Molecular simulations: fundamentals and practice
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Weinheim
Wiley-VCH
[2020]
|
| Schlagworte: | |
| Online-Zugang: | http://www.wiley-vch.de/publish/dt/books/ISBN978-3-527-34105-4/ Inhaltsverzeichnis |
| Beschreibung: | xv, 326 Seiten Illustrationen, Diagramme 24.4 cm x 17 cm |
| ISBN: | 9783527341054 |
Internformat
MARC
| LEADER | 00000nam a22000008c 4500 | ||
|---|---|---|---|
| 001 | BV046801885 | ||
| 003 | DE-604 | ||
| 005 | 20210311 | ||
| 007 | t | ||
| 008 | 200709s2020 gw a||| |||| 00||| eng d | ||
| 015 | |a 19,N47 |2 dnb | ||
| 016 | 7 | |a 1199635707 |2 DE-101 | |
| 020 | |a 9783527341054 |c : circa EUR 89.00 (DE) (freier Preis) |9 978-3-527-34105-4 | ||
| 024 | 3 | |a 9783527341054 | |
| 028 | 5 | 2 | |a Bestellnummer: 1134105 000 |
| 035 | |a (OCoLC)1182906213 | ||
| 035 | |a (DE-599)DNB1199635707 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BW | ||
| 049 | |a DE-29T |a DE-11 |a DE-B768 |a DE-20 |a DE-703 | ||
| 084 | |a WD 2200 |0 (DE-625)148163: |2 rvk | ||
| 084 | |a WD 9200 |0 (DE-625)148253: |2 rvk | ||
| 084 | |a 540 |2 sdnb | ||
| 100 | 1 | |a Alavi, Saman |e Verfasser |0 (DE-588)1213910218 |4 aut | |
| 245 | 1 | 0 | |a Molecular simulations |b fundamentals and practice |c Saman Alavi |
| 264 | 1 | |a Weinheim |b Wiley-VCH |c [2020] | |
| 300 | |a xv, 326 Seiten |b Illustrationen, Diagramme |c 24.4 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Molekulardynamik |0 (DE-588)4170370-4 |2 gnd |9 rswk-swf |
| 653 | |a Bioinformatics & Computational Biology | ||
| 653 | |a Bioinformatik | ||
| 653 | |a Bioinformatik u. Computersimulationen in der Biowissenschaften | ||
| 653 | |a Biowissenschaften | ||
| 653 | |a CHD0: Computational Chemistry u. Molecular Modeling | ||
| 653 | |a Chemie | ||
| 653 | |a Chemistry | ||
| 653 | |a Computational Chemistry & Molecular Modeling | ||
| 653 | |a Computational Chemistry u. Molecular Modeling | ||
| 653 | |a LSG0: Bioinformatik u. Computersimulationen in der Biowissenschaften | ||
| 653 | |a Life Sciences | ||
| 653 | |a MS90: Materialwissenschaften / Theorie, Modellierung u. Simulation | ||
| 653 | |a Materials Science | ||
| 653 | |a Materialwissenschaften | ||
| 653 | |a Materialwissenschaften / Theorie, Modellierung u. Simulation | ||
| 653 | |a Theory, Modeling & Simulation | ||
| 689 | 0 | 0 | |a Molekulardynamik |0 (DE-588)4170370-4 |D s |
| 689 | 0 | 1 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 710 | 2 | |a Wiley-VCH |0 (DE-588)16179388-5 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-527-69953-7 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-527-69946-9 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, oBook |z 978-3-527-69945-2 |
| 856 | 4 | 2 | |m X:MVB |u http://www.wiley-vch.de/publish/dt/books/ISBN978-3-527-34105-4/ |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032210631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Datensatz im Suchindex
| _version_ | 1805066192132505600 |
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| adam_text |
CONTENTS
PREFACE
XIII
1
INTRODUCTION
-
STUDYING
SYSTEMS
FROM
TWO
VIEWPOINTS
1
2
CLASSICAL
MECHANICS
AND
NUMERICAL
METHODS
5
2.1
MECHANICS
-
THE
STUDY
OF
MOTION
5
2.2
CLASSICAL
NEWTONIAN
MECHANICS
6
2.3
ANALYTICAL
SOLUTIONS
OF
NEWTONS
EQUATIONS
AND
PHASE
SPACE
8
2.3.1
MOTION
OF
AN
OBJECT
UNDER
CONSTANT
GRAVITATIONAL
FORCE
8
2.3.2
ONE-DIMENSIONAL
HARMONIC
OSCILLATOR
10
2.3.3
RADIAL
FORCE
FUNCTIONS
IN
THREE
DIMENSIONS
12
2.3.4
MOTION
UNDER
THE
INFLUENCE
OF
A
DRAG
FORCE
15
2.4
NUMERICAL
SOLUTION
OF
NEWTON
S
EQUATIONS:
THE
EULER
METHOD
17
2.5
MORE
EFFICIENT
NUMERICAL
ALGORITHMS
FOR
SOLVING
NEWTON
*
S
EQUATIONS
20
2.5.1
THE
VERLET
ALGORITHM
20
2.5.2
THE
LEAPFROG
ALGORITHM
21
2.5.3
THE
VELOCITY
VERLET
ALGORITHM
22
2.5.4
CONSIDERATIONS
FOR
NUMERICAL
SOLUTION
OF
THE
EQUATIONS
OF
MOTION
23
2.6
EXAMPLES
OF
USING
NUMERICAL
METHODS
FOR
SOLVING
NEWTON
S
EQUATIONS
OF
MOTION
25
2.6.1
MOTION
NEAR
THE
EARTHS
SURFACE
UNDER CONSTANT
GRAVITATIONAL
FORCE
25
2.6.2
ONE-DIMENSIONAL
HARMONIC
OSCILLATOR
26
2.7
NUMERICAL
SOLUTION
OF
THE
EQUATIONS
OF
MOTION
FOR
MANY-ATOM
SYSTEMS
28
2.8
THE
LAGRANGIAN
AND
HAMILTONIAN
FORMULATIONS
OF
CLASSICAL
MECHANICS
29
CHAPTER
2
APPENDICES
32
2.
