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Ab initio MD: CPMD • Energies Conserved total energy Physical total energy (EHAM) (ECLASSIC) Electronic (potential) energy: oscillatory (EKS) Fictitious kinetic energy of the electrons: bound oscillations around a constant value, i.e. the electrons do not heat up (T e = measure for the deviation from the BO surface) (EKINC) Restrictions of CP MD: • Number of atoms ≈ 100 – 1000 • Δt ≈ 0.1 fs • t ≈ few tens of ps
Ab initio MD: CPMD • How to control adiaba4city? • Dynamics of Kohn-‐Sham orbitals as superposi4on of harmonic orbital classical fields, where ε j and ε i are the eigenvalues of occupied and unoccupied (virtual) orbitals: • Lowest frequency: ω e min ∝ E gap µ • The frequency increases like the square root of the energy difference E gap , which is is the energy difference between HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied MO). • The frequency increases as the inverse of the square root for a decreasing fic44ous mass parameter μ. • To ensure adiaba4city, the difference to the highest phonon frequency should be large: ω min max e − ω n • The only adjustable parameter is μ (thus also called adiaba4city parameter) • Decreasing μ (lower kine4c energy, closer to BO surface) not only shi‚s the electronic spectrum upwards on the frequency scale as desired, but also stretches the en4re spectrum leading to an increase of the maximum frequency according to ω max e ∝ E cut µ where E cut is the largest kine4c energy in an expansion of the wave func4on in terms of a plane wave basis set. ω ij = ( ) µ 2 ε j − ε i ω n max
Page 1 and 2:
From Molecular to Con/nuum Phys
Page 3 and 4:
Car-Parinello / Molecular Mechanics
Page 5 and 6:
Potential Energy Surfaces • Geome
Page 7 and 8:
Molecular Dipole Moments • Molecu
Page 9 and 10:
Quantum Mechanical Dipole Moments
Page 11 and 12:
Molecular Dipole Moments Alignment
Page 13 and 14:
Dipole Moment Of Acetone • Proced
Page 15 and 16:
Internal Coordinates Bond lengths
Page 17 and 18:
CPMD Input • General - Sec4ons:
Page 19 and 20:
CPMD Input • &SYSTEM … &END
Page 21 and 22:
Choosing the Plane Wave Cutoff •
Page 23 and 24:
CPMD Input • &ATOMS … &END (
Page 25 and 26:
CPMD Output • Header - Date whe
Page 27 and 28:
CPMD Output • Atoms: coordinates
Page 29 and 30:
CPMD Output • Distribu4on among
Page 31 and 32:
CPMD Output • Ini4al guess for
Page 33 and 34:
CPMD Output • Geometry op4miza4o
Page 35 and 36:
CPMD Output • Geometry op4miza4o
Page 37 and 38: CPMD Output • Geometry op4miza4o
Page 39 and 40: Force field: Bonded terms (not used
Page 41 and 42: Acetone in Water: Electrostatic Int
Page 45 and 46: Running Gaussian 1. Set the envir
Page 49 and 50: Antechamber - automates the proce
Page 51 and 52: Antechamber - automates the proce
Page 53 and 54: Antechamber - rapid genera4on of
Page 55 and 56: Acetone: Pre-Equilibration • Clas
Page 57 and 58: Acetone: Topology File %VERSION VER
Page 59 and 60: Acetone in Water: Water Box - Autom
Page 61 and 62: Water Models - Water models diffe
Page 63 and 64: Water Models http://www.lsbu.ac.uk/
Page 65 and 66: Sander: Pre-Equilibration • 1. C
Page 67 and 68: Sander: Usage
Page 69 and 70: Sander: 1. Restrained Minimization
Page 71 and 72: Sander: 2. Unrestrained Minimizatio
Page 73 and 74: Sander: 3. MD at 300 K (NVT ensembl
Page 75 and 76: Vibrational Motions • High-‐f
Page 77 and 78: Statistical Thermodynamics • Cano
Page 79 and 80: Sander: 3. MD at 300 K (Heating)
Page 81 and 82: Sander: 4. MD at 300 K / 1 atm (NPT
Page 83 and 84: Analysis and Processing: Reimaging
Page 85 and 86: Ab initio MD • Born-‐Oppenhei
Page 87: Ab initio MD: CPMD • Adiaba4c se
Page 91 and 92: QM/MM: Production • Controlling
Page 93 and 94: QM/MM • Combina4on of accuracy
Page 95 and 96: QM/MM: Electrostatic interaction
Page 97 and 98: QM/MM: CPMD/GROMOS • Hamiltonian
Page 99 and 100: QM/MM: CPMD/GROMOS • Long-‐ra
Page 101 and 102: QM/MM: CPMD/GROMOS • Forces •
Page 103 and 104: QM/MM Input: Classical Input File T
Page 105 and 106: QM/MM Input: Classical Topology Fil
Page 107 and 108: QM/MM Input: Classical Topology Fil
Page 109 and 110: QM/MM Input: QM Part - CPMD Input &
Page 111 and 112: QM/MM Input: QM Part - CPMD Input &
Page 113 and 114: QM/MM Output: Simulated Annealing
Page 115 and 116: Car-Parrinello Lagrangian L = T −
Page 117 and 118: QM/MM Output: Simulated Annealing
Page 119 and 120: QM/MM Output: Simulated Annealing 9
Page 121 and 122: QM/MM: Test - Result: temperature
Page 123 and 124: QM/MM: Heating - Hea4ng of the s
Page 125 and 126: QM/MM: Production • QM/MM-‐CP
Page 127 and 128: QM/MM: Dipole Moment Calculation -
Page 129 and 130: QM/MM: Dipole Moment Calculation
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