , 231.467 ] , [ 6 0 . 2 5 1 , 3 .7 9 3 , 233.806 ] ]
Atoms=[a601 , a602 , a603 , a604 , b605 , b606 , b607 , a608 , a609 , a610 , a611 , a612 , a613 , a614 , b615 ] f o r i i n range ( 0 , 1 5 ) : Molecuul=Atoms [ i ] Mg=Molecuul [ 0 ] Mgx=Mg[ 0 ] Mgy=Mg[ 1 ] Mgz=Mg[ 2 ] d e f mgx(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] xn=Mg[ 0 ] r e t u r n xn d e f mgy(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] yn=Mg[ 1 ] r e t u r n yn d e f mgz(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] zn=Mg[ 2 ] r e t u r n zn d e f nax (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] xn=na [ 0 ] r e t u r n xn d e f nay (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] yn=na [ 1 ] r e t u r n yn d e f naz (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] zn=na [ 2 ] r e t u r n zn d e f nbx (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ]
xn=nb [ 0 ] r e t u r n xn d e f nby (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] yn=nb [ 1 ] r e t u r n yn d e f nbz (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] zn=nb [ 2 ] r e t u r n zn d e f ncx (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] xn=nc [ 0 ] r e t u r n xn d e f ncy (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] yn=nc [ 1 ] r e t u r n yn d e f ncz (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] zn=nc [ 2 ] r e t u r n zn d e f ndx (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] xn=nd [ 0 ] r e t u r n xn d e f ndy (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] yn=nd [ 1 ] r e t u r n yn d e f ndz (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] zn=nd [ 2 ] r e t u r n zn d e f blob (x , y , z , n) : #A = 1 alpha =100
r e t u r n np . exp ( −((x−mgx(n) ) **2 + (y−mgy(n) ) **2 + ( z−mgz(n) ) **2) /(2* alpha ) ) d e f blobna (x , y , z , n) :
alpha=100
r e t u r n np . exp ( −((x−nax (n) ) **2 + (y−nay (n) ) **2 + ( z−naz (n) ) **2) /(2* alpha ) ) d e f blobnb (x , y , z , n) :
alpha=100
r e t u r n np . exp ( −((x−nbx (n) ) **2 + (y−nby (n) ) **2 + ( z−nbz (n) ) **2) /(2* alpha ) ) d e f blobnc (x , y , z , n) :
alpha=100
r e t u r n np . exp ( −((x−ncx (n) ) **2 + (y−ncy (n) ) **2 + ( z−ncz (n) ) **2) /(2* alpha ) ) d e f blobnd (x , y , z , n) :
alpha=100
r e t u r n np . exp ( −((x−ndx (n) ) **2 + (y−ndy (n) ) **2 + ( z−ndz (n) ) **2) /(2* alpha ) )
KbT=204 e n e r g i e s=w d e f boltzman ( i ) : r e t u r n np . exp(−( e n e r g i e s [ i ]−min ( e n e r g i e s ) ) /(KbT) ) totdens=0 t o t c o e f f =0 b o l t z c o n s t a n t=0 f o r i i n range ( 0 , 1 5) : b o l t z c o n s t a n t+=boltzman ( i ) d e f t o t c o e f f ( ) : b o l t z c o e f f i c i e n t =[] f o r n i n range ( 0 , 1 5) : t o t c o e f f =0 f o r i i n range ( 0 , 1 5) : t o t c o e f f+=boltzman ( i ) / b o l t z c o n s t a n t * e x c i t o n s [ i ] [ n ]**2 b o l t z c o e f f i c i e n t . append ( t o t c o e f f ) r e t u r n b o l t z c o e f f i c i e n t b o l t z c o e f f i c i e n t=t o t c o e f f ( )