A.1
SEPARATION
OF
MOTION
IN
TWO-PARTICLE
SYSTEMS
WITH
RADIAL
FORCES
32
2.A.2
MOTION
UNDER
SPHERICALLY
SYMMETRIC
FORCES
33
3
INTRA-
AND
INTERMOLECULAR
POTENTIALS
IN
SIMULATIONS
39
3.1
INTRODUCTION
-
ELECTROSTATIC
FORCES
BETWEEN
ATOMS
39
3.2
QUANTUM
MECHANICS
AND
MOLECULAR
INTERACTIONS
40
VIII
CONTENTS
3.2.1
THE
SCHRODINGER
EQUATION
40
3.2.2
THE
BORN-OPPENHEIMER
APPROXIMATION
42
3.3
CLASSICAL
INTRAMOLECULAR
POTENTIAL
ENERGY
FUNCTIONS
FROM
QUANTUM
MECHANICS
44
3.3.1
INTRAMOLECULAR
POTENTIALS
45
3.3.2
BOND
STRETCH
POTENTIALS
48
3.3.3
ANGLE
BENDING
POTENTIALS
51
3.3.4
TORSIONAL
POTENTIALS
51
3.3.5
THE
1-4,
1-5,
AND
FARTHER
INTRAMOLECULAR INTERACTIONS
53
3.4
INTERMOLECULAR
POTENTIAL
ENERGIES
54
3.4.1
ELECTROSTATIC
INTERACTIONS
54
3.4.1.1
THE
POINT
CHARGE
APPROXIMATION
55
3.4.1.2
THE
MULTIPOLE
DESCRIPTION
OF
CHARGE
DISTRIBUTION
59
3.4.1.3
POLARIZABILITY
61
3.4.2
VAN
DER
WAALS
INTERACTIONS
63
3.5
FORCE
FIELDS
64
3.5.1
WATER
FORCE
FIELDS
64
3.5.2
THE
AMBER
FORCE
FIELD
66
3.5.3
THE
OPTS
FORCE
FIELD
68
3.5.4
THE
CHARMM
FORCE
FIELD
69
3.5.5
OTHER
FORCE
FIELDS
69
CHAPTER
3
APPENDICES
71
3.
A.1
THE
BORN-OPPENHEIMER
APPROXIMATION
TO
DETERMINE
THE
NUCLEAR
SCHRODINGER
EQUATION
71
4
THE
MECHANICS
OF
MOLECULAR
DYNAMICS
73
4.1
INTRODUCTION
73
4.2
SIMULATION
CELL
VECTORS
73
4.3
SIMULATION
CELL
BOUNDARY
CONDITIONS
75
4.4
SHORT-RANGE
INTERMOLECULAR
POTENTIALS
79
4.4.1
CUTOFF
RADIUS
AND
THE
MINIMUM
IMAGE
CONVENTION
79
4.4.2
NEIGHBOR
LISTS
82
4.5
LONG-RANGE
INTERMOLECULAR
POTENTIALS:
EWALD
SUMS
84
4.6
SIMULATING
RIGID
MOLECULES
88
CHAPTER
4
APPENDICES
92
4.
A.1
FOURIER
TRANSFORM
OF
GAUSSIAN
AND
ERROR
FUNCTIONS
92
4.
A.2
ELECTROSTATIC
FORCE
EXPRESSION
FROM
THE
EWALD
SUMMATION
TECHNIQUE
94
4.
A.3
THE
METHOD
OF
LAGRANGE
UNDETERMINED
MULTIPLIERS
95
4.
A.4
LAGRANGIAN
MULTIPLIER
FOR
CONSTRAINED
DYNAMICS
98
5
PROBABILITY
THEORY
AND
MOLECULAR
SIMULATIONS
101
5.1
INTRODUCTION:
DETERMINISTIC
AND
STOCHASTIC
PROCESSES
101
5.2
SINGLE
VARIABLE
PROBABILITY
DISTRIBUTIONS
103
5.2.1
DISCRETE
STOCHASTIC
VARIABLES
103
5.2.2
CONTINUOUS
STOCHASTIC
VARIABLES
104
5.3
MULTIVARIABLE
DISTRIBUTIONS:
INDEPENDENT
VARIABLES
AND
CONVOLUTION
106
CONTENTS
IX
5.4
THE
MAXWELL-BOLTZMANN
VELOCITY
DISTRIBUTION
111
5.4.1
THE
CONCEPT
OF
TEMPERATURE
FROM
THE
MECHANICAL
ANALYSIS
OF
AN
IDEAL
GAS
112
5.4.2
THE
MAXWELL-BOLTZMANN
DISTRIBUTION
OF
VELOCITIES
FOR
AN
IDEAL
GAS
115
5.4.3
ENERGY
DISTRIBUTIONS
FOR
COLLECTIONS
OF
MOLECULES
IN
AN
IDEAL
GAS
120
5.4.4
GENERATING
INITIAL
VELOCITIES
IN
MOLECULAR
SIMULATIONS
123
5.5
PHASE
SPACE
DESCRIPTION
OF
AN
IDEAL
GAS
125
CHAPTER
5
APPENDICES
127
5.
