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remove mention of lesson and module instead of resource
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_build/classical_methods/intro.md

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# Classical methods
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**Classical methods** is a phrase used to describe techniques that make use of a potential model (sometimes called a force-field) to simulated chemical systems.
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These can be molecular dynamics (which we will cover in this module), Monte Carlo, Langevin dynamics, etc.
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These can be molecular dynamics (which we will cover in this resource), Monte Carlo, Langevin dynamics, etc.
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In order to simulate a **real** chemical system, it is necessary to model the electrons and their interactions.
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This is achieved by using quantum mechanical calculations, where the energy of a chemical system is calculated by finding an approximate solution to the Schrödinger equation.
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The first is some ground-state quantum mechanical method (e.g. density functional theory), however as mentioned above these are limited in system size.
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The alternative involves modelling the electron distributions with some mathematical function to determine the potential energy.
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These **potential models** are usually faster to calculate than the quantum mechanical method and therefore may be used on larger systems.
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However, this **simplification** does have a drawback in that the correct potential models must be determined for each system to accurately determine the energy.
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However, this **simplification** does have a drawback in that the correct potential models must be determined for each system to accurately determine the energy.

_build/important_considerations/ensembles.md

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---
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## Ensembles
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The molecular dynamics algorithm outlined in the previous lesson makes use of the NVE ensemble (also known as the microcanonical ensemble), where the number of particles (N), volume of the system (V), and energy of the system (E) are all **kept constant**.
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The molecular dynamics algorithm outlined in the previously makes use of the NVE ensemble (also known as the microcanonical ensemble), where the number of particles (N), volume of the system (V), and energy of the system (E) are all **kept constant**.
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This is not the only, or the most accurate, ensemble that exists, there is also other such as:
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- NVT (canonical): number of particles (N), volume of system (V), temperature of the simulation (T)
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- NPT (isothermal-isobaric): number of particles (N), pressure of system (P), temperature of the simulation (T)
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$$ v_i = v_i \sqrt{\dfrac{T_{\text{target}}}{\bar{T}}}, $$
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where $T_{\text{target}}$ is the target temperature for the themostat, and $\bar{T}$ is the average simulation temperature.
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pylj [[1,2](#references)], the software that you shall use in the next lesson uses this method for producing an NVT simulation, using the `heat_bath` function.
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pylj [[1,2](#references)], the software that you shall use later uses this method for producing an NVT simulation, using the `heat_bath` function.
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Various **other methods** for thermostatting exist, such as the Anderson, Nosé-Hoover, or the Berendsen [[3-6](#references)].
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In order to achieve the NPT ensemble, it is necessary to use a **barostat** in addition to a thermostat.

_build/important_considerations/pbc.md

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</center>
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When a particle reaches the cell wall it moves into the adjecent cell, and since all the cells are identical, it appears on the other side.
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The code below modifies the `update_pos` and `get_acceleration` functions from the previous lesson to account for the periodic boundary condition.
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The code below modifies the `update_pos` and `get_acceleration` functions defined previously to account for the periodic boundary condition.
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_build/molecular_dynamics/intro.md

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In the above equation, $r_x$ is the distance between the two particles in the $x$-dimension and $\mathbf{r}$ is the overall distance vector.
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The above equation must be determined to find the force in each dimension.
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However, this lesson will **only** consider particles interacting in a one-dimensional space.
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However, currently we will **only** consider particles interacting in a one-dimensional space.
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The Python code below shows how to determine the acceleration on each atom of argon due to each other atom of argon.
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Due to Newton's third law, we are able to **increase the efficiency** of this algorithm as the force on atom $i$ will be equal and opposite to the force on atom $j$.

_build/parameterisation/intro.md

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Commonly this involves either experimental measurements, e.g. X-ray crystallography, or quantum mechanical calculations; we will be focusing on the latter.
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More can be found out about quantum mechanical calculations in the textbooks mentioned in the introduction (in particular Jeremy Harvey's Computational Chemistry Primer [[1](#references)]).
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However, for our current purposes we only need to remember the previous lesson where it was introduced that quantum calculations are more accurate than classical simulations.
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However, for our current purposes we only need to remember that quantum calculations are more accurate than classical simulations.
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### Quantum mechanical calculations
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These are more accurate then classical simulations. However, they are severely limited in the system size, with a maximum simulation size in the order of hundreds atoms.
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### Parameterising a Lennard-Jones interaction
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We will stick with the example of a Lennard-Jones interaction, however the arguments and methods discussed are **extensible to all different interaction types**.
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To generate the potential energy model between two particles of argon, we could conduct quantum mechanical calculations at a range of inter-atom separations, from 3 to 8 Å, finding the energy between the two particles at each separation.
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content/classical_methods/intro.md