f 2=open ( 'C: \ Users \ Gebruiker \Desktop\ Studie \ S c r i p t i e \EnergyFINAL . dx ' , 'w ' ) f 2 . write ( '# Data c a l c u l a t e d by Thomas f u n c t i o n \n ' )
f 2 . write ( " o b j e c t 1 c l a s s g r i d p o s i t i o n s counts %s %s %s \n" %(xrechthoek , yrechthoek , zrechthoek ) )
f 2 . write ( " o r i g i n %s %s %s \n" %(x0 , y0 , z0 ) ) f 2 . write ( ' d e l t a 1 0 0\n ' )
f 2 . write ( ' d e l t a 0 1 0\n ' ) f 2 . write ( ' d e l t a 0 0 1\n ' )
f 2 . write ( " o b j e c t 2 c l a s s g r i d c o n n e c t i o n s counts %s %s %s \n"%(xrechthoek , yrechthoek , zrechthoek ) )
f 2 . write ( " o b j e c t 3 c l a s s array type double rank 0 items %s data f o l l o w s \n\n"%( xrechthoek * yrechthoek * zrechthoek ) )
#c r e a t i n g e n e r g y c o e f f i c i e n t d e f t o t c o e f f e n e r g i e ( ) : E c o e f f i c i e n t =[] f o r n i n range ( 0 , 1 5) : t o t c o e f f =0 f o r i i n range ( 0 , 1 5) :
t o t c o e f f +=(e x c i t o n s [ i ] [ n ] * * 2 ) *( e n e r g i e s [ i ]−min ( e n e r g i e s ) ) /(max( e n e r g i e s ) −min ( e n e r g i e s ) ) E c o e f f i c i e n t . append ( t o t c o e f f ) r e t u r n E c o e f f i c i e n t E c o e f f i c i e n t=t o t c o e f f e n e r g i e ( ) E c o e f f i c i e n t=t o t c o e f f e n e r g i e ( )
##r e a t i n g a box , m u l t i p l y i n g t h e b l o b s with t h e b o l t z c o e f f i c i e n t and e n e r g i e s . totdens=0 f o r x i i n range (1 , xrechthoek +1) : f o r y i i n range (1 , yrechthoek +1) : f o r z i i n range (1 , zrechthoek +1) : totdens=0 f o r n i n range ( 0 , 1 5) :
totdens=totdens+b o l t z c o e f f i c i e n t [ n ] * E c o e f f i c i e n t [ n ] * ( blobna ( x i+x0 , y i+ y0 , z i+z0 , n)+blobnb ( x i+x0 , y i+y0 , z i+z0 , n)+blobnc ( x i+x0 , y i+y0 , z i+z0 , n)+blobnd ( x i+x0 , y i+y0 , z i+z0 , n) )
f 2 . wri te ( s t r ( totdens )+' ' ) i f z i % 3 == 0 :
f 2 . write ( ' \n ' )
f 2 . write ( ' \ nobject " d e n s i t y ( element N) [A^−3]" c l a s s f i e l d ' ) f 2 . c l o s e ( )
Listing 2. Boltzmann equilibrium energy probability
import numpy as np import math
import operator
from numpy import l i n a l g as LA
#wat i s h e t middelpunt van de r e c h t h o e k ? x0 = 0 y0 = −25 z0 = 195 #wat i s de g r o o t t e van de r e c h t h o e k ? xrechthoek=70 yrechthoek=85 zrechthoek=90 np . s e t _ p r i n t o p t i o n s ( p r e c i s i o n =2, suppress=True ) w, v = LA. e i g ( np . array ( [ [15400 , −45.18 , 1 1 . 5 6 , 2 . 7 6 , 2 . 3 , 3 . 2 6 , −2.26 , −4.93 , 1 . 2 9 , −52.08 , 3 . 8 6 , 5 . 7 3 , −9.78 , 1 . 0 2 , 0 . 3 4 ] , [ −45.18 , 15205 , 3 4 . 05 , 6 . 8 7 , 6 . 2 1 , 6 . 5 7 , −9.26 , −27.33 , −10.66 , 8 . 8 1 , 1 7 .4 8 , −5.69 , 2 . 4 6 , 1 . 8 8 , 0 . 9 5 ] , [ 1 1 . 5 6 , 34 . 0 5 , 15039 , −5.7 , −13.14 , 1 . 3 8 , 8 . 4 2 , 176.92 , 1 4 . 8 2 , −4.35 , −1.7 , 2 . 6 7 , −7.07 , −11.49 , −2.24] , [ 2 . 7 6 , 6 . 8 7 , −5.7 , 15453 , 8 4 . 9 5 , 2 9 . 1 6 , −1.05 , −7.7 , −5.58 , −3.28 , 1 . 9 4 , 0 . 6 2 , −3.62 , 4 . 7 5 , 1 . 8 ] , [ 2 . 3 , 6 . 2 1 , −13.14 , 84 . 9 5 , 15750 , 6 0 . 87 , −3.31 , −4.08 , −3.41 , −2.91 , 3 . 3 6 , 1 . 3 5 ,
