Problem Set 9 Solutions

More documents

Recommendations

Info

2 2. Continued b.) Describe the 3-21G basis set for methane. The 3-21G basis set is a split valence double zeta basis set. For hydrogen atom, a split valence double zeta basis consists of two 1s orbitals, denoted 1s and 1sʹ′. Note that for the H atom, because the 1s electron is considered the valence shell a double zeta basis set is used. For the carbon atom, a split valence double zeta basis set consists of a single 1s orbital, along with two 2s and two each of 2p x , 2p y , and 2p z orbitals, for a total of 9 basis functions. The basis functions in a split valence double zeta basis set are denoted 1s, 2s, 2sʹ′, 2p(3), and 2pʹ′(3). For the methane molecule, CH 4 , the 3-21G basis set consists of the basis functions shown in the table below. Atom/Basis Functions No. Basis No. Atoms TOTAL Functions C -- 1s 2s 2s' 2p(3) 2p'(3) 9 1 9 H -- 1s 1s' 2 4 8 TOTAL NO. BASIS FUNCTIONS = 17 c.) Describe the 6-31G* basis set for methane. Explain why the HF energies for the 3- 21G and 6-31G* basis sets are lower than the HF energy calculated from the STO-3G basis set. The 6-31G* basis set is a split valence double zeta basis set with added polarization functions on nonhydrogen atoms. For hydrogen atom, the split valence double zeta basis consists of two 1s orbitals, denoted 1s and 1sʹ′. For the carbon atom, a split valence double zeta basis set consists of a single 1s orbital, along with two 2s and a double set of 2p orbitals, 2p(3) and 2pʹ′(3). The extra polarization functions indicated by the * refer to carbon only and add a d(5) set, for a total of 14 basis functions on carbon. For the methane molecule, CH 4 , the 6-31G* basis set consists of the basis functions shown in the table below. Atom/Basis Functions No. Basis No. Atoms TOTAL Functions C -- 1s 2s 2s' 2p(3) 2p'(3) d(5) 14 1 14 H -- 1s 1s' 2 4 8 TOTAL NO. BASIS FUNCTIONS = 22 As the number of basis functions increases, the description of the wavefunction improves; therefore, the energy of the system drops (we know that energy of the approximate wavefunction always is greater than or equal to the exact result by the Variation Principle). Since the number of basis functions increases from STO-3G to 3-21G to 6-31G*, the energy decreases correspondingly.
3 3. Suppose you want to carry out ab initio molecular orbital calculations on the benzaldehyde molecule, C 6 H 5 CHO. a). Describe a minimal basis set for benzaldehyde, including the total number of AOs. A minimal basis set for benzaldehyde consists of a single 1s orbital on each H atom and a 1s, 2s, and set of three 2p orbitals on C and O. The table below gives the minimal basis set for benzaldehyde. Atom/Basis Functions No. Basis No. Atoms TOTAL Functions C -- 1s 2s 2p(3) 5 7 35 O -- 1s 2s 2p(3) 5 1 5 H -- 1s 1 6 6 TOTAL NO. BASIS FUNCTIONS = 46 b). Describe the 6-31G(d) basis set for benzaldehyde, including the total number of AOs. The 6-31G(d) basis set is a split valence double zeta basis set plus polarization functions added to nonhydrogen atoms. The 6-31G(d) basis set for benzaldehyde consists of the basis functions shown in the table below. Atom/Basis Functions No. Basis No. Atoms TOTAL Functions C -- 1s 2s 2s' 2p(3) 2p'(3) d(5) 14 7 98 O -- 1s 2s 2s' 2p(3) 2p'(3) d(5) 14 1 14 H -- 1s 1s' 2 6 12 TOTAL NO. BASIS FUNCTIONS = 124 c). Describe the 6-311G(d,p) basis set for benzaldehyde, including the total number of AOs. The 6-311G(d,p) basis set is a split valence triple zeta basis set plus polarization functions added to all atoms. The 6-311G(d,p) basis set for benzaldehyde consists of the basis functions shown in the table below. Atom/Basis Functions No. Basis No. Atoms TOTAL Functions C -- 1s 2s 2s' 2sʺ″ 2p(3) 2p'(3) 2pʺ″(3) d(5) 18 7 126 O -- 1s 2s 2s' 2sʺ″ 2p(3) 2p'(3) 2pʺ″(3) d(5) 18 1 18 H -- 1s 1s' 1sʺ″ p(3) 6 6 36 TOTAL NO. BASIS FUNCTIONS = 180
Page 1: Chemistry 460 Dr. Jean M. Standard
Page 5 and 6: 5 4. a.) Continued 0.6 0.5 G1(x) G2
Page 7 and 8: 7 5 b.) continued The third MO (whi
Page 9 and 10: 9 6. A Hartree-Fock SCF calculation

Problem Set 9 Solutions

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?