Introduction to QCH Methods

(KFC/MOMO)

Mgr. Petr SklenovskýMgr. Tomáš Zelený

29. 11. 2010

Molecular Mechanics vs.

Quantum Mechanics

Molecular Mechanics (MM)Molecular Mechanics (MM)

● Huge systems with solvent, Huge systems with solvent, membrane, etc.membrane, etc.

● Molecular Dynamics (MD)Molecular Dynamics (MD)● PES sampling (replica PES sampling (replica

exchange, Sim. Annealing)exchange, Sim. Annealing)

Quantum Mechanics (QM)Quantum Mechanics (QM)

ab initioab initio● Nonempirical approachNonempirical approach● Chemical reactionsChemical reactions● NMR, IR, Raman, CD NMR, IR, Raman, CD

spectraspectra● Photochemical reactionsPhotochemical reactions

The Schrödinger Equation

ĤĤ = E = EHamiltonian energy operator

WavefunctionEigenvalue-energy

QM approximations

- The time-independent Schrödinger equation

- The Born-Oppenheimer Approximation

- The Independent Particle Approximation

Hartree-Fock (HF) Theory

Self-Consistent Field (SCF)

EE(corr)(corr) = E(exact) - E(HF) = E(exact) - E(HF)

Basis Sets● Basis sets Basis sets →→ AO AO →→ MO (Each molecular orbital has MO (Each molecular orbital has

a uniquely defined orbital energy.)a uniquely defined orbital energy.)

Example: C atom basis set Example: C atom basis set 6-31G6-31Gblueblue: : 1s1s “ core” orbital (6 GTO) “ core” orbital (6 GTO)

redred and and greengreen: valence orbitals : valence orbitals ((2s2s and and 2px, 2py, 2pz2px, 2py, 2pz))

● EACH valence orbital 3 GTO EACH valence orbital 3 GTO

+ 1 GTO (in total, C involves 22 + 1 GTO (in total, C involves 22 GTO)GTO)

QCH Methods● SemiempiricalSemiempirical

– CNDO, INDO, NDDO, ZINDO, MINDO, PM6, AM1, etc. CNDO, INDO, NDDO, ZINDO, MINDO, PM6, AM1, etc. ● DFTDFT

– GGA, LDA, hybrid, etc.GGA, LDA, hybrid, etc.● Ab-initioAb-initio

– Hartree-Fock – BO + one-electron, Slater, MOLCAOHartree-Fock – BO + one-electron, Slater, MOLCAO– Post HFPost HF

● MP2, CI, CC, etc.MP2, CI, CC, etc.

Most Used QCH Programs● WindowsWindows

– HyperChem, Titan, Spartan, Gaussian, ArguslabHyperChem, Titan, Spartan, Gaussian, Arguslab● UnixUnix

– Gaussian, Mopac, Turbomole, MolPro, MolCAS, GamessGaussian, Mopac, Turbomole, MolPro, MolCAS, Gamess

Gaussian 03● Energy

● Empirical – Amber, MM2, Dreiding, UFF● Semiempirical – CNDO, INDO, MINDO/3, MNDO, PM3, ...● Self Consistent Field (SCF) methods – RHF, UHF, ROHF● Perturbation theory methods – MPX, where X <2,3,4,5>● Configuration interaction – CIS, CISD, ...● Coupled cluster theory methods – CCD, CCSD, CCSD(T), CCSDT, QCISD, ...● Density Functional Theory (DFT) methods – LSDA, GGA, meta-GGA, hybrid, …● High accurate energies – Complete Basis Set (CBS, G1, G2, … )● Multiconfigurational methods – CASSCF, RASSCF, CAS(PT2/MP2), ...● Excited states energies – TD-HF, TD-DFT, CI-S, SAC-CI, ZINDO, …

● Gradients and optimizations● Analytic gradients (derivations)● Minimas and saddle points optimization● Internal reaction coordinate (IRC)● QM/MM technique “ ONIOM” - two or three layers● Conical Intersections (CI) search – SA-CASSCF● Analytic second derivatives, polarizabilities, hyperpolarizabilities, multipole moments● Rotations and vibrations – harmonic approximation, anharmonic● IR, Raman intensities

