So about hacker. How we look at the nature via gadget, via observation. Now it is the most modern skills being hacker? Who are Hackers? Investigatiors from one side, bad guys from another. Its the modern profession and titile IT specialist, but the nature are still the unidentified.
Look at the background
Singe Point calculation
Singlet state calculation
IR Spectrum
Look at the background
Both molecular and quantum mechanics methods rely on the
Born-Oppenheimer approximation. In quantum mechanics, the Schrödinger equation (1) gives the wave
functions and energies of a molecule.
HY = EY (1)
where
H is the molecular Hamiltonian,
Y is the wave function,
E is the energy.
The molecular Hamiltonian is
composed of these operators:
- the kinetic energy of the nuclei
(N) and electrons (E),
- nuclear-nuclear (NN) and
electron-electron repulsion (EE),
- and the attraction between nuclei
and electrons (NE)
(equation 1).
H (kinetic energy)N + (kinetic energy)E = + (repulsion)NN + (repulsion)EE + (attraction)NE (2)
Nuclei have many times more mass
than electrons. During a very small period of time when the movement of heavy
nuclei is negligible, electrons are moving so fast that their distribution is smooth.
This leads to the approximation that the electron distribution is dependent
only on the fixed positions of nuclei and not on their velocities. This
approximation allows two simplifications of the molecular Hamiltonian. The
nuclear kinetic energy term drops out of the molecular Hamiltonian. The nuclear
kinetic energy term drops out (equation 3).
H = (kinetic energy)E + (repulsion)NN + (repulsion)EE + (attraction)NE (3)
Since the nuclear-nuclear repulsion
is constant for a fixed configuration of atoms, this term also drops out. The
Hamiltonian is now purely electronic.
Helectronic = (kinetic energy)E + (repulsion)EE + (attraction)NE (4)
After solving the electronic
Schrödinger equation (equation 4), to calculate a potential energy surface, you
must add back nuclear-nuclear repulsions (equation 5).
HelectronicYelectronic = EelectronicYelectronic
VPES = Eelectronic + (repulsion)NN (5)
What is the Calculation chemisty? Is it only academic science and it time over leaveing experiments only for Ph.D students or this scince have future. Here I write only my experience to show the possibility of computational possibility and thinking about it.
Lets start with Water.
H2O - WATER (hydrogen oxide) H2O, they say. m. 18.016, just a steady Port.
hydrogen with oxygen. The liquid is odorless, taste and color.
The structure and physical properties of the molecule.
Hydrogen and oxygen atoms in water
molecules are located in the corners of an isosceles triangle with the length
of the O-H 0.0957 nm;
valence angle H-O-H 104,5 °;
dipole moment of 6.17 * 10-30 * m
Cl;
molecular polarizability 1.45 * 10-3
Nm3;
the average quadrupole time - 1.87 *
10-41 m2 * Kl,
the ionization energy of 12.6 eV,
proton affinity of 7.1 eV.
The length of the chemical bond - the distance between the nuclei of atoms
chemically bonded. The length of chemical bonds - an important physical
quantity that determines the geometric dimensions of the chemical bond, its
extent in space.
Valence angle
- the angle formed by the directions of chemical (covalent) bonds emanating
from a single atom. Knowledge of bond angles is necessary to determine the
molecular geometry. The valence angles depend on the individual characteristics
of the attached atoms and the hybridization of the atomic orbitals of the
central atom. For simple molecular bond angle as the other geometric parameters
of the molecule can be calculated by methods of quantum chemistry.
Experimentally, they are determined from the values of the moments of inertia
of the molecules obtained by the analysis of their rotational spectra (see.
Infrared spectroscopy, molecular spectra, Microwave spectroscopy). Valence
angle of complex molecules is determined by diffraction structural analysis.
Polarizability
is the ability to form instantaneous dipoles. It is a property of matter.
Polarizabilities determine the dynamical response of a bound system to external
fields, and provide insight into a molecule's internal structure.
The electric dipole moment - vector physical quantity characterizing, along with net charge (and
less frequently used higher multipole moments), the electrical properties of a
system of charged particles (charge distribution) in the sense that it produces
and field action on it of external fields.