−2.28 , 7 . 5 , −1.52] , [ 3 . 2 6 , 6 . 5 7 , 1 . 3 8 , 2 9 . 1 6 , 6 0 . 8 7 , 15856 , −4.54 , −13.53 , 0 . 7 2 , −3.12 , 3 . 0 3 , 0 . 6 2 , −3.69 , 2 . 3 2 , −0.97] , [ −2.26 , −9.26 , 8 . 4 2 , −1.05 , −3.31 , −4.54 , 15793 , 5 3 .4 6 , 5 1 .9 2 , 4 . 4 9 , −0.61 , −2.06 , 1 . 5 2 , −1.32 , 2 4 . 0 7 ] , [ −4.93 , −27.33 , 176.92 , −7.7 , −4.08 , −13.53 , 5 3 .4 6 , 15731 , 2 . 8 7 , 5 . 7 2 , −2.89 , −3.37 , 2 . 9 4 , 38 .5 9 , 8 . 1 4 ] , [ 1 . 2 9 , −10.66 , 1 4 . 8 2 , −5.58 , −3.41 , 0 . 7 2 , 5 1 . 92 , 2 . 8 7 , 15232 , −26.23 , 1 6 .7 9 , 7 . 3 6 , −2.29 , 2 . 4 3 , 7 . 4 1 ] , [ −52.08 , 8 . 8 1 , −4.35 , −3.28 , −2.91 , −3.12 , 4 . 4 9 , 5 . 7 2 , −26.23 , 15345 , 134.65 , −9.82 , 5 . 7 6 , −0.51 , 0 . 7 2 ] , [ 3 . 8 6 , 1 7. 48 , −1.7 , 1 . 9 4 , 3 . 3 6 , 3 . 0 3 , −0.61 , −2.89 , 1 6 . 7 9 , 134.65 , 15223 , −2.82 , 2 . 1 5 , 1 . 3 5 , 0 . 3 1 ] , [ 5 . 7 3 , −5.69 , 2 . 6 7 , 0 . 6 2 , 1 . 3 5 , 0 . 6 2 , −2.06 , −3.37 , 7 . 3 6 , −9.82 , −2.82 , 15190 , −79.1 , −1.08 , −0.8] , [ −9.78 , 2 . 4 6 , −7.07 , −3.62 , −2.28 , −3.69 , 1 . 5 2 , 2 . 9 4 , −2.29 , 5 . 7 6 , 2 . 1 5 , −79.1 , 15068 , −0.81 , −0.06] , [ 1 . 0 2 , 1 . 8 8 , −11.49 , 4 . 7 5 , 7 . 5 , 2 . 3 2 , −1.32 , 3 8 . 5 9 , 2 . 4 3 , −0.51 , 1 . 3 5 , −1.08 , −0.81 , 15190 , −1.66] , [ 0 . 3 4 , 0 . 9 5 , −2.24 , 1 . 8 , −1.52 , −0.97 , 2 4. 0 7 , 8 . 1 4 , 7 . 4 1 , 0 . 7 2 , 0 . 3 1 , −0.8 , −0.06 , −1.66 , 1 5 8 0 0 ] ] ) ) matrix=np . array ( v ) m=matrix . transpose ( ) #nu z i j n de c o e f f i c i e n t s h o r i z o n t a a l ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! e x c i t o n s =[v1 , v2 , v3 , v4 , v5 , v6 , v7 , v8 , v9 , v10 , v11 , v12 , v13 , v14 , v15 ]=[m[ 0 ] ,m[ 1 ] ,m[ 2 ] ,m[ 3 ] ,m [ 4 ] ,m[ 5 ] ,m[ 6 ] ,m[ 7 ] ,m[ 8 ] ,m[ 9 ] ,m[ 1 0 ] ,m[ 1 1 ] ,m[ 1 2 ] ,m[ 1 3 ] ,m[ 1 4 ] ] #CLA a601 = [ [ 2 0 . 4 3 1 , 18.837 , 236.758 ] , [ 1 8 . 9 1 2 , 19.838 , 2 3 5 . 7 5 8 ] , [ 2 1 . 4 4 8 , 18.620 , 235.000 ] , [ 2 2 . 0 2 1 , 18.248 ,237.931 ] , [ 1 9 . 7 1 3 , 19.396 , 238.583 ] ] a602 = [ [ 2 9 . 9 1 0 , 12.038 , 231.085 ] , [ 2 9 . 5 2 7 , 10.005 , 231.225 ] , [ 3 1 . 0 4 8 , 11.695 , 229.425 ] , [ 2 9 . 8 2 6 , 14.076 ,230.791 ] , [ 2 8 . 4 4 5 , 12.488 , 232.431 ] ] a603 = [ [ 3 6 . 7 8 1 , 13.826 , 221.572 ] , [ 3 5 . 3 6 6 , 12.306 , 221.466 ] , [ 3 5 . 2 7 6 , 15.191 , 221.803 ] , [ 3 8 . 1 8 3 , 15.249 ,221.053 ] , [ 3 8 . 2 5 2 , 12.611 , 220.855 ] ] a604 = [ [ 5 0 . 5 7 0 , 26.287 , 225.916 ] , [ 5 1 . 5 3 2 , 26.428 ,224.083 ] , [ 4 9 . 8 5 2 , 24.452 , 225.378 ] , [ 5 0 . 0 7 6 , 26.075 ,227.906 ] , [ 5 1 . 5 7 5 , 27.890 , 226.675 ] ] a608 = [ [ 4 4 . 1 7 7 , 8 . 8 54 , 220.971 ] , [ 4 3 . 0 9 4 , 7 . 0 8 3 , 220.885 ] , [ 4 5 . 4 3 1 , 8 . 1 3 9 , 219.527 ] , [ 4 4 . 8 5 9 , 10.797 , 220.825 ] , [ 42.733 , 9 .7 8 1 , 222.068 ] ] a609 = [ [ 4 4 . 5 6 7 , 13.401 , 237.595 ] , [ 4 4 . 