SUMMARIES: W1-W8. LECTURE NOTE. CHEM3123 PDF

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Theories A theory expresses the behaviour of a physical system in a way that can be tested. The theory of classical mechanics, eg F = ma The theory of quantum mechanics, eg H � = E � Theories have limits of applicability Models A model involves a set of assumptions that simplify a theory so it can b...

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Theories A theory expresses the behaviour of a physical system in a way that can be tested. • The theory of classical mechanics, eg F = ma • The theory of quantum mechanics, eg H � = E � Theories have limits of applicability Models A model involves a set of assumptions that simplify a theory so it can be utilised to solve or gain understanding of a given (practical) problem. • Hybridization (sp3 etc) is a model for quantum mechanics that allows us to understand the geometry of organic molecules • Models should be derived from underlying theories • Models should be well-defined • Models are validated by comparison to experiment and/or more detailed theory Models have limits of applicability Why Model? • Explanation – to explain an outcome in terms of underlying physical principles, eg why an organic reaction yields a given product • Prediction – to apply a model in an unknown situation eg to predict results of a new (difficult, dangerous) experiment • Interpretation – extracting information from a model to determine how outcome depends on specific parameters. • After the fact, eg of the possible products, which one formed, • Before the fact, eg to optimise experimental conditions to obtain a given product • Discovery – modelling can discover new, emergent behaviour • Cheap – computers are getting cheaper, faster and have more memory • Resource-Friendly – there are no experimental consumables or chemical wastes • Safe – there is no risk of blowing up a fume hood Chemical Models A chemical model is a representation of some aspect of a chemical system that is simplified so as to be intelligible while still effectively capturing some aspect of reality. Making a Model For all practical purposes the basic physical equations governing the behaviour of a system at the molecular level can only be solved approximately. An accurate, reliable model should: • contain the essential physics and chemistry, • be computationally tractable, • preferably be amenable to systematic refinement. John Pople’s Golden Rule: Before applying a particular model to an (experimentally) unknown situation it is essential to apply the same model to situations where experimental information (for similar systems) is available • Unless the model performs satisfactorily in cases where we know the answer, there is little point in using it to probe the unknown • Conversely, if the model does work well in known situations this lends confidence to the results obtained in the unknown case. Computational Modelling • Calculations (on a computer) used to test theories and models by solving the mathematical equations that define theory or the model • Calculations (on a computer) used to predict the outcomes of a theory or model

• Computational models should be well-defined, efficient, be accurate for the problem at hand and provide results in a way that is easy to interpret and understand. • Predicting the structure of a molecule • Scoring how well a drug molecule can bind to a protein active site General Modelling Strategies: Dimensional Analysis Physical phenomena are typically characterised by one or more length scales and energy scales An Example: The Belousov-Zhabotinsky Reaction • A simple model (Ball, 1994) that captures the essence of the Belousov-Zhabotinsky reaction is essentially three coupled reactions: A + B → 2A (R1) B + C → 2B (R2) C + A → 2C (R3)

The concentration of A grows proportionately to itself (exponential increase) As A increases, C increases and the concentration of B grows. The concentration of A then decreases due to interaction between A and B. Predator-Prey interactions

L2 Key Python Syntax: Comments Comment Lines are crucially important!! • Comments are not executed by the computer. They are used to clarify code: • To remind the user of the units of a variable • To explain what the code is doing • To make the code more readable for future people who might use it • They can be used to prevent execution of a command when testing code • You can use the “Cell Type” within a Jupyter Python 3 notebook • You can indicate a comment in a code cell with # • Comments can be whole lines or parts of a line, eg following a Python command to explain it: deltaH = -541.5 # change in enthalpy in kJ/mol • Multiple comment lines need a # at the beginning of each line Key Python Syntax: Variables Variables are ways of storing data. A variable and its type are created when you assign it. • Common variable types are: • strings (str) are alphanumeric sequences, like words: name = “Meredith”, name = ‘Meredith’ • integers (int) can be positive, negative or zero: Temp = 25 + 273 • floating point numbers (float) are real numbers: deltaH = -541.5 • The function type() returns the variable type of a variable • Variables are case sensitive, name, Name and NAME are different variables • You can define multiple variables at once: deltaH, deltaS, temp = -541.5, 10.4, 298 • Casting specifies or changes a variable type: • deltaG_string = str(deltaG) defines a new string variable, from a floating point variable Key Python Syntax: Lists Lists are a data structure that can group several values or variables together.

• Lists are defined (declared) using square brackets [], where the list values are separated by commas • List items are indexed, Python indexing starts at 0, the first item is [0], the second it [1]etc • The function len returns the list length • List items can be any data type • List elements can be used in calculations • Lists can be sliced # This is a list energy_kcal = [-13.4, -2.7, 5.4, 42.1] # energies from an American paper in kcal/mol # I can determine its length energy_length = len(energy_kcal) # print the list length print('The length of this list is', energy_length) The length of this list is 4 Key Python Syntax: Loops Loops let you repeat something for every element in a list. Loops are indicated by a colon, :, and by indenting Key Python Syntax: Common Operations Logic Operations • equal to == • not equal to != • greater than > • less than < • greater than or equal to >= • less than or equal to...