Polarization diffuse functions polarization diffuse

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Polarization / Diffuse Functions Polarization / Diffuse Functions Polarization: Add AO with higher angular momentum (L) to give more flexibility Example: 3-21G*, 6-31G*, 6-31G**, etc. Diffusion: Add AO with very small exponents for systems with very diffuse electron densities such as anions or excited states Example: 6-31+G*, 6-311++G**
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its.unc.edu 34 Correlation-Consistent Basis Functions Correlation-Consistent Basis Functions a family of basis sets of increasing size can be used to extrapolate to the basis set limit cc-pVDZ – DZ with d’s on heavy atoms, p’s on H cc-pVTZ – triple split valence, with 2 sets of d’s and one set of f’s on heavy atoms, 2 sets of p’s and 1 set of d’s on hydrogen cc-pVQZ, cc-pV5Z, cc-pV6Z can also be augmented with diffuse functions (aug-cc-pVXZ)
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its.unc.edu 35 Pseudopotentials, Effective Core Potentials Pseudopotentials, Effective Core Potentials core orbitals do not change much during chemical interactions valence orbitals feel the electrostatic potential of the nuclei and of the core electrons can construct a pseudopotential to replace the electrostatic potential of the nuclei and of the core electrons reduces the size of the basis set needed to represent the atom (but introduces additional approximations) for heavy elements, pseudopotentials can also include of relativistic effects that otherwise would be costly to treat
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its.unc.edu 36 Correlation Energy Correlation Energy HF does not include correlations anti-parallel electrons E exact – E HF = E correlation Post HF Methods: Configuration Interaction ( CI, MCSCF, CCSD ) Møller-Plesset Perturbation series ( MP2, MP4 ) Density Functional Theory ( DFT )
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its.unc.edu 37 Configuration-Interaction (CI) Configuration-Interaction (CI) In Hartree-Fock theory, the n -electron wavefunction is approximated by one single Slater-determinant, denoted as: This determinant is built from n orthonormal spin-orbitals. The spin-orbitals that form are said to be occupied . The other orthonormal spin-orbitals that follow from the Hartree-Fock calculation in a given one-electron basis set of atomic orbitals (AOs) are known as virtual orbitals. For simplicity, we assume that all spin-orbitals are real. In electron-correlation or post-Hartree-Fock methods, the wavefunction is expanded in a many-electron basis set that consists of many determinants. Sometimes, we only use a few determinants, and sometimes, we use millions of them: In this notation, is a Slater- determinant that is obtained by replacing a certain number of occupied orbitals by virtual ones. Three questions: 1. Which determinants should we include? 2. How do we determine the expansion coefficients? 3. How do we evaluate the energy (or other properties)? HF HF c HF CI
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its.unc.edu 38 Truncated configuration interaction: CIS, CISD, CISDT, etc.
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