6 5 9 , 12.448 , 239.434 ] , [ 4 3 . 4 0 9 , 14.862 , 238.434 ] , [ 4 4 . 9 5 6 , 14.474 , 235.880 ] , [ 4 6 . 0 6 8 , 12.251 , 236.828 ] ] a610 = [ [ 2 9 . 7 5 8 , 21.907 , 243.215 ] , [ 3 0 . 5 4 0 , 20.874 , 244.838 ] , [ 2 8 . 3 2 5 , 22.708 , 244.430 ] , [ 2 9 . 3 8 1 , 23.201 , 241.652 ] , [ 3 1 . 3 7 6 , 21.485 , 242.047 ] ] a611 = [ [ 3 8 . 8 9 9 , 23.585 , 239.802 ] , [ 4 0 . 1 2 3 , 22.575 , 241.143 ] , [ 4 0 . 5 5 7 , 24.149 , 238.748 ] , [ 3 7 . 6 5 7 , 24.948 , 238.874 ] , [ 3 7 . 2 9 3 , 2 3 . 4 7 8 , 241.051 ] ] a612 = [ [ 2 9 . 2 8 3 , 30.852 , 226.594 ] , [ 2 9 . 1 8 2 , 32.780 , 227.360 ] , [ 2 9 . 6 1 2 , 30.128 , 228.476 ] , [ 2 8 . 9 3 1 , 2 8 . 9 9 7 , 225.768 ] , [ 2 8 . 4 9 6 , 3 1 . 4 3 3 , 224.805 ] ] a613 = [ [ 2 6 . 3 8 7 , 36.644 , 233.403 ] , [ 2 4 . 3 9 9 , 37.087 , 233.010 ] , [ 2 6 . 5 2 9 , 38.317 , 234.573 ] , [ 2 8 . 1 6 3 , 3 5 . 8 3 6 , 234.066 ] , [ 2 6 . 2 1 8 , 34.782 , 232.589 ] ] a614 = [ [ 4 8 . 0 1 9 , 3 . 2 10 , 213.347 ] , [ 4 9 . 5 0 7 , 2 . 9 0 5 , 211.931 ] , [ 4 7 . 4 9 4 , 4. 9 4 6 , 212.407 ] , [ 4 6 . 3 0 1 , 3 . 1 2 2 , 214.485 ] , [ 4 8 . 1 9 7 , 1 .3 1 0 , 214.068 ] ] #CLB b605 = [ [ 5 2 . 8 2 5 , 20.456 , 219.914 ] , [ 5 3 . 7 6 3 , 19.086 , 221.028 ] , [ 5 1 . 0 1 4 , 19.639 , 220.407 ] , [ 5 1 . 9 4 9 , 22.136 , 219.094 ] , [ 5 4 . 5 0 3 , 21.585 , 219.619 ] ] b606 = [ [ 4 5 . 6 5 1 , 23.940 , 215.055 ] , [ 4 4 . 2 5 0 , 25.207 ,214.402 ] , [ 4 4 . 2 5 4 , 22.923 , 216.149 ] , [ 4 7 . 1 0 0 ,22.499 ,215.366 ] , [ 4 7 . 1 2 0 , 2 4 . 6 9 2 , 213.855 ] ]
b607 = [ [ 5 0 . 4 5 8 , 7 . 6 1 3 , 229.243 ] , [ 5 0 . 4 4 4 , 9.611 ,229.216 ] , [ 5 2 . 4 4 8 , 7.606 ,228.769 ] , [ 5 0 . 4 6 8 , 5 .59 9 , 229.707 ] , [ 4 8 . 6 0 3 , 7 .4 6 2 , 230.084 ] ]
b615 = [ [ 6 0 . 9 7 2 , 4 . 0 1 2 , 231.907 ] , [ 6 2 . 5 4 0 , 5 .1 1 3 , 232.478 ] , [ 6 1 . 3 9 8 , 4 .3 77 , 229.939 ] , [ 5 9 . 1 2 6 , 3 . 1 8 8 , 231.467 ] , [ 6 0 . 2 5 1 , 3 .7 9 3 , 233.806 ] ]
Atoms=[a601 , a602 , a603 , a604 , b605 , b606 , b607 , a608 , a609 , a610 , a611 , a612 , a613 , a614 , b615 ] f o r i i n range ( 0 , 1 5 ) : Molecuul=Atoms [ i ] Mg=Molecuul [ 0 ] Mgx=Mg[ 0 ] Mgy=Mg[ 1 ] Mgz=Mg[ 2 ] d e f mgx(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] xn=Mg[ 0 ] r e t u r n xn d e f mgy(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] yn=Mg[ 1 ] r e t u r n yn d e f mgz(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] zn=Mg[ 2 ] r e t u r n zn d e f nax (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] xn=na [ 0 ] r e t u r n xn d e f nay (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] yn=na [ 1 ] r e t u r n yn d e f naz (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] zn=na [ 2 ] r e t u r n zn d e f nbx (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] xn=nb [ 0 ] r e t u r n xn d e f nby (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] yn=nb [ 1 ] r e t u r n yn d e f nbz (n) :
Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] zn=nb [ 2 ] r e t u r n zn d e f ncx (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] xn=nc [ 0 ] r e t u r n xn d e f ncy (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] yn=nc [ 1 ] r e t u r n yn d e f ncz (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] zn=nc [ 2 ] r e t u r n zn d e f ndx (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] xn=nd [ 0 ] r e t u r n xn d e f ndy (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] yn=nd [ 1 ] r e t u r n yn d e f ndz (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] zn=nd [ 2 ] r e t u r n zn d e f blob (x , y , z , n) : #A = 1 alpha = 20
r e t u r n np . exp ( −((x−mgx(n) ) **2 + (y−mgy(n) ) **2 + ( z−mgz(n) ) **2) /(2* alpha ) ) d e f blobna (x , y , z , n) :
alpha=20
r e t u r n np . exp ( −((x−nax (n) ) **2 + (y−nay (n) ) **2 + ( z−naz (n) ) **2) /(2* alpha ) ) d e f blobnb (x , y , z , n) :
alpha=20
r e t u r n np . exp ( −((x−nbx (n) ) **2 + (y−nby (n) ) **2 + ( z−nbz (n) ) **2) /(2* alpha ) ) d e f blobnc (x , y , z , n) :
alpha=20
r e t u r n np . exp ( −((x−ncx (n) ) **2 + (y−ncy (n) ) **2 + ( z−ncz (n) ) **2) /(2* alpha ) ) d e f blobnd (x , y , z , n) :
alpha=20
f 1=open ( 'C: \ Users \ Gebruiker \Desktop\ Studie \ S c r i p t i e \ e x c i t a t i o n F I N A L n o c o e f f i c i e n t . dx ' , 'w ' )
#change t h e anglstrom to 200 ,020 ,003 and t h e box times 0.5 f 1 . write ( '# Data c a l c u l a t e d by Tomas f u n c t i o n \n ' )
f 1 . write ( " o b j e c t 1 c l a s s g r i d p o s i t i o n s counts %s %s %s \n" %(xrechthoek , yrechthoek , zrechthoek ) )
f 1 . write ( " o r i g i n %s %s %s \n" %(x0 , y0 , z0 ) ) f 1 . write ( ' d e l t a 1 0 0\n ' )
f 1 . write ( ' d e l t a 0 1 0\n ' ) f 1 . write ( ' d e l t a 0 0 1\n ' )
f 1 . write ( " o b j e c t 2 c l a s s g r i d c o n n e c t i o n s counts %s %s %s \n"%(xrechthoek , yrechthoek , zrechthoek ) )
f 1 . write ( " o b j e c t 3 c l a s s array type double rank 0 items %s data f o l l o w s \n\n"%( xrechthoek * yrechthoek * zrechthoek ) )
KbT=204 e n e r g i e s=w d e f boltzman ( i ) : r e t u r n np . exp(−( e n e r g i e s [ i ]−min ( e n e r g i e s ) ) /(KbT) ) totdens=0 t o t c o e f f =0 b o l t z c o n s t a n t=0 f o r i i n range ( 0 , 1 5 ) : b o l t z c o n s t a n t+=boltzman ( i ) d e f t o t c o e f f ( ) : E c o e f f i c i e n t =[] f o r n i n range ( 0 ,1 5) : t o t c o e f f =0 f o r i i n range ( 0 ,1 5) : t o t c o e f f+=boltzman ( i ) / b o l t z c o n s t a n t * e x c i t o n s [ i ] [ n ]**2 E c o e f f i c i e n t . append ( t o t c o e f f ) r e t u r n E c o e f f i c i e n t b o l t z c o e f f i c i e n t=t o t c o e f f ( ) f o r x i i n range (1 , xrechthoek +1) : f o r y i i n range (1 , yrechthoek +1) : f o r z i i n range (1 , zrechthoek +1) : totdens=0 f o r n i n range ( 0 ,1 5 ) :
totdens=totdens +(blobna ( x i+x0 , y i+y0 , z i+z0 , n)+blobnb ( x i+x0 , y i+y0 , z i+z0 , n)+blobnc ( x i+x0 , y i+y0 , z i+z0 , n)+blobnd ( x i+x0 , y i+y0 , z i+z0 , n) ) f 1 . wri te ( s t r ( totdens )+' ' )