A.1
NORMALIZATION,
MEAN,
AND
STANDARD
DEVIATION
OF
THE
GAUSSIAN
FUNCTION
127
5.
A.2
CONVOLUTION
OF
GAUSSIAN
FUNCTIONS
128
5.
A.3
THE
VIRIAL
EQUATION
AND
THE
MICROSCOPIC
MECHANICAL
VIEW
OF
PRESSURE
131
5.
A.4
USEFUL
MATHEMATICAL
RELATIONS
AND
INTEGRAL
FORMULAS
133
5.A.4.1
STIRLINGS
APPROXIMATION
FOR
N!
133
5.
A
.4.2
EXPONENTIAL
INTEGRALS
134
5.A.4.3
GAUSSIAN
INTEGRALS
134
5.A.4.4
BETA
FUNCTION
INTEGRALS
134
5.A.5
ENERGY
DISTRIBUTION
FOR
THREE
MOLECULES
135
5.A.6
DERIVING
THE
BOX-MULLER
FORMULA
FOR
GENERATING
A
GAUSSIAN
DISTRIBUTION
136
6
STATISTICAL
MECHANICS
IN
MOLECULAR
SIMULATIONS
139
6.1
INTRODUCTION
139
6.2
DISCRETE
STATES
IN
QUANTUM
MECHANICAL
SYSTEMS
140
6.3
DISTRIBUTIONS
OF
A
SYSTEM
AMONG
DISCRETE
ENERGY
STATES
142
6.4
SYSTEMS
WITH
NON-INTERACTING
MOLECULES:
THE
P-SPACE
APPROACH
145
6.5
INTERACTING
SYSTEMS
AND
ENSEMBLES:
THE
Y-SPACE
APPROACH
AND
THE
CANONICAL
ENSEMBLE
148
6.5.1
THERMODYNAMICS
QUANTITIES
152
6.5.2
FLUCTUATIONS
IN
THERMODYNAMIC
QUANTITIES
IN
THE
CANONICAL
ENSEMBLE
154
6.5.3
CANONICAL
ENSEMBLE
FOR
SYSTEMS
WITH
NON-INTERACTING
MOLECULES
156
6.5.4
A
PHYSICAL
INTERPRETATION
OF
THE
CANONICAL
PARTITION
FUNCTION
157
6.6
OTHER
CONSTRAINTS
COUPLING
THE
SYSTEM
TO
THE
ENVIRONMENT
158
6.6.1
ISOTHERMAL-ISOBARIC
ENSEMBLE
(FIXED
N,
P,
AND
T)
158
6.6.2
GRAND
CANONICAL
ENSEMBLE
(FIXED
P,
V,
AND
T)
163
6.6.3
MICROCANONICAL
ENSEMBLE
(FIXED
N,
V,
AND
E)
166
6.6.4
ISENTHALPIC-ISOBARIC
ENSEMBLE
(FIXED
N,
P,
AND
H)
167
6.7
CLASSICAL
STATISTICAL
MECHANICS
167
6.7.1
THE
CANONICAL
ENSEMBLE
167
6.7.2
THE
ISOTHERMAL-ISOBARIC
ENSEMBLE
169
6.7.3
THE
GRAND
CANONICAL
ENSEMBLE
169
6.7.4
THE
MICROCANONICAL
ENSEMBLE
170
6.7.5
ISENTHALPIC-ISOBARIC
ENSEMBLE
170
6.8
STATISTICAL
MECHANICS
AND
MOLECULAR
SIMULATIONS
171
CONTENTS
CHAPTER
6
APPENDICES
172
6.
A.1
QUANTUM
MECHANICAL
DESCRIPTION
AND
DETERMINATION OF
THE
LAGRANGE
MULTIPLIER
0
AND
PRESSURE
FOR
AN
IDEAL
GAS
172
6.
A.2
DETERMINATION
OF
THE
LAGRANGE
MULTIPLIER
0
IN
SYSTEMS
WITH
INTERACTING
MOLECULES
174
6.
A.3
SUMMARY
OF
STATISTICAL
MECHANICAL
FORMULAS
175
7
THERMOSTATS
AND
BAROSTATS
177
7.1
INTRODUCTION
177
7.2
CONSTANT
PRESSURE
MOLECULAR
DYNAMICS
(THE ISOBARIC
ENSEMBLES)
178
7.2.1
NON-ISOTROPIC
VOLUME
VARIATION:
THE
PARRINELLO-RAHMAN
METHOD
184
7.3
CONSTANT
TEMPERATURE
MOLECULAR
DYNAMICS
185
7.3.1
EXTENDED
SYSTEM
METHOD:
THE
NOSE-HOOVER
THERMOSTAT
185
7.3.2
THE
BERENDSEN
THERMOSTAT
190
7.4
COMBINED
CONSTANT
TEMPERATURE-CONSTANT
PRESSURE
MOLECULAR
DYNAMICS
192
7.5
SCOPE
OF
MOLECULAR
SIMULATIONS
WITH
THERMOSTATS
AND
BAROSTATS
195
CHAPTER
7
APPENDICES
196
7.
A.1
ANDERSEN
BAROSTAT
AND
THE
ISOBARIC-ISENTHALPIC
ENSEMBLE
196
7.
A.2
THE
LAGRANGIAN
FOR
A
CONSTANT
PRESSURE
SYSTEM
WITH
NON-ISOTROPIC
VOLUME
CHANGE:
THE
PARRINELLO-RAHMAN
METHOD
196
7.