● Properties of molecules● Population analysis, multipole series expansion, electrostatic potential● NMR shielding tensors (HF, DFT, MP2)● CD, VCD● Electron affinities, Ionization potentials● Spin-orbit coupling● Hyperfine splitting spectra

● Solvating models● Polarisable continuum model – PCM, C-PCM, COSMO (COnductor-like Screening MOdel)● Isodesmic surface - IPCM, SCI-PCM

Stockholm, 1998

PES at Different Electronic States

EXERCISES1.1. Calculation of the electrostatic potentialCalculation of the electrostatic potential

2.2. Calculation of the IR spectrum of HCHOCalculation of the IR spectrum of HCHO

3.3. Relaxed scan of HRelaxed scan of H22O O

4.4. Calculation of the ionization potentialCalculation of the ionization potential

1. Calculation of the electrostatic potential

a)a) Draw the formamide molecule (NHDraw the formamide molecule (NH22CHO).CHO).

b)b) Set the Ab Initio method in HyperChem. The Set the Ab Initio method in HyperChem. The used basis set will be 6-31G**. Spin pairing will used basis set will be 6-31G**. Spin pairing will be set to RHF. The spin multiplicity must be set be set to RHF. The spin multiplicity must be set to 1 and the total charge to 0. to 1 and the total charge to 0.

c)c) Perform a Single Point calculation. After that, Perform a Single Point calculation. After that, perform the geometry optimization.perform the geometry optimization.

d)d) Go to Plot Molecular Graphs and then to the Go to Plot Molecular Graphs and then to the Molecular Properties card. Choose Electrostatic Molecular Properties card. Choose Electrostatic Potential and visualize it in 2D Contours. Potential and visualize it in 2D Contours.

1. Calculation of the electrostatic potential

2. Calculation of the IR spectrum of HCHO

a)a) Go to the Gaussian program in Windows.Go to the Gaussian program in Windows.

b)b) Create an input file. The input file for HCHO Create an input file. The input file for HCHO opt. in Gaussian is given in “Ulohy do cviceni z opt. in Gaussian is given in “Ulohy do cviceni z vypocetni chemie” (pages 21-22).vypocetni chemie” (pages 21-22).

c)c) Set the name and path of the output file and Set the name and path of the output file and run the optimization.run the optimization.

d)d) As soon as the calculation is completed, go to As soon as the calculation is completed, go to the GaussView program and plot the IR the GaussView program and plot the IR spectrum. Display each vibrational mode and spectrum. Display each vibrational mode and discuss their energies. How many vibrational discuss their energies. How many vibrational modes are visible for HCHO? modes are visible for HCHO?

3. Relaxed scan of H2O

a)a) Go to the Gaussian program in Windows.Go to the Gaussian program in Windows.

b)b) Edit the input file. The example of the input file for Edit the input file. The example of the input file for relaxed scan calculations can be found in “Ulohy relaxed scan calculations can be found in “Ulohy do cviceni z vypocetni chemie” (page 18). Scan of do cviceni z vypocetni chemie” (page 18). Scan of the H-O-H angle will be carried out.the H-O-H angle will be carried out.

c)c) Set the name and path for the output file and run Set the name and path for the output file and run the scan. The scan should end within several the scan. The scan should end within several seconds.seconds.

d)d) Open the output file in Notepad. Find the energy Open the output file in Notepad. Find the energy value (after opt.) for each step. Plot the data value (after opt.) for each step. Plot the data Energy vs. H-O-H angle. Energy vs. H-O-H angle.

4. Calculation of the ionization potentiala)a) Go to the HyperChem program.Go to the HyperChem program.

b)b) Find out what is the Koopmans' theorem.Find out what is the Koopmans' theorem.

c)c) Draw the CHDraw the CH44 molecule and calculate the Ab molecule and calculate the Ab Initio SP energy. Then, go to Compute Initio SP energy. Then, go to Compute → → Orbitals and list the energy of the HOMO Orbitals and list the energy of the HOMO orbital(s).orbital(s).

d)d) Compare the CHCompare the CH44 ionization potential(s) with ionization potential(s) with the value(s) deposited in the NIST database the value(s) deposited in the NIST database ((http://webbook.nist.gov/chemistry/http://webbook.nist.gov/chemistry/). ).

4. Calculation of the ionization potential