i f z i % 3 == 0 : f 1 . wr ite ( ' \n ' )
f 1 . write ( ' \ nobject " d e n s i t y ( element N) [A^−3]" c l a s s f i e l d ' ) f 1 . c l o s e ( )
import numpy as np import math
import operator
from numpy import l i n a l g as LA
#wat i s h e t middelpunt van de r e c h t h o e k ? x0 = 0 y0 = −25 z0 = 195 #wat i s de g r o o t t e van de r e c h t h o e k ? xrechthoek=70 yrechthoek=85 zrechthoek=90 np . s e t _ p r i n t o p t i o n s ( p r e c i s i o n =2, suppress=True ) w, v = LA. e i g ( np . array ( [ [15400 , −45.18 , 1 1 . 5 6 , 2 . 7 6 , 2 . 3 , 3 . 2 6 , −2.26 , −4.93 , 1 . 2 9 , −52.08 , 3 . 8 6 , 5 . 7 3 , −9.78 , 1 . 0 2 , 0 . 3 4 ] , [ −45.18 , 15205 , 3 4 . 0 5 , 6 . 8 7 , 6 . 2 1 , 6 . 5 7 , −9.26 , −27.33 , −10.66 , 8 . 8 1 , 1 7 . 4 8 , −5.69 , 2 . 4 6 , 1 . 8 8 , 0 . 9 5 ] , [ 1 1 . 5 6 , 34 . 0 5 , 15039 , −5.7 , −13.14 , 1 . 3 8 , 8 . 4 2 , 176.92 , 1 4 . 8 2 , −4.35 , −1.7 , 2 . 6 7 , −7.07 , −11.49 , −2.24] , [ 2 . 7 6 , 6 . 8 7 , −5.7 , 15453 , 84 .9 5 , 2 9 . 16 , −1.05 , −7.7 , −5.58 , −3.28 , 1 . 9 4 , 0 . 6 2 , −3.62 , 4 . 7 5 , 1 . 8 ] , [ 2 . 3 , 6 . 2 1 , −13.14 , 84 .9 5 , 15750 , 6 0 . 8 7 , −3.31 , −4.08 , −3.41 , −2.91 , 3 . 3 6 , 1 . 3 5 , −2.28 , 7 . 5 , −1.52] , [ 3 . 2 6 , 6 . 5 7 , 1 . 3 8 , 2 9 . 16 , 6 0 . 87 , 15856 , −4.54 , −13.53 , 0 . 7 2 , −3.12 , 3 . 0 3 , 0 . 6 2 , −3.69 , 2 . 3 2 , −0.97] , [ −2.26 , −9.26 , 8 . 4 2 , −1.05 , −3.31 , −4.54 , 15793 , 5 3 .4 6 , 5 1 .9 2 , 4 . 4 9 , −0.61 , −2.06 , 1 . 5 2 , −1.32 , 2 4 . 0 7 ] , [ −4.93 , −27.33 , 176.92 , −7.7 , −4.08 , −13.53 , 53 .4 6 , 15731 , 2 . 8 7 , 5 . 7 2 , −2.89 , −3.37 , 2 . 9 4 , 38 .5 9 , 8 . 1 4 ] , [ 1 . 2 9 , −10.66 , 1 4 . 8 2 , −5.58 , −3.41 , 0 . 7 2 , 5 1 .9 2 , 2 . 8 7 , 15232 , −26.23 , 1 6 . 7 9 , 7 . 3 6 , −2.29 , 2 . 4 3 , 7 . 4 1 ] , [ −52.08 , 8 . 8 1 , −4.35 , −3.28 , −2.91 , −3.12 , 4 . 4 9 , 5 . 7 2 , −26.23 , 15345 , 134.65 , −9.82 , 5 . 7 6 , −0.51 , 0 . 7 2 ] , [ 3 . 8 6 , 1 7. 48 , −1.7 , 1 . 9 4 , 3 . 3 6 , 3 . 0 3 , −0.61 , −2.89 , 1 6 . 7 9 , 134.65 , 15223 , −2.82 , 2 . 1 5 , 1 . 3 5 , 0 . 3 1 ] , [ 5 . 7 3 , −5.69 , 2 . 6 7 , 0 . 6 2 , 1 . 3 5 , 0 . 6 2 , −2.06 , −3.37 , 7 . 3 6 , −9.82 , −2.82 , 15190 , −79.1 , −1.08 , −0.8] , [ −9.78 , 2 . 4 6 , −7.07 , −3.62 , −2.28 , −3.69 , 1 . 5 2 , 2 . 9 4 , −2.29 , 5 . 7 6 , 2 . 1 5 , −79.1 , 15068 , −0.81 , −0.06] , [ 1 . 0 2 , 1 . 8 8 , −11.49 , 4 . 7 5 , 7 . 5 , 2 . 3 2 , −1.32 , 3 8 . 5 9 , 2 . 4 3 , −0.51 , 1 . 3 5 , −1.08 , −0.81 , 15190 , −1.66] , [ 0 . 3 4 , 0 . 9 5 , −2.24 , 1 . 8 , −1.52 , −0.97 , 2 4 . 0 7 , 8 . 1 4 , 7 . 4 1 , 0 . 7 2 , 0 . 3 1 , −0.8 , −0.06 , −1.66 , 1 5 8 0 0 ] ] ) ) matrix=np . array ( v ) m=matrix . transpose ( ) #nu z i j n de c o e f f i c i e n t s h o r i z o n t a a l ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! e x c i t o n s =[v1 , v2 , v3 , v4 , v5 , v6 , v7 , v8 , v9 , v10 , v11 , v12 , v13 , v14 , v15 ]=[m[ 0 ] ,m[ 1 ] ,m[ 2 ] ,m[ 3 ] ,m [ 4 ] ,m[ 5 ] ,m[ 6 ] ,m[ 7 ] ,m[ 8 ] ,m[ 9 ] ,m[ 1 0 ] ,m[ 1 1 ] ,m[ 1 2 ] ,m[ 1 3 ] ,m[ 1 4 ] ] e n e r g i e s=w #CLA