A.3
NOSE
THERMOSTAT
SYSTEM
AND
THE
CANONICAL
ENSEMBLE
DISTRIBUTION
FUNCTION
197
8 SIMULATIONS
OF
STRUCTURAL
AND
THERMODYNAMIC
PROPERTIES
199
8.1
INTRODUCTION
199
8.2
SIMULATIONS
OF
SOLIDS,
LIQUIDS,
AND
GASES
200
8.2.1
SETTING
UP
INITIAL
STRUCTURES
FOR
MOLECULAR
SIMULATIONS
OF
SOLIDS,
LIQUIDS,
AND
GASES
202
8.3
THE
RADIAL
DISTRIBUTION
FUNCTION
205
8.4
SIMULATIONS
OF
SOLUTIONS
211
8.5
SIMULATIONS
OF
BIOLOGICAL
MOLECULES
214
8.6
SIMULATION
OF
SURFACE
TENSION
219
8.7
STRUCTURAL
ORDER
PARAMETERS
224
8.8
STATISTICAL
MECHANICS
AND
THE
RADIAL
DISTRIBUTION
FUNCTION
227
8.9
LONG-RANGE
(TAIL)
CORRECTIONS
TO
THE
POTENTIAL
232
CHAPTER
8
APPENDICES
233
8.
A.1
FORCE
FIELDS
FOR
SIMULATIONS
IN
THE
FIGURES
OF
CHAPTER
8
233
8.
A.
1.1
NITROGEN
FORCE
FIELD
233
8.A.
1.2
NACL
SIMULATION
FORCE
FIELD
233
8.
A.2
THE
PDB
FILE
FORMAT
234
9
SIMULATIONS
OF
DYNAMIC
PROPERTIES
237
9.1
INTRODUCTION
237
9.2
MOLECULAR
MOTIONS
AND
THE
MEAN
SQUARE
DISPLACEMENT
237
9.2.1
MOTION
IN
BULK
PHASES
237
CONTENTS
XI
9.2.2
MOTION
IN
CONFINED
SPACES
AND
ON
SURFACES
244
9.3
MOLECULAR
VELOCITIES
AND
TIME
CORRELATION
FUNCTIONS
247
9.3.1
COLLISIONS
AND
THE
VELOCITY
AUTOCORRELATION
FUNCTION
247
9.3.2
TIME
CORRELATION
FUNCTIONS
FOR
STATIONARY
SYSTEMS
251
9.4
ORIENTATION
AUTOCORRELATION
FUNCTIONS
251
9.5
HYDROGEN
BONDING DYNAMICS
253
9.6
MOLECULAR
MOTIONS
ON
NANOPARTICLES:
THE
LINDEMANN
INDEX
254
9.7
MICROSCOPIC
DETERMINATION
OF
TRANSPORT
COEFFICIENTS
256
9.7.1
THE
TRANSPORT
COEFFICIENTS
256
9.7.2
NONEQUILIBRIUM
MOLECULAR
DYNAMICS
SIMULATIONS
OF
TRANSPORT
COEFFICIENTS
261
9.7.3
THE
GREEN-KUBO
RELATIONS
AND
SIMULATION
OF
TRANSPORT
COEFFICIENTS
261
CHAPTER
9
APPENDICES
263
9.
A.1
BROWNIAN
MOTION
AND
THE
LANGEVIN
EQUATION
263
9.
A.2
THE
DISCRETE
RANDOM
WALK
MODEL
OF
DIFFUSION
265
9.
A.3
THE
SOLUTION
OF
THE
DIFFUSION
EQUATION
267
9.
A.4
RELATION
BETWEEN
MEAN
SQUARE
DISPLACEMENT
AND
DIFFUSION
COEFFICIENT
268
10
MONTE
CARLO
SIMULATIONS
269
10.1
INTRODUCTION
269
10.2
THE
CANONICAL
MONTE
CARLO
PROCEDURE
270
10.2.1.1
DETERMINING
WHICH
MOLECULE
TO
MOVE
273
10.2.1.2
DETERMINING
WHETHER
A
TRANSLATION
OR
ROTATION
IS
PERFORMED
273
10.2.1.3
TRANSLATION
MOVES
274
10.2.1.4
ROTATIONAL
MOVES
274
10.3
THE
CONDITION
OF
MICROSCOPIC
REVERSIBILITY
AND
IMPORTANCE
SAMPLING
277
10.4
MONTE
CARLO
SIMULATIONS
IN
OTHER
ENSEMBLES
279
10.4.1
GRAND
CANONICAL
MONTE
CARLO
SIMULATIONS
279
10.4.2
ISOTHERMAL-ISOBARIC
MONTE
CARLO
SIMULATIONS
283
10.4.3
BIASED
MONTE
CARLO
SAMPLING
METHODS
284
10.5
GIBBS
ENSEMBLE
MONTE
CARLO
SIMULATIONS
285
10.5.1
SIMULATIONS
OF
LIQUID-GAS
PHASE
EQUILIBRIUM
285
10.6
SIMULATIONS
OF
GAS
ADSORPTION
IN
POROUS
SOLIDS
288
10.6.1
SIMULATIONS
OF
THE
GAS
ADSORPTION
ISOTHERM
AND
HEAT
OF
ADSORPTION
288
10.6.2
FORCE
FIELDS
FOR
GAS
ADSORPTION
SIMULATIONS
291
10.6.3
BLOCK
AVERAGING
OF
DATA
FROM
MONTE
CARLO
AND
MOLECULAR
DYNAMICS
SIMULATIONS
291
CHAPTER
10
APPENDICES
295
10.
A.