The simplest system of charges,
which has a certain (not depending on the choice of coordinates) of non-zero
dipole moment - is a dipole (two point particles with the same largest of
opposite charges).
The ionization energy - the energy of a communication, or as it is sometimes called, the
first ionization potential (I1), is the lowest energy needed to remove an
electron from a free atom in its lowest energy (ground) state on infinity. The ionization energy is one of the main
characteristics of the atom from which depend largely on the nature and
strength of chemical bonds formed by an atom. From the atomic ionization energy
also depend significantly on reducing properties of the corresponding simple
substance.
Electron affinity - can be any atom or molecule to the electron, or anions or molecules
to the proton. The most important E. s. the atom the electron and molecular
anions and the proton. Usually it expressed in eV per unit (atom, molecule,
ion) or kcal / g-atom. E. s. the atom the electron has an energy that is
released (positive affinity) or absorbed (negative affinity) in the case of
accession to the atom the electron, becoming the anion.
When interaction. with other water
molecules. atoms, ions and molecules, including with other molecules in the
water condenses. phases, these parameters vary.
We create the molecule of water but still dont know what inside. Lets glance inside. What helps us - molecular mechanics and molecular dynamics.
I) Setup the Molecular Mechanics
Molecular mechanical force fields
use the equations of classical mechanics to describe the potential energy
surfaces and physical properties of molecules. A molecule is described as a
collection of atoms that interact with each other by simple analytical
functions. This description is called a force field. One component of a force
field is the energy arising from compression and stretching a bond.
Why we use AMBER?
The AMBER (Assisted Model
Building and Energy Refinement) is based on a force field developed for protein
and nucleic acid computations by members of the Peter Kollman research group at
the University of California, San Francisco. The original AMBER has become one
of the more widely used academic force fields and extensive work has gone into
developing it — resulting in a number of versions of the method and associated
parameters.
Before we know something about molecular we should make the Geometry optimization to find the minimum of potential energy - the most stable condition of molecular.
We do it.
The minimum represents the potential
energy closest to the starting structure of a molecule.
We will use the
Polak-Ribiere
as the minimization algorithm. This algorithm is a good general-purpose
optimizer. Both Polak-Ribiere and Fletcher-Reeves
perform a series of one-dimensional searches, or cycles, in conjugate gradient directions.
Different algorithms might be appropriate in different circumstances.
RMS gradient
Use 0.1 for the RMS gradient condition,
and the default values for the other variables.
Geometry Optimization
To carry out a geometry optimization
(minimization), HyperChem starts with a set of Cartesian coordinates for a
molecule and tries to find a new set of coordinates with a minimum potential
energy. The potential energy surface is very complex, even for a molecule
containing only a few dihedral angles.
Since minimization calculations
cannot cross or penetrate potential energy barriers, the molecular structure
found during an optimization may be a local and not a global minimum.
The minimum represents the potential energy closest to the starting
structure of a molecule. Researchers frequently use minimizations to generate a structure at a
stationary point for a subsequent single point calculation or to remove
excessive strain in a molecule, preparing it for a molecular dynamics
simulation.
Singe Point calculation
A single point calculation determines
molecular properties, such as energy or spin density, of a defined molecular
structure. Normally, these calculations are for stationary points on a
potential energy surface. Occasionally, you may want to characterize the potential
energy surface by calculating the energies of a grid of points on the surface.
You can use those results to generate a contour plot of the surface.
With HyperChem, you can use either
molecular or quantum mechanical methods for single point calculations. The
calculation provides an energy and the gradient of that energy. The gradient is
the root-mean-square of the derivative of the energy with respect to Cartesian
coordinates. At a minimum the forces on atoms (the gradient) are zero. The size
of the gradient can provide qualitative information to determine if a structure
is close to a minimum.
I) Single Point
PolakRibiere optimizer
Energy=0.000015
Gradient=0.068458 Converged=YES (2 cycles 8 points).
Bond=1.21803e-005 Angle=3.248e-006 Dihedral=0 Vdw=0 H-bond=0
Electrostatic=0.
