computational chemistry

Question 1

computational chemistry definition

Answer 1

comparing/linking experimental data with theory via computational modelling

Question 2

what is a calculation in computational chemistry?

Answer 2

a function which runs input data/models to get an output

Question 3

computational cost definition

Answer 3

how long a calculation takes to run / how long before calculation converges (is completed) - depends on processors used + quality and intensiveness of calculation

Question 4

why is compramise so important in computational chemistry?

Answer 4

low quality calculations work faster, higher quality calculations take longer, compromise between quality of data and speed of calculation

Question 5

what are the 7 main methods in order of increasing quality

Answer 5

MM
SE
MD
PBC
QM/MM
DFT
HF

Question 6

what is MM + common versions + how does it work?

Answer 6

molecular mechanics
versions = UFF
treats atoms as balls + springs, uses classical physics

Question 7

what is SE + common versions + how does it work?

Answer 7

semi empirical
versions = PM3, PM6, AM1
uses approximations to simplify/lower the computational method

Question 8

what is HF + common versions + how does it work?

Answer 8

hartree fock
versions = HF only
a sum of many electron wavefunctions, fails to capture exchange / correlation

Question 9

what is DFT + common versions + how does it work?

Answer 9

density functional theory
versions = PBE, BP86, MO6, B3LYP, wB97XD
uses functions to describe electron density rather than 4 parameters for every electron

Question 10

what is PBC + common versions + how does it work?

Answer 10

periodic boundary conditions
versions = any HF or DFT
used for periodic repeating structures e.g. solids

Question 11

what is MD + common versions + how does it work?

Answer 11

molecular dynamics
versions = MM or SE
applies newtonian physics to atoms/models

Question 12

what is QM/MM + common versions + how does it work?

Answer 12

a hybrid: quantum mech + molecular mech
versions for QM = SE, HF or DFT
splits the system, core = QM, outer = MM

Question 13

what do QM/MM, DFT, HF and CC, MP2, CI have in common?

Answer 13

(CC, MP2 and CI are all very high quality methods)
all methods are on the higher quality end and all use schrodingers equation

Question 14

what are inputs in computational chemistry?

Answer 14

models of molecules built from scratch via graphical user interface (GUI) or imported x-ray crystal structures
geometries of atom connectivity is described with cartesian and internal coordinates

Question 15

constraint definition

Answer 15

a limit/restriction on a parameter - keeps it constant
these are added to calculations to ensure consistency between calculations

Question 16

optimisation definition

Answer 16

the process by which we can find the lowest energy structure

Question 17

give a limitation of optimisation calculations + how to work around this

Answer 17

there is a danger that optimisation processes can trap you in a local minimum, when the global minimum is the real lowest energy structure/point
to work around this, a conformational search can be used to test many starting geometries
continue comparing parameters to previous criteria until any changes result in no further decrease in energy, this is the end point of the calculation

Question 18

why are flatter minima harder to find that steep minima?

Answer 18

the optimisation runs using the information given by the gradient, if the minima is shallower the gradient value is smaller making the minima harder to find, whereas if the minima is steep, the gradient value is much larger and the minima is much easier to find

Question 19

cycle definition

Answer 19

one circuit
the number of cycles done depends on the number of atoms in your system (=N)

Question 20

what is the maximum number of cycles?

Answer 20

3N - usually this is enough, but is the system is very small or input is very far from the minimum more than 3N cycles may be needed, needs ‘scf=xqc’

Question 21

how are chemical reactions modelled?

Answer 21

as a potential energy surface = a multidimensional reaction surface that describes all possible reaction mechanisms - looking at just one molecule isn’t always enough to find the lowest energy state of the system

Question 22

reaction coordinate definition

Answer 22

the few pathways relevant to the progress of a reaction + location of a minimum/stationary point

Question 23

stationary point definition

Answer 23

the point on a graph where the gradient = 0, either minima or maxima

Question 24

how do humans limit the determination of stationary points in a reaction coordinate/scheme?

Answer 24

as humans control the function + what the computer looks for, we start to become the limiting factor as you cant search for things you haven’t thought of

Question 25

transition state definition

Answer 25

geometry linking the local minimum structures (therefore is a maximum, = the energetic barrier to interconvert between minima structures)

Question 26

what are the 2 main methods to identify transition states?