1
THERMODYNAMIC
RELATION
FOR
THE
HEAT
OF
ADSORPTION
295
REFERENCES
297
INDEX
317 |
| adam_txt |
CONTENTS
PREFACE
XIII
1
INTRODUCTION
-
STUDYING
SYSTEMS
FROM
TWO
VIEWPOINTS
1
2
CLASSICAL
MECHANICS
AND
NUMERICAL
METHODS
5
2.1
MECHANICS
-
THE
STUDY
OF
MOTION
5
2.2
CLASSICAL
NEWTONIAN
MECHANICS
6
2.3
ANALYTICAL
SOLUTIONS
OF
NEWTONS
EQUATIONS
AND
PHASE
SPACE
8
2.3.1
MOTION
OF
AN
OBJECT
UNDER
CONSTANT
GRAVITATIONAL
FORCE
8
2.3.2
ONE-DIMENSIONAL
HARMONIC
OSCILLATOR
10
2.3.3
RADIAL
FORCE
FUNCTIONS
IN
THREE
DIMENSIONS
12
2.3.4
MOTION
UNDER
THE
INFLUENCE
OF
A
DRAG
FORCE
15
2.4
NUMERICAL
SOLUTION
OF
NEWTON
S
EQUATIONS:
THE
EULER
METHOD
17
2.5
MORE
EFFICIENT
NUMERICAL
ALGORITHMS
FOR
SOLVING
NEWTON
*
S
EQUATIONS
20
2.5.1
THE
VERLET
ALGORITHM
20
2.5.2
THE
LEAPFROG
ALGORITHM
21
2.5.3
THE
VELOCITY
VERLET
ALGORITHM
22
2.5.4
CONSIDERATIONS
FOR
NUMERICAL
SOLUTION
OF
THE
EQUATIONS
OF
MOTION
23
2.6
EXAMPLES
OF
USING
NUMERICAL
METHODS
FOR
SOLVING
NEWTON
S
EQUATIONS
OF
MOTION
25
2.6.1
MOTION
NEAR
THE
EARTHS
SURFACE
UNDER CONSTANT
GRAVITATIONAL
FORCE
25
2.6.2
ONE-DIMENSIONAL
HARMONIC
OSCILLATOR
26
2.7
NUMERICAL
SOLUTION
OF
THE
EQUATIONS
OF
MOTION
FOR
MANY-ATOM
SYSTEMS
28
2.8
THE
LAGRANGIAN
AND
HAMILTONIAN
FORMULATIONS
OF
CLASSICAL
MECHANICS
29
CHAPTER
2
APPENDICES
32
2.
A.1
SEPARATION
OF
MOTION
IN
TWO-PARTICLE
SYSTEMS
WITH
RADIAL
FORCES
32
2.A.2
MOTION
UNDER
SPHERICALLY
SYMMETRIC
FORCES
33
3
INTRA-
AND
INTERMOLECULAR
POTENTIALS
IN
SIMULATIONS
39
3.1
INTRODUCTION
-
ELECTROSTATIC
FORCES
BETWEEN
ATOMS
39
3.2
QUANTUM
MECHANICS
AND
MOLECULAR
INTERACTIONS
40
VIII
CONTENTS
3.2.1
THE
SCHRODINGER
EQUATION
40
3.2.2
THE
BORN-OPPENHEIMER
APPROXIMATION
42
3.3
CLASSICAL
INTRAMOLECULAR
POTENTIAL
ENERGY
FUNCTIONS
FROM
QUANTUM
MECHANICS
44
3.3.1
INTRAMOLECULAR
POTENTIALS
45
3.3.2
BOND
STRETCH
POTENTIALS
48
3.3.3
ANGLE
BENDING
POTENTIALS
51
3.3.4
TORSIONAL
POTENTIALS
51
3.3.5
THE
1-4,
1-5,
AND
FARTHER
INTRAMOLECULAR INTERACTIONS
53
3.4
INTERMOLECULAR
POTENTIAL
ENERGIES
54
3.4.1
ELECTROSTATIC
INTERACTIONS
54
3.4.1.1
THE
POINT
CHARGE
APPROXIMATION
55
3.4.1.2
THE
MULTIPOLE
DESCRIPTION
OF
CHARGE
DISTRIBUTION
59
3.4.1.3
POLARIZABILITY
61
3.4.2
VAN
DER
WAALS
INTERACTIONS
63
3.5
FORCE
FIELDS
64
3.5.1
WATER
FORCE
FIELDS
64
3.5.2
THE
AMBER
FORCE
FIELD
66
3.5.3
THE
OPTS
FORCE
FIELD
68
3.5.4
THE
CHARMM
FORCE
FIELD
69
3.5.5
OTHER
FORCE
FIELDS
69
CHAPTER
3
APPENDICES
71
3.
A.1
THE
BORN-OPPENHEIMER
APPROXIMATION
TO
DETERMINE
THE
NUCLEAR
SCHRODINGER
EQUATION
71
4
THE
MECHANICS
OF
MOLECULAR
DYNAMICS
73
4.1
INTRODUCTION
73
4.2
SIMULATION
CELL
VECTORS
73
4.3
SIMULATION
CELL
BOUNDARY
CONDITIONS
75
4.4
SHORT-RANGE
INTERMOLECULAR
POTENTIALS
79
4.4.1
CUTOFF
RADIUS
AND
THE
MINIMUM
IMAGE
CONVENTION
79
4.4.2
NEIGHBOR
LISTS
82
4.5
LONG-RANGE
INTERMOLECULAR
POTENTIALS:
EWALD
SUMS
84
4.6
SIMULATING
RIGID
MOLECULES
88
CHAPTER
4
APPENDICES
92
4.
A.1
FOURIER
TRANSFORM
OF
GAUSSIAN
AND
ERROR
FUNCTIONS
92
4.