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# Classical methods
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**Classical methods** is a phrase used to describe techniques that make use of a potential model (sometimes called a force-field) to simulated chemical systems.
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These can be molecular dynamics (which we will cover in this module), Monte Carlo, Langevin dynamics, etc.
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These can be molecular dynamics (which we will cover in this resource), Monte Carlo, Langevin dynamics, etc.
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In order to simulate a **real** chemical system, it is necessary to model the electrons and their interactions.
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This is achieved by using quantum mechanical calculations, where the energy of a chemical system is calculated by finding an approximate solution to the Schrödinger equation.
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The first is some ground-state quantum mechanical method (e.g. density functional theory), however as mentioned above these are limited in system size.
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The alternative involves modelling the electron distributions with some mathematical function to determine the potential energy.
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These **potential models** are usually faster to calculate than the quantum mechanical method and therefore may be used on larger systems.
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However, this **simplification** does have a drawback in that the correct potential models must be determined for each system to accurately determine the energy.
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However, this **simplification** does have a drawback in that the correct potential models must be determined for each system to accurately determine the energy.

content/important_considerations/ensembles.md

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## Ensembles
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The molecular dynamics algorithm outlined in the previous lesson makes use of the NVE ensemble (also known as the microcanonical ensemble), where the number of particles (N), volume of the system (V), and energy of the system (E) are all **kept constant**.
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The molecular dynamics algorithm outlined in the previously makes use of the NVE ensemble (also known as the microcanonical ensemble), where the number of particles (N), volume of the system (V), and energy of the system (E) are all **kept constant**.
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This is not the only, or the most accurate, ensemble that exists, there is also other such as:
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- NVT (canonical): number of particles (N), volume of system (V), temperature of the simulation (T)
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- NPT (isothermal-isobaric): number of particles (N), pressure of system (P), temperature of the simulation (T)
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$$ v_i = v_i \sqrt{\dfrac{T_{\text{target}}}{\bar{T}}}, $$
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where $T_{\text{target}}$ is the target temperature for the themostat, and $\bar{T}$ is the average simulation temperature.
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pylj [[1,2](#references)], the software that you shall use in the next lesson uses this method for producing an NVT simulation, using the `heat_bath` function.
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pylj [[1,2](#references)], the software that you shall use later uses this method for producing an NVT simulation, using the `heat_bath` function.
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Various **other methods** for thermostatting exist, such as the Anderson, Nosé-Hoover, or the Berendsen [[3-6](#references)].
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In order to achieve the NPT ensemble, it is necessary to use a **barostat** in addition to a thermostat.

content/important_considerations/pbc.ipynb

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"metadata": {},
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"source": [
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"When a particle reaches the cell wall it moves into the adjecent cell, and since all the cells are identical, it appears on the other side. \n",
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"The code below modifies the `update_pos` and `get_acceleration` functions from the previous lesson to account for the periodic boundary condition."
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"The code below modifies the `update_pos` and `get_acceleration` functions defined previously to account for the periodic boundary condition."
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]
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},
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{

content/molecular_dynamics/intro.ipynb

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"\n",
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"In the above equation, $r_x$ is the distance between the two particles in the $x$-dimension and $\\mathbf{r}$ is the overall distance vector. \n",
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"The above equation must be determined to find the force in each dimension. \n",
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"However, this lesson will **only** consider particles interacting in a one-dimensional space. \n",
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"However, currently we will **only** consider particles interacting in a one-dimensional space. \n",
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"\n",
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"The Python code below shows how to determine the acceleration on each atom of argon due to each other atom of argon. \n",
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"Due to Newton's third law, we are able to **increase the efficiency** of this algorithm as the force on atom $i$ will be equal and opposite to the force on atom $j$. "

content/parameterisation/intro.ipynb

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"Commonly this involves either experimental measurements, e.g. X-ray crystallography, or quantum mechanical calculations; we will be focusing on the latter. \n",
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"\n",
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"More can be found out about quantum mechanical calculations in the textbooks mentioned in the introduction (in particular Jeremy Harvey's Computational Chemistry Primer [[1](#references)]).\n",
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"However, for our current purposes we only need to remember the previous lesson where it was introduced that quantum calculations are more accurate than classical simulations."
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"However, for our current purposes we only need to remember that quantum calculations are more accurate than classical simulations."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Parameterising a Lennard-Jones interaction\n",
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"\n",
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"We will stick with the example of a Lennard-Jones interaction, however the arguments and methods discussed are **extensible to all different interaction types**. \n",
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"To generate the potential energy model between two particles of argon, we could conduct quantum mechanical calculations at a range of inter-atom separations, from 3 to 8 Å, finding the energy between the two particles at each separation.\n",
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"\n",

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