Download DFT on Cyclic(alkyl)(amino)carbenes

Structure of Presentation
• Theory and Computation
– Methods: HF, DFT (B3LYP), MP2
– Basis sets: 6-31g*, 6-31g**, cc-pvtz
• Molecules of Interest
– Methylene (H2C)
Theory and Computation
Methods and Basis Sets
Quantum Mechanics
(and Math)
(review)
• H = E 
• Time-dependent wave equation:
• we are most interested in the energy of stationary
states and thus can ignore the phase
Kinetic Energy
Potential Energy
Quantum Mechanics
(and Math)
(review)
• In molecules we must treat each particle this way! (nucleus +
electrons)
• Molecular Hamiltonian:
Ke nuclei
Ke e-
Ue-n
Ue-e
Un-n
Methods
Born-Oppenheimer Approximation:
Hartree-Fock Method
• Accounts for electron exchange
– anti-symmetric exchange or spin wave functions
• but not for correlation
– Mean field approximation
True Correlation
Mean-field
Methods
• HF
Etrue= EHF + Ecorr
• Moller – Plesset 2nd order (MP2)
– Perturbation model
– Finds solutions by adding a “correction” to HF
• DFT
• Uses densities instead of wavefunctions
• Different functionals treat Exc differently
Source: Sousa, S. et al General Performance of Density Functionals . J. Phys. Chem. A 2007, 111, 1043910452
Functionals I have been using B3LYP
*most popular in literature*
In B3LYP:
EHF parameter is semi-empirically
obtained
a, b, and c are optimized on a set of
known molecules
- Thus “Hybrid”
a = 0.2
b = 0.72
c = 0.81
Source: Sousa, S. et al General Performance of Density Functionals . J. Phys. Chem. A 2007, 111, 1043910452
Contracted Gaussian-type orbitals (CGTO)
Basis Sets
normalization
Number of
gaussians
Variationally
optimized
Controls
width of
gaussian
L=a+b+c
(angular momentum)
Why CGTO?
1. Easy to compute with gaussians
2. Gaussians are not accurate enough
3. Linear combination of enough gaussians can
approximate a more accurate slater-type orbital
Good conceptual explanation: http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/basis-sets.pdf
Basis sets
• 6-31g*
Treatment of Core Orbitals
– 6 primitive gaussians per orbital (n = 6)
Treatment of valence orbitals
each valence orbital is comprised of 2 “orbitals”
1.
2.
One composed of 3 primitive gaussians (n=3)
One composed of 1 primitive gaussian (n=1)
*= addition of d-polarization functions above He
• 6-31g**
** = addition of p-polarization functions on H
Good conceptual explanation: http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/basis-sets.pdf
Example
• Carbon atom orbitals
– Minimal basis set
• 1s, 2s, 2px, 2py, and 2pz orbitals
• A total of 5 orbital basis for carbon
– 6-31g
• 6 gaussians to mimic a 1s
• 3 + 1 gaussians to mimic 2s, 2px, 2py, and 2pz EACH
– Adding up gaussians:
» 4 “valence orbitals” from two CGTOs each
• Two CGTO made of 3 GTO and one GTO, respectively
• Total of 16 primitive gaussians to describe valence orbitals
• Total of 22 primitive gaussians to describe carbon
– 6-31g*
• Adds 6 d-orbital CGTO to allow polarization of non-H atoms
– 6-31g**
• Adds 3 p-orbital CGTO to polarize H-atoms
Basis sets
• cc-pvtz
– Correlation consistent – polarized valence triple zeta
– Adds extra functions per atom to describe polarization better
Atoms
cc-pVTZ
(from Gaussian
H
3s,2p,1d
website)
He
3s,2p,1d
Li-Be
4s,3p,2d,1f
B-Ne
4s,3p,2d,1f
Na-Ar
5s,4p,2d,1f
Ca
6s,5p,3d,1f
Sc-Zn
7s,6p,4d,2f,1g
Ga-Kr
6s,5p,3d,1f
Good conceptual explanation: http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/basis-sets.pdf
Molecules of Interest
Methylene
Top-down
Side view
Singlet
ΔE = 9.09 kcal/mol
Triplet
Source: Carter, E.; Goddard, W. Electron correlation, basis sets, and the methylene singlet–triplet gap. JCP. 1987,
86, 862-865
Singlet
B3LYP/cc-pvtz
Methylene
SCF E(b3lyp-triplet) = -24,578.5 kcal/mol
SCF E(b3lyp-singlet) = -24,566.7 kcal/mol
ΔEts = 11.8 kcal/mol
-86.464
kcal/mol
-155.294
-162.423
-176.604
Triplet
Methylene
(evaluating accuracy)
Computational Results:
ΔEts(HF) = 28.43 kcal/mol
ΔEts(b3lyp) = 11.8 kcal/mol
ΔEts(MP2) = 28.50 kcal/mol
Experimental Results:
ΔE = 9.09 kcal/mol