A.2
ELECTROSTATIC
FORCE
EXPRESSION
FROM
THE
EWALD
SUMMATION
TECHNIQUE
94
4.
A.3
THE
METHOD
OF
LAGRANGE
UNDETERMINED
MULTIPLIERS
95
4.
A.4
LAGRANGIAN
MULTIPLIER
FOR
CONSTRAINED
DYNAMICS
98
5
PROBABILITY
THEORY
AND
MOLECULAR
SIMULATIONS
101
5.1
INTRODUCTION:
DETERMINISTIC
AND
STOCHASTIC
PROCESSES
101
5.2
SINGLE
VARIABLE
PROBABILITY
DISTRIBUTIONS
103
5.2.1
DISCRETE
STOCHASTIC
VARIABLES
103
5.2.2
CONTINUOUS
STOCHASTIC
VARIABLES
104
5.3
MULTIVARIABLE
DISTRIBUTIONS:
INDEPENDENT
VARIABLES
AND
CONVOLUTION
106
CONTENTS
IX
5.4
THE
MAXWELL-BOLTZMANN
VELOCITY
DISTRIBUTION
111
5.4.1
THE
CONCEPT
OF
TEMPERATURE
FROM
THE
MECHANICAL
ANALYSIS
OF
AN
IDEAL
GAS
112
5.4.2
THE
MAXWELL-BOLTZMANN
DISTRIBUTION
OF
VELOCITIES
FOR
AN
IDEAL
GAS
115
5.4.3
ENERGY
DISTRIBUTIONS
FOR
COLLECTIONS
OF
MOLECULES
IN
AN
IDEAL
GAS
120
5.4.4
GENERATING
INITIAL
VELOCITIES
IN
MOLECULAR
SIMULATIONS
123
5.5
PHASE
SPACE
DESCRIPTION
OF
AN
IDEAL
GAS
125
CHAPTER
5
APPENDICES
127
5.
A.1
NORMALIZATION,
MEAN,
AND
STANDARD
DEVIATION
OF
THE
GAUSSIAN
FUNCTION
127
5.
A.2
CONVOLUTION
OF
GAUSSIAN
FUNCTIONS
128
5.
A.3
THE
VIRIAL
EQUATION
AND
THE
MICROSCOPIC
MECHANICAL
VIEW
OF
PRESSURE
131
5.
A.4
USEFUL
MATHEMATICAL
RELATIONS
AND
INTEGRAL
FORMULAS
133
5.A.4.1
STIRLINGS
APPROXIMATION
FOR
N!
133
5.
A
.4.2
EXPONENTIAL
INTEGRALS
134
5.A.4.3
GAUSSIAN
INTEGRALS
134
5.A.4.4
BETA
FUNCTION
INTEGRALS
134
5.A.5
ENERGY
DISTRIBUTION
FOR
THREE
MOLECULES
135
5.A.6
DERIVING
THE
BOX-MULLER
FORMULA
FOR
GENERATING
A
GAUSSIAN
DISTRIBUTION
136
6
STATISTICAL
MECHANICS
IN
MOLECULAR
SIMULATIONS
139
6.1
INTRODUCTION
139
6.2
DISCRETE
STATES
IN
QUANTUM
MECHANICAL
SYSTEMS
140
6.3
DISTRIBUTIONS
OF
A
SYSTEM
AMONG
DISCRETE
ENERGY
STATES
142
6.4
SYSTEMS
WITH
NON-INTERACTING
MOLECULES:
THE
P-SPACE
APPROACH
145
6.5
INTERACTING
SYSTEMS
AND
ENSEMBLES:
THE
Y-SPACE
APPROACH
AND
THE
CANONICAL
ENSEMBLE
148
6.5.1
THERMODYNAMICS
QUANTITIES
152
6.5.2
FLUCTUATIONS
IN
THERMODYNAMIC
QUANTITIES
IN
THE
CANONICAL
ENSEMBLE
154
6.5.3
CANONICAL
ENSEMBLE
FOR
SYSTEMS
WITH
NON-INTERACTING
MOLECULES
156
6.5.4
A
PHYSICAL
INTERPRETATION
OF
THE
CANONICAL
PARTITION
FUNCTION
157
6.6
OTHER
CONSTRAINTS
COUPLING
THE
SYSTEM
TO
THE
ENVIRONMENT
158
6.6.1
ISOTHERMAL-ISOBARIC
ENSEMBLE
(FIXED
N,
P,
AND
T)
158
6.6.2
GRAND
CANONICAL
ENSEMBLE
(FIXED
P,
V,
AND
T)
163
6.6.3
MICROCANONICAL
ENSEMBLE
(FIXED
N,
V,
AND
E)
166
6.6.4
ISENTHALPIC-ISOBARIC
ENSEMBLE
(FIXED
N,
P,
AND
H)
167
6.7
CLASSICAL
STATISTICAL
MECHANICS
167
6.7.1
THE
CANONICAL
ENSEMBLE
167
6.7.2
THE
ISOTHERMAL-ISOBARIC
ENSEMBLE
169
6.7.3
THE
GRAND
CANONICAL
ENSEMBLE
169
6.7.4
THE
MICROCANONICAL
ENSEMBLE
170
6.7.5
ISENTHALPIC-ISOBARIC
ENSEMBLE
170
6.8
STATISTICAL
MECHANICS
AND
MOLECULAR
SIMULATIONS
171
CONTENTS
CHAPTER
6
APPENDICES
172
6.
A.1
QUANTUM
MECHANICAL
DESCRIPTION
AND
DETERMINATION OF
THE
LAGRANGE
MULTIPLIER
0
AND
PRESSURE
FOR
AN
IDEAL
GAS
172
6.