a601 = [ [ 2 0 . 4 3 1 , 18.837 , 236.758 ] , [ 1 8 . 9 1 2 , 19.838 , 2 3 5 . 7 5 8 ] , [ 2 1 . 4 4 8 , 18.620 , 235.000 ] , [ 2 2 . 0 2 1 , 18.248 ,237.931 ] , [ 1 9 . 7 1 3 , 19.396 , 238.583 ] ] a602 = [ [ 2 9 . 9 1 0 , 12.038 , 231.085 ] , [ 2 9 . 5 2 7 , 10.005 , 231.225 ] , [ 3 1 . 0 4 8 , 11.695 , 229.425 ] , [ 2 9 . 8 2 6 , 14.076 ,230.791 ] , [ 2 8 . 4 4 5 , 12.488 , 232.431 ] ] a603 = [ [ 3 6 . 7 8 1 , 13.826 , 221.572 ] , [ 3 5 . 3 6 6 , 12.306 , 221.466 ] , [ 3 5 . 2 7 6 , 15.191 , 221.803 ] , [ 3 8 . 1 8 3 , 15.249 ,221.053 ] , [ 3 8 . 2 5 2 , 12.611 , 220.855 ] ] a604 = [ [ 5 0 . 5 7 0 , 26.287 , 225.916 ] , [ 5 1 . 5 3 2 , 26.428 ,224.083 ] , [ 4 9 . 8 5 2 , 24.452 , 225.378 ] , [ 5 0 . 0 7 6 , 26.075 ,227.906 ] , [ 5 1 . 5 7 5 , 27.890 , 226.675 ] ] a608 = [ [ 4 4 . 1 7 7 , 8 . 8 54 , 220.971 ] , [ 4 3 . 0 9 4 , 7 . 0 8 3 , 220.885 ] , [ 4 5 . 4 3 1 , 8. 1 3 9 , 219.527 ] , [ 4 4 . 8 5 9 , 10.797 , 220.825 ] , [ 42.733 , 9 .7 8 1 , 222.068 ] ] a609 = [ [ 4 4 . 5 6 7 , 13.401 , 237.595 ] , [ 4 4 . 6 5 9 , 12.448 , 239.434 ] , [ 4 3 . 4 0 9 , 14.862 , 238.434 ] , [ 4 4 . 9 5 6 , 14.474 , 235.880 ] , [ 4 6 . 0 6 8 , 12.251 , 236.828 ] ] a610 = [ [ 2 9 . 7 5 8 , 21.907 , 243.215 ] , [ 3 0 . 5 4 0 , 20.874 , 244.838 ] , [ 2 8 . 3 2 5 , 22.708 , 244.430 ] , [ 2 9 . 3 8 1 , 23.201 , 241.652 ] , [ 3 1 . 3 7 6 , 21.485 , 242.047 ] ] a611 = [ [ 3 8 . 8 9 9 , 23.585 , 239.802 ] , [ 4 0 . 1 2 3 , 22.575 , 241.143 ] , [ 4 0 . 5 5 7 , 24.149 , 238.748 ] , [ 3 7 . 6 5 7 , 24.948 , 238.874 ] , [ 3 7 . 2 9 3 , 2 3 . 4 7 8 , 241.051 ] ] a612 = [ [ 2 9 . 2 8 3 , 30.852 , 226.594 ] , [ 2 9 . 1 8 2 , 32.780 , 227.360 ] , [ 2 9 . 6 1 2 , 30.128 , 228.476 ] , [ 2 8 . 9 3 1 , 2 8 . 9 9 7 , 225.768 ] , [ 2 8 . 4 9 6 , 3 1 . 4 3 3 , 224.805 ] ] a613 = [ [ 2 6 . 3 8 7 , 36.644 , 233.403 ] , [ 2 4 . 3 9 9 , 37.087 , 233.010 ] , [ 2 6 . 5 2 9 , 38.317 , 234.573 ] , [ 2 8 . 1 6 3 , 3 5 . 8 3 6 , 234.066 ] , [ 2 6 . 2 1 8 , 34.782 , 232.589 ] ] a614 = [ [ 4 8 . 0 1 9 , 3 . 2 10 , 213.347 ] , [ 4 9 . 5 0 7 , 2 . 9 0 5 , 211.931 ] , [ 4 7 . 4 9 4 , 4 . 9 4 6 , 212.407 ] , [ 4 6 . 3 0 1 , 3 . 1 22 , 214.485 ] , [ 4 8 . 1 9 7 , 1 .3 1 0 , 214.068 ] ] #CLB b605 = [ [ 5 2 . 8 2 5 , 20.456 , 219.914 ] , [ 5 3 . 7 6 3 , 19.086 , 221.028 ] , [ 5 1 . 0 1 4 , 19.639 , 220.407 ] , [ 5 1 . 9 4 9 , 22.136 , 219.094 ] , [ 5 4 . 5 0 3 , 21.585 , 219.619 ] ] b606 = [ [ 4 5 . 6 5 1 , 23.940 , 215.055 ] , [ 4 4 . 2 5 0 , 25.207 ,214.402 ] , [ 4 4 . 2 5 4 , 22.923 , 216.149 ] , [ 4 7 . 1 0 0 ,22.499 ,215.366 ] , [ 4 7 . 1 2 0 , 2 4 . 6 9 2 , 213.855 ] ] b607 = [ [ 5 0 . 4 5 8 , 7 . 6 1 3 , 229.243 ] , [ 5 0 . 4 4 4 , 9.611 ,229.216 ] , [ 5 2 . 4 4 8 , 7.606 ,228.769 ] , [ 5 0 . 4 6 8 , 5 .5 9 9 , 229.707 ] , [ 4 8 . 6 0 3 , 7 .4 6 2 , 230.084 ] ] b615 = [ [ 6 0 . 9 7 2 , 4 . 0 1 2 , 231.907 ] , [ 6 2 . 5 4 0 , 5 .1 1 3 , 232.478 ] , [ 6 1 . 3 9 8 , 4 .3 77 , 229.939 ] , [ 5 9 . 1 2 6 , 3 .1 8 8 , 231.467 ] , [ 6 0 . 2 5 1 , 3 .7 9 3 , 233.806 ] ]
