noncovalent interactions and symmetry-adapted perturbation...
TRANSCRIPT
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Noncovalent Interactionsand
Symmetry-Adapted Perturbation Theory
Ed HohensteinJune 29th 2010
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Outline• Introduction• Nonbonded Interactions
• Energy Components• Computational Considerations
• Symmetry-Adapted Perturbation Theory• General Theory• Electrostatics
• Implementation of SAPT• Density Fitting and Cholesky Decompositions• Factorization of Higher-order Corrections
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Noncovalent Interactions in Chemistry• Organic Crystals
• Lattice Energy• Structure
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Noncovalent Interactions in Chemistry• Organic Crystals
• Lattice Energy• Structure
• Nucleic Acids
• H-bonding• Stacking• Intercalation
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Noncovalent Interactions in Chemistry• Organic Crystals
• Lattice Energy• Structure
• Nucleic Acids
• H-bonding• Stacking• Intercalation
• Nanotechnology
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• Organic Crystals
• Lattice Energy• Structure
• Nucleic Acids
• H-bonding• Stacking• Intercalation
• Nanotechnology
• Proteins
• Structure• Solvation• Ligand Binding
Noncovalent Interactions in Chemistry
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Energy Components
• Electrostatics• Classical Coulombic interactions
• Induction• Multipole – induced multipole• Charge Transfer
• London Dispersion• Exchange-Repulsion
• Purely quantum mechanical effect
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Electrostatics
• Coulombic Interaction• Multipole expansion
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Induction• Response Term
• Dipole -> Induced Dipole
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Dispersion• London Dispersion Forces
• Instantaneous charge fluctuations
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Exchange-Repulsion
• Quantum Mechanical Effect• Pauli Repulsion• Not related to any physical observables
• Interchanging of electronic coordinates• Contributions from:
• Orbital Overlap• Exchange Integrals
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• Accuracy• Mean field theory• Quality of the density
• Charge Interpenetration
Computing Electrostatics and Induction
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Computing Electrostatics and Induction
• Accuracy• Mean field theory• Quality of the density
• Charge InterpenetrationX
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Computing Dispersion• Electron Correlation• HF and DFT Fail!
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Symmetry-Adapted Perturbation Theory
• Directly computes interaction energies• Perturbational• Supermolecular
• Computes each component separately• Free from BSSE• Size extensive• Size consistent
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General SAPT
Electronic Schrödinger Equation
Define zeroth-order Hamiltonian for each monomer
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Interaction Potential
Define Intermolecular Operator
Explict form of V:
Full Dimer Hamiltonian
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Electrostatic Interactions
Use intermolecular operator
Integrate over the density of A and B
Why do the number of electrons appear?
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Alternative Formulation
Use second quantized form of V
Evaluate the expectation value of V
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Electrostatics Cont.
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Electrostatics Cont.
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Electrostatic Interaction in SAPT
In terms of spin orbitals:
After spin integration:
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SAPT0
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SAPT2
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Approximate Two-Electron Integrals in SAPT
• SAPT0• Scales O(o3v2)• Requires o2v2 integrals
• Conventional Integral Transformation• Scales O(oNAO
4)
• Density Fitting and Cholesky Decompositions
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Density Fitting Approximation
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Cholesky Decompositions
• Work is shifted away from the transformation
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SAPT0 Factorizations
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SAPT2 Factorizations