A.2
DETERMINATION
OF
THE
LAGRANGE
MULTIPLIER
0
IN
SYSTEMS
WITH
INTERACTING
MOLECULES
174
6.
A.3
SUMMARY
OF
STATISTICAL
MECHANICAL
FORMULAS
175
7
THERMOSTATS
AND
BAROSTATS
177
7.1
INTRODUCTION
177
7.2
CONSTANT
PRESSURE
MOLECULAR
DYNAMICS
(THE ISOBARIC
ENSEMBLES)
178
7.2.1
NON-ISOTROPIC
VOLUME
VARIATION:
THE
PARRINELLO-RAHMAN
METHOD
184
7.3
CONSTANT
TEMPERATURE
MOLECULAR
DYNAMICS
185
7.3.1
EXTENDED
SYSTEM
METHOD:
THE
NOSE-HOOVER
THERMOSTAT
185
7.3.2
THE
BERENDSEN
THERMOSTAT
190
7.4
COMBINED
CONSTANT
TEMPERATURE-CONSTANT
PRESSURE
MOLECULAR
DYNAMICS
192
7.5
SCOPE
OF
MOLECULAR
SIMULATIONS
WITH
THERMOSTATS
AND
BAROSTATS
195
CHAPTER
7
APPENDICES
196
7.
A.1
ANDERSEN
BAROSTAT
AND
THE
ISOBARIC-ISENTHALPIC
ENSEMBLE
196
7.
A.2
THE
LAGRANGIAN
FOR
A
CONSTANT
PRESSURE
SYSTEM
WITH
NON-ISOTROPIC
VOLUME
CHANGE:
THE
PARRINELLO-RAHMAN
METHOD
196
7.
A.3
NOSE
THERMOSTAT
SYSTEM
AND
THE
CANONICAL
ENSEMBLE
DISTRIBUTION
FUNCTION
197
8 SIMULATIONS
OF
STRUCTURAL
AND
THERMODYNAMIC
PROPERTIES
199
8.1
INTRODUCTION
199
8.2
SIMULATIONS
OF
SOLIDS,
LIQUIDS,
AND
GASES
200
8.2.1
SETTING
UP
INITIAL
STRUCTURES
FOR
MOLECULAR
SIMULATIONS
OF
SOLIDS,
LIQUIDS,
AND
GASES
202
8.3
THE
RADIAL
DISTRIBUTION
FUNCTION
205
8.4
SIMULATIONS
OF
SOLUTIONS
211
8.5
SIMULATIONS
OF
BIOLOGICAL
MOLECULES
214
8.6
SIMULATION
OF
SURFACE
TENSION
219
8.7
STRUCTURAL
ORDER
PARAMETERS
224
8.8
STATISTICAL
MECHANICS
AND
THE
RADIAL
DISTRIBUTION
FUNCTION
227
8.9
LONG-RANGE
(TAIL)
CORRECTIONS
TO
THE
POTENTIAL
232
CHAPTER
8
APPENDICES
233
8.
A.1
FORCE
FIELDS
FOR
SIMULATIONS
IN
THE
FIGURES
OF
CHAPTER
8
233
8.
A.
1.1
NITROGEN
FORCE
FIELD
233
8.A.
1.2
NACL
SIMULATION
FORCE
FIELD
233
8.
A.2
THE
PDB
FILE
FORMAT
234
9
SIMULATIONS
OF
DYNAMIC
PROPERTIES
237
9.1
INTRODUCTION
237
9.2
MOLECULAR
MOTIONS
AND
THE
MEAN
SQUARE
DISPLACEMENT
237
9.2.1
MOTION
IN
BULK
PHASES
237
CONTENTS
XI
9.2.2
MOTION
IN
CONFINED
SPACES
AND
ON
SURFACES
244
9.3
MOLECULAR
VELOCITIES
AND
TIME
CORRELATION
FUNCTIONS
247
9.3.1
COLLISIONS
AND
THE
VELOCITY
AUTOCORRELATION
FUNCTION
247
9.3.2
TIME
CORRELATION
FUNCTIONS
FOR
STATIONARY
SYSTEMS
251
9.4
ORIENTATION
AUTOCORRELATION
FUNCTIONS
251
9.5
HYDROGEN
BONDING DYNAMICS
253
9.6
MOLECULAR
MOTIONS
ON
NANOPARTICLES:
THE
LINDEMANN
INDEX
254
9.7
MICROSCOPIC
DETERMINATION
OF
TRANSPORT
COEFFICIENTS
256
9.7.1
THE
TRANSPORT
COEFFICIENTS
256
9.7.2
NONEQUILIBRIUM
MOLECULAR
DYNAMICS
SIMULATIONS
OF
TRANSPORT
COEFFICIENTS
261
9.7.3
THE
GREEN-KUBO
RELATIONS
AND
SIMULATION
OF
TRANSPORT
COEFFICIENTS
261
CHAPTER
9
APPENDICES
263
9.
A.1
BROWNIAN
MOTION
AND
THE
LANGEVIN
EQUATION
263
9.
A.2
THE
DISCRETE
RANDOM
WALK
MODEL
OF
DIFFUSION
265
9.
A.3
THE
SOLUTION
OF
THE
DIFFUSION
EQUATION
267
9.