Answer 26

- guessing the structure using software to find the midpoint between start and end structures - computing scans along reaction coordinate to find the potential maximum structure - this can be subjective as it requires chemical knowledge to select bond length/angle/dihedral

Question 27

how are optimisations to a transition state different to normal optimisations?

Answer 27

normal optimisations aim to locate a minimum on the potential energy surface, whereas transition states are maxima and so transition state optimisations aim to find a first order saddle point on potential energy surface - because it is a maxima being located and not a minima, these optimisations also require tighter convergence threshholds

Question 28

how can a transition state be identified?

Answer 28

a transition state should have one negative imaginary frequency as it is a maximum, this frequency corresponds to the pathway between reactant product, the reaction coordinate

Question 29

what are the 6 calculation types?

Answer 29

energy frequency optimisation IRC scan NMR

Question 30

what does an energy calculation do + what will output geometry be?

Answer 30

energy/single point calculations calculate input geometry without modifying for specified geometry output is same as input

Question 31

what does a frequency calculation do + what will output geometry be?

Answer 31

freq/frequency single point calculations calculate the thermodynamics for input geometry without modifying it output is same as input

Question 32

what does an optimisation calculation do + what will output geometry be?

Answer 32

opt/optimisation to a minimum/optimisation to a transition state (Berny) calculations change structural paramters on input geometry until minimum/maximum stationary point found on potential energy surface output = minimum/maximum stationary point

Question 33

what does an IRC calculation do + what will output geometry be?

Answer 33

intrinsic coordinate reaction calculations follow the motion of the imaginary frequency of a transition state to locate minima either side of the maxima output is 2 intermediates on either side of the transition state structure

Question 34

what does a scan calculation do + what will output geometry be?

Answer 34

scan/constraint calculations calculate a defined parameter to be higher or lower plotted with the maxima - a potential transition state output is constrained, likely not a minimum

Question 35

what does an NMR calculation do + what will output geometry be?

Answer 35

calculates vectors on an atomic model output is same as input

Question 36

what do optimisation strategies do?

Answer 36

for any optimisation strategy, there will be an attempt to locate the potential energy (v) minimum for coordinates R

Question 37

give 3 types of optimisation strategy

Answer 37

- random change in coordinates - the algorithm/method moves the atom position randomly and checks if this results in an energy decrease - steepest descent - uses gradient to get directions, to ensure the progression is down the well towards the lowest point in energy - newton-raphson - uses gradient and inverse of hessian as a quadratic optimisation to find the maximum point b y taking small steps, this is sueful for then you're very close to the minimum/maximum point

Question 38

how can optimisations be made easier?

Answer 38

the starting geometry should be made as reasonable as possible, this can be achieved by using x-ray structures or modified structures based on previous successful optimisations

Question 39

when is an optimisation considered officially converged?

Answer 39

when the change in total energy, the gradient, and the suggested atom displacements are all below the assigned threshold value

Question 40

absolute energy definition

Answer 40

the output energy from calculation - this is a combination of nucleus-nucleus repulsion energy, electron-nucleus attraction energy, electron-electron repulsion energy, and electronic kinetic energy

Question 41

hartree definition

Answer 41

the negative electric potential energy of the electron in a H atom in its ground state, which is approximately twice its ionisation energy

Question 42

what is necessary to compare 2 calculations + why?

Answer 42

the number of atoms and electrons must be the same exactly - can be a combination of calculations that are summed to equate to the same number of atoms and electrons this means methodology errors are less substantial, as the same approximations are used and so cancel out, meaning relative energies can be accurately compared

Question 43

when does relative energy = 0 in the system?

Answer 43

at the starting point/species

Question 44

what is ΔE?

Answer 44

energy change = energy product - energy reactant

Question 45

can isomers be compared?

Answer 45

isomer = molecules with the same number of atoms and electrons so yes they can be compared

Question 46

basis set definition

Answer 46

describes atomic orbitals using mathematical functions called basis functions - an infinite number of functions is needed for the basis set to be complete (not possible)

Question 47

why is it important to compromise on basis functions?

Answer 47

the more basis functions you have to describe an atom the better it'll look/the more accurate it'll be but this also increases computing time

Question 48

how do you decide how many basis sets should be used?

Answer 48

this depends on what is being modelled - smaller atoms won't need as many basis sets whereas with larger atoms usually approximations are made (e.g. we don't need to look at all core electrons, focus on more important/relevant valence electrons)

Question 49

basis set limit definition

Answer 49

when the output can no longer be improved by increasing number of basis sets

Question 50

what are the 2 types of basis functions?

