CHE3935. Lecture 4 Quantum Mechanical Simulation Methods Continued

Transcription

1 CHE3935 Lecture 4 Quantum Mechanical Simulation Methods Continued 1

2 OUTLINE Review Introduction to CPMD MD and ensembles The functionals of density functional theory Return to ab initio methods Binding energies Level of theory Basis set superposition errors Complete basis set limit calculations Playing with Gaussian Viewing CPMD results 2

3 Review What have we done? Describe how quantum mechanical calculations are carried out. What questions do you have? 3

4 Brief CPMD Overview This is a periodic DFT method specifically designed for efficient ab initio MD simulations Uses plane waves & pseudopotentials Uses the Car-Parrinello method Files needed: Input file, e.g., 01_2H2O-wave.inp Pseudopotentials for each atom type Look at the input file: vi 03_2H2O-MD.inp Look at O_q6 4

5 Pseudopotentials for CPMD The pseudopotentials required to run CPMD must be generated in some way. There are a huge number of different pseudopotentials, most of which will not work for CPMD. Two sources of CPMD pseudopotentials are: Goedecker-Teter-Hutter: Dispersion corrected: 5

6 CPMD: Things To Do Optimize the wavefunction (SCF calculation) Use the wavefunction from previous job in a new calculation Optimize the geometry Run molecular dynamics: NVE (constant energy) NVT Nosé-Hoover chains NVT Berendsen thermostat NVT temperature scaling 6

7 First Things First Optimize the wavefunction: Edit the 01_2H2O-wave.inp file. Identify and discuss different parts of the file. Change parameters as desired: CONVERGENCE ORBITALS (see CPMD manual) GC-CUTOFF (see CPMD manual) CUTOFF (see CPMD manual) 1 Rydberg (Ry) = 0.5 Hartree 1 Ha = 2 Ry = kj/mol = kcal/mol = ev = J ISOTOPES. Note we are simulating D 2 O, not H 2 O.Why? qsub run01.batch 7

8 Optimization (Local Minimum) View the 02_2H2O-geoopt.inp file. Look at the options: OPTIMIZE GEOMETRY XYZ (look at CPMD manual) CONVERGENCE GEOMETRY MAXSTEP Make a new directory and copy the needed files. What files do you need? Check the 02_2H2O-geoopt.inp file. Submit the optimization job: qsub run02.batch 8

9 Statistical Mechanical Review Molecular dynamics is essentially based on Newton s equations of motion: F = mm F = V = mm In the absence of external (non-conservative) forces integration of the equations of motion leads to interconversion of potential (V) and kinetic ( 1 2 mv2 = T) energies Hence, the Hamiltonian (H = T + V) or total energy is conserved. This is the so-called microcanonical ensemble, AKA NVE ensemble. However, most of the time we want to study systems in the canonical or NVT ensemble There are many ways to approximate the NVT ensemble in MD, but none of them is perfect (exact) and most of them are dangerous (my opinion). 9

10 CPMD: MD Options Molecular dynamics options: NVE (constant energy) TEMPERATURE 400 NVT Nosé-Hoover chains NOSE IONS 400.0d d0 NOSE ELECTRONS d d0 NVT Berendsen thermostat BERENDSEN IONS NVT temperature scaling TEMPCONTROL IONS Make changes to 03_2H2O-MD.inp If run01.batch has finished then qsub run03.batch, else wait 10

11 Back To Ab Initio Methods Another look at basis sets Pople basis sets Notation X-YZ, where X=# of primitive Gaussians for each core electron basis function, YZ indicates two basis functions used for each valence electron orbitals, Y, Z =# of primitive Gaussian functions 3-21G is a small basis set, but double zeta quality. 6-31G is a moderate basis set. 6-31G* adds polarization functions (higher angular momentum) G adds diffuse functions (additional Gaussians with small exponent coefficients, α in e αr2. Correlation-consistent basis sets cc-pvxz = x-zeta (double, triple, etc.) quality basis set. aug-cc-pvxz = augmented with diffuse functions. 11