A.4
RELATION
BETWEEN
MEAN
SQUARE
DISPLACEMENT
AND
DIFFUSION
COEFFICIENT
268
10
MONTE
CARLO
SIMULATIONS
269
10.1
INTRODUCTION
269
10.2
THE
CANONICAL
MONTE
CARLO
PROCEDURE
270
10.2.1.1
DETERMINING
WHICH
MOLECULE
TO
MOVE
273
10.2.1.2
DETERMINING
WHETHER
A
TRANSLATION
OR
ROTATION
IS
PERFORMED
273
10.2.1.3
TRANSLATION
MOVES
274
10.2.1.4
ROTATIONAL
MOVES
274
10.3
THE
CONDITION
OF
MICROSCOPIC
REVERSIBILITY
AND
IMPORTANCE
SAMPLING
277
10.4
MONTE
CARLO
SIMULATIONS
IN
OTHER
ENSEMBLES
279
10.4.1
GRAND
CANONICAL
MONTE
CARLO
SIMULATIONS
279
10.4.2
ISOTHERMAL-ISOBARIC
MONTE
CARLO
SIMULATIONS
283
10.4.3
BIASED
MONTE
CARLO
SAMPLING
METHODS
284
10.5
GIBBS
ENSEMBLE
MONTE
CARLO
SIMULATIONS
285
10.5.1
SIMULATIONS
OF
LIQUID-GAS
PHASE
EQUILIBRIUM
285
10.6
SIMULATIONS
OF
GAS
ADSORPTION
IN
POROUS
SOLIDS
288
10.6.1
SIMULATIONS
OF
THE
GAS
ADSORPTION
ISOTHERM
AND
HEAT
OF
ADSORPTION
288
10.6.2
FORCE
FIELDS
FOR
GAS
ADSORPTION
SIMULATIONS
291
10.6.3
BLOCK
AVERAGING
OF
DATA
FROM
MONTE
CARLO
AND
MOLECULAR
DYNAMICS
SIMULATIONS
291
CHAPTER
10
APPENDICES
295
10.
A.
1
THERMODYNAMIC
RELATION
FOR
THE
HEAT
OF
ADSORPTION
295
REFERENCES
297
INDEX
317 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Alavi, Saman |
| author_GND | (DE-588)1213910218 |
| author_facet | Alavi, Saman |
| author_role | aut |
| author_sort | Alavi, Saman |
| author_variant | s a sa |
| building | Verbundindex |
| bvnumber | BV046801885 |
| classification_rvk | WD 2200 WD 9200 |
| ctrlnum | (OCoLC)1182906213 (DE-599)DNB1199635707 |
| discipline | Chemie / Pharmazie Biologie |
| discipline_str_mv | Chemie / Pharmazie Biologie |
| format | Book |
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| id | DE-604.BV046801885 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:56:05Z |
| indexdate | 2024-07-20T03:14:26Z |
| institution | BVB |
| institution_GND | (DE-588)16179388-5 |
| isbn | 9783527341054 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032210631 |
| oclc_num | 1182906213 |
| open_access_boolean | |
| owner | DE-29T DE-11 DE-B768 DE-20 DE-703 |
| owner_facet | DE-29T DE-11 DE-B768 DE-20 DE-703 |
| physical | xv, 326 Seiten Illustrationen, Diagramme 24.4 cm x 17 cm |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | Wiley-VCH |
| record_format | marc |
| spelling | Alavi, Saman Verfasser (DE-588)1213910218 aut Molecular simulations fundamentals and practice Saman Alavi Weinheim Wiley-VCH [2020] xv, 326 Seiten Illustrationen, Diagramme 24.4 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Molekulardynamik (DE-588)4170370-4 gnd rswk-swf Bioinformatics & Computational Biology Bioinformatik Bioinformatik u. Computersimulationen in der Biowissenschaften Biowissenschaften CHD0: Computational Chemistry u. Molecular Modeling Chemie Chemistry Computational Chemistry & Molecular Modeling Computational Chemistry u. Molecular Modeling LSG0: Bioinformatik u. Computersimulationen in der Biowissenschaften Life Sciences MS90: Materialwissenschaften / Theorie, Modellierung u. Simulation Materials Science Materialwissenschaften Materialwissenschaften / Theorie, Modellierung u. Simulation Theory, Modeling & Simulation Molekulardynamik (DE-588)4170370-4 s Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 Wiley-VCH (DE-588)16179388-5 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-527-69953-7 Erscheint auch als Online-Ausgabe, EPUB 978-3-527-69946-9 Erscheint auch als Online-Ausgabe, oBook 978-3-527-69945-2 X:MVB http://www.wiley-vch.de/publish/dt/books/ISBN978-3-527-34105-4/ DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032210631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alavi, Saman Molecular simulations fundamentals and practice Monte-Carlo-Simulation (DE-588)4240945-7 gnd Molekulardynamik (DE-588)4170370-4 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4170370-4 |
| title | Molecular simulations fundamentals and practice |
| title_auth | Molecular simulations fundamentals and practice |
| title_exact_search | Molecular simulations fundamentals and practice |
| title_exact_search_txtP | Molecular simulations fundamentals and practice |
| title_full | Molecular simulations fundamentals and practice Saman Alavi |
| title_fullStr | Molecular simulations fundamentals and practice Saman Alavi |
| title_full_unstemmed | Molecular simulations fundamentals and practice Saman Alavi |
| title_short | Molecular simulations |
| title_sort | molecular simulations fundamentals and practice |
| title_sub | fundamentals and practice |
| topic | Monte-Carlo-Simulation (DE-588)4240945-7 gnd Molekulardynamik (DE-588)4170370-4 gnd |
| topic_facet | Monte-Carlo-Simulation Molekulardynamik |
| url | http://www.wiley-vch.de/publish/dt/books/ISBN978-3-527-34105-4/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032210631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT alavisaman molecularsimulationsfundamentalsandpractice AT wileyvch molecularsimulationsfundamentalsandpractice |