Answer 50

slater type orbitals (STOs) gaussian type orbitals (GTOs)

Question 51

what is the difference between STOs and GTOs?

Answer 51

STOs have better wave function description but are hard to computationally manipulate GTOs give a poorer fit but linear combinations make overlap and integral calculations easier STOs use spherical coordinates whereas GTOs use cartesian coordinates - visually, pointed top for STO vs curve slope for GTO, STO is steeper at short distances and have slower decay

Question 52

how are GTOs and STOs similar?

Answer 52

both have an exponential dependency on distance from nuclei - as r increases function tends to 0

Question 53

when are STOs used?

Answer 53

in minimal basis sets, they approximate electron density better they are cheap but low accuracy, results are not publishable

Question 54

minimal basis set definition

Answer 54

these use just one basis function per atomic orbital - single zeta basis set written as STO-nG, where n = no. gaussian primtive functions

Question 55

when are GTOs used?

Answer 55

used in split-valence basis sets

Question 56

split valence set definition

Answer 56

more than one basis function is used to represent each valence orbital written as X-YZG, where X = no. primitive gaussians (core basis functions) Y and Z = basis functions describing valence, composed of a linear combination of Y and Z primitive gaussian functions respectively

Question 57

can GTOs be turned into STO type functions?

Answer 57

sums of GTOs/primitives can be used to achieve a slater type function, they easily multiply

Question 58

how does exponent affect the GTO function?

Answer 58

larger exponent = tighter function, whereas a smaller exponent = more diffuse function - using this and height as a scaling factor, many different GTOs can be combined and normalised to receive a basis function that resembles STO functions

Question 59

what is the maximum for GTOs on y axis?

Answer 59

maximum is y = 1, as it only describes 1 electron

Question 60

outline the relation between basis functions and atomic orbitals

Answer 60

basis functions are mathematical functions to describe orbitals

Question 61

what is the difference between single/double/triple zeta functions?

Answer 61

single = 1 basis function per atomic orbital double = 2 basis functions per atomic orbital triple = 3 basis functions per atomic orbital this affect the name of the basis set - 2 numbers after hyphen = double zeta, 3 numbers after = triple set

Question 62

how does zeta affect accuracy?

Answer 62

larger zeta = greater accuracy

Question 63

what does * mean in split valence basis set naming?

Answer 63

* means its a polarisation function, this adds an auxiliary function with an additional node (orbital of higher angular momentum), allowing orbitals to be more asymmetrical around the nucleus * = polarisation to all except H and He ** = polarisation to all

Question 64

what does + mean in split valence basis set naming?

Answer 64

+ or 'aug' means augmented, this adds a larger auxiliary function (a higher principle QN) making it a diffuse function, allowing electron density to be described further out - shallow GTOs better represent the tail portion of atomic orbitals that are further from nuclei, this is important for anions/other large soft molecular systems + = diffuse added to all atoms except H and He ++ = diffuse added to all atoms

Question 65

how does basis set affect optimisation?

Answer 65

optimising with a bigger basis set is computationally expensive

Question 66

how can basis sets be changed to work around computational costs when optimising?

Answer 66

the geometry should first be optimised with a smaller basis set, then a single point calculation can be done with a larger basis set on the output geometry - this provides an improved energy value without as much additional cost

Question 67

when is basis set correction most important?

Answer 67

when optimising anionic molecules - we need the smallest basis set for the problem, and are mostly interested in chemical behaviour of valence electrons rather than core electrons, which aren't as involved although they account for the larger contribution to the total computed energy for the electronic structure

Question 68

how are core electrons accounted for when compromising computational cost via basis set correction?

Answer 68

pseudopotentials/effective core potentials (ECPs) are often used to account for core electrons

Question 69

how do ECPs work?

Answer 69

they use an approximation to replace the complicated effects of the core electrons, making calculations cheaper for elements larger than Ar, it uses a frozen core approach, replacing electrons with an effective potential and focusing on computing valence electrons, reducing computation cost and basis set size, while still allowing relativistic effects to be dealt with

Question 70

how to choose basis sets?

Answer 70

depends on the problem/goal - transition metal complexes need larger basis sets on the metal and coordination sphere, but can tolerate a smaller basis set for remaining atoms - NMR/EPR spectroscopy calculations need to describe core electrons