12 Calculation of Binding Energies Binding energy between a pair of molecules (1 and 2) can be expressed as: E b = E 12, c E 1 E 2 Where the geometry of the cluster is relaxed or optimized with respect to the isolated molecules. Binding energies: Weigh luggage by weighing a loaded 747 with and without your luggage. Very demanding calculation requires extremely high precision and accuracy. 12

13 Level of Theory: Binding Energies Inclusion of electron correlation is critical for weakly bound clusters. See JCP, 112, 4465, arlj/papers/h2potential.pdf Make a plot of the binding energy vs. level of theory from your H2-LT calculations: HF, MP2, MP3, MP4, CCSD(T). How do your calculations compare with the published data? 13

14 Basis Set Superpostion Errors BSSE=Error due to using an incomplete basis set to represent the wavefunction. It always lowers the energy (wavefunction from one molecules borrows the wavefunction on the other molecule to lower its energy). Counterpoise corrections approximately account for the error Binding energy between molecules 1 & 2: E b = E 12, c E 1 E 2 Where the complex may have a different geometry (relaxed, denoted as c) compared with the single molecules. CP: E CP = E 1Bq, c + E(Bq2, c) E 1, c E 2, c The CP corrected binding energy is E b,cp = E b E CP. For the special case of no relaxation E b,cp = E 12 E 1Bq E(Bq2) 14

15 BSSE Error Example Use H2-CP results to compute E b, E CP, and E b,cp. This is for 3.4 Å separation. What basis set is being used? What level of theory? Why aren t the corrected binding energies the same for each basis set? 15

16 Counterpoise Corrections Made Easy! G09 has a counterpoise keyword that you can use to automatically compute the CP corrections. Copy the H2dimerCP.in and H2dimerCP.log files from /home/kjohnson/karlj/che3935/g09/h2-cp/ Look at the input and output. Compare with your own CP calculations. 16

17 Complete Basis Set Extrapolation We have seen that counterpoise corrections are only approximate. Moreover, there is still an error from having a finite basis set, even with corrections for BSSE. The ideal calculation would be carried out with an infinite (i.e., complete) basis set we can t do that so the next best thing is to extrapolate to the complete basis set limit, AKA CBS limit. Klopper et al. proposed E n = E + a n 3 where E is the CBS limit binding energy, n is the basis set index. 17

18 Viewing CPMD Results(1) Go to the class webpage: 35/ Click the Download Winscp link and save the file. Click the Download VMD folder (zipped) link and save the file Go to the downloads folder, right click the winscp436.zip file and choose Extract All Do the same for the VMD.zip file 18

19 Viewing CPMD Results(2) Launch WinSCP.exe by clicking on it and login to frank.sam.pitt.edu Navigate to the directory on frank containing the TRAJEC.xyz file and copy this to your local machine. Go to the VMD directory and launch vmd.exe Click on File, New Molecule then Browse in the popup box. Find the TRAJEC.xyz file and click Load In the VMD Main box click Graphics, Representations From the Drawing Method dropdown box select Dynamic Bonds and increase the Bond Resolution to 21 or so (click the double right arrow) Then click Create Rep at the top left and select VWD from the Drawing Method list. Change the Sphere Scale to 0.4 and the Sphere Resolution to 22 or so. 19

20 Viewing CPMD Results(3) You can use VMD to measure the distance between two atoms: Mouse, Label, Bonds Select two atoms by clicking on them. Play the trajectory Now make a graph: Graphics, Labels, Bonds, Select bond, then click Graph Similarly, VMD can measure angles between three atoms. VMD can do an amazing amount of really useful stuff. 20

21 Viewing CPMD Results(4) CPMD produces a file called ENERGIES that contains output from the MD run. Copy this file to your local drive with winscp Open it with Excel (All Files, import using space delimited) You can plot the data to see the temperature, energy, etc. as a function of time. The headings are: NFI EKINC TEMPP EKS ECLASSIC EHAM DIS TCPU NFI=frame number; EKINC=fictitious kinetic energy of electrons; TEMPP=temperature of ions, from the kinetic energy of the ions, EKIONS; EKS=Kohn-Sham energy; ECLASSIC=EKS+EKIONS; EHAM=ECLASSIC+EKINC (this is a conserved quantity in NVE); DIS=displacement of ions; TCPU=cpu time for the step 21