Atoms=[a601 , a602 , a603 , a604 , b605 , b606 , b607 , a608 , a609 , a610 , a611 , a612 , a613 , a614 , b615 ] f o r i i n range ( 0 , 1 5 ) : Molecuul=Atoms [ i ] Mg=Molecuul [ 0 ] Mgx=Mg[ 0 ] Mgy=Mg[ 1 ] Mgz=Mg[ 2 ] d e f mgx(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] xn=Mg[ 0 ] r e t u r n xn d e f mgy(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] yn=Mg[ 1 ] r e t u r n yn d e f mgz(n) : Molecuul=Atoms [ n ] Mg=Molecuul [ 0 ] zn=Mg[ 2 ] r e t u r n zn
d e f nax (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] xn=na [ 0 ] r e t u r n xn d e f nay (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] yn=na [ 1 ] r e t u r n yn d e f naz (n) : Molecuul=Atoms [ n ] na=Molecuul [ 1 ] zn=na [ 2 ] r e t u r n zn d e f nbx (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] xn=nb [ 0 ] r e t u r n xn d e f nby (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] yn=nb [ 1 ] r e t u r n yn d e f nbz (n) : Molecuul=Atoms [ n ] nb=Molecuul [ 2 ] zn=nb [ 2 ] r e t u r n zn d e f ncx (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] xn=nc [ 0 ] r e t u r n xn d e f ncy (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] yn=nc [ 1 ] r e t u r n yn d e f ncz (n) : Molecuul=Atoms [ n ] nc=Molecuul [ 3 ] zn=nc [ 2 ] r e t u r n zn d e f ndx (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] xn=nd [ 0 ] r e t u r n xn d e f ndy (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] yn=nd [ 1 ]
r e t u r n yn d e f ndz (n) : Molecuul=Atoms [ n ] nd=Molecuul [ 4 ] zn=nd [ 2 ] r e t u r n zn d e f blob (x , y , z , n) : #A = 1 alpha =100
r e t u r n np . exp ( −((x−mgx(n) ) **2 + (y−mgy(n) ) **2 + ( z−mgz(n) ) **2) /(2* alpha ) ) d e f blobna (x , y , z , n) :
alpha=100
r e t u r n np . exp ( −((x−nax (n) ) **2 + (y−nay (n) ) **2 + ( z−naz (n) ) **2) /(2* alpha ) ) d e f blobnb (x , y , z , n) :
alpha=100
r e t u r n np . exp ( −((x−nbx (n) ) **2 + (y−nby (n) ) **2 + ( z−nbz (n) ) **2) /(2* alpha ) ) d e f blobnc (x , y , z , n) :
alpha=100
r e t u r n np . exp ( −((x−ncx (n) ) **2 + (y−ncy (n) ) **2 + ( z−ncz (n) ) **2) /(2* alpha ) ) d e f blobnd (x , y , z , n) :
alpha=100
r e t u r n np . exp ( −((x−ndx (n) ) **2 + (y−ndy (n) ) **2 + ( z−ndz (n) ) **2) /(2* alpha ) )
KbT=204 e n e r g i e s=w d e f boltzman ( i ) : r e t u r n np . exp(−( e n e r g i e s [ i ]−min ( e n e r g i e s ) ) /(KbT) ) totdens=0 t o t c o e f f =0 b o l t z c o n s t a n t=0 f o r i i n range ( 0 , 1 5) : b o l t z c o n s t a n t+=boltzman ( i ) d e f t o t c o e f f ( ) : b o l t z c o e f f i c i e n t =[] f o r n i n range ( 0 , 1 5) : t o t c o e f f =0 f o r i i n range ( 0 , 1 5) : t o t c o e f f+=boltzman ( i ) / b o l t z c o n s t a n t * e x c i t o n s [ i ] [ n ]**2 b o l t z c o e f f i c i e n t . append ( t o t c o e f f ) r e t u r n b o l t z c o e f f i c i e n t b o l t z c o e f f i c i e n t=t o t c o e f f ( )
f 2=open ( 'C: \ Users \ Gebruiker \Desktop\ Studie \ S c r i p t i e \ EnergyFINALnocoefficient . dx ' , 'w ' )