Single Point,
MolecularMechanics, molecule = C:\Users\Lisa-Alisa\Desktop\H2O\water.hin.
Total
Energy=0.000015 Gradient=0.068464.
Bond=1.21827e-005 Angle=3.24823e-006 Dihedral=0 Vdw=0 H-bond=0
Electrostatic=0.
Then we investigate the method Ab initio
II) Ab initio
Ab initio
(from the lat -. "From the beginning") - study the phenomenon of the
natural laws without additional empirical assumptions or special models.
Ab initio quantum chemistry methods are computational chemistry methods based on quantum
chemistry. The term ab initio
was first used in quantum chemistry by Robert Parr and coworkers, including
David Craig in a semiempirical study on the excited states of benzene. The all
methods based on to solve the Schrödinger equation. In the Hartree–Fock method
and the configuration interaction method, this approximation allows one to
treat the Schrödinger equation as a "simple" eigenvalue (собственное значение) equation of the electronic molecular
Hamiltonian, with a discrete set of solutions.
Polak-Ribiere
as the minimization algorithm. This algorithm is a good general-purpose
optimizer. Both Polak-Ribiere and Fletcher-Reeves
perform a series of one-dimensional searches, or cycles, in conjugate gradient directions.
Different algorithms might be appropriate in different circumstances.
RMS gradient
Use 0.1 for the RMS gradient condition,
and the default values for the other variables.
The text boxes for RMS gradient and
maximum cycles let you set conditions for ending a calculation. When the
calculation reaches either of these criteria, the calculation ends.
RHF calculation in computational physics and chemistry, the Hartree–Fock (HF) method
is a method of approximation for the determination of the wave function and the
energy of a quantum many-body system in a stationary state.
AbInitio
PolakRibiere optimizer
Convergence limit =
0.0000100 Iteration limit = 50
Accelerate
convergence = YES
Optimization
algorithm = Polak-Ribiere
Criterion of RMS
gradient = 0.1000 kcal/(A mol) Maximum
cycles = 45
The initial guess
of the MO coefficients is from eigenvectors of the core Hamiltonian.
Shell Types: S,
S=P.
RHF Calculation:
RHF calculation in computational physics and
chemistry, the Hartree–Fock (HF) method is a method of approximation for the
determination of the wave function and the energy of a quantum many-body system
in a stationary state.
Singlet state
calculation
Number of electrons
= 10
Number of
Doubly-Occupied Levels = 5
Charge on the
System = 0
Total Orbitals
(Basis Functions) = 7
Primitive Gaussians
= 21
Starting HyperGauss
calculation with 7 basis functions and 21 primitive Gaussians.
2-electron Integral
buffers will be 32000 words (double precision) long.
Two electron
integrals will use a cutoff of
1.00000e-010
Regular integral
format is used.
231 integrals have been
produced.
E=-47041.8164
Grad=0.025 Conv=YES(3 cycles 10 points) [Iter=1 Diff=0.00000]
ENERGIES AND
GRADIENT
Total Energy = -47041.8163877 (kcal/mol)
Total Energy = -74.965896964 (a.u.)
Electronic Kinetic
Energy = 46761.1574396 (kcal/mol)
Electronic Kinetic
Energy = 74.518638516 (a.u.)
The Virial
(-V/T) = 2.0060
eK, ee and eN
Energy = -52630.8235968 (kcal/mol)
Nuclear Repulsion
Energy =
5589.0072091 (kcal/mol)
RMS Gradient = 0.0255718 (kcal/mol/Ang)
MOLECULAR POINT
GROUP
C2V
Single Point, AbInitio, molecule =
C:\Users\Lisa-Alisa\Desktop\H2O\water.hin.
Convergence limit =
0.0000100 Iteration limit = 50
Accelerate
convergence = YES
Computing gradient
is requested.
The initial guess
of the MO coefficients is from eigenvectors of the core Hamiltonian.
Shell Types: S,
S=P.
RHF Calculation:
RHF calculation in computational physics and
chemistry, the Hartree–Fock (HF) method is a method of approximation for the
determination of the wave function and the energy of a quantum many-body system
in a stationary state.
Singlet state calculation
Number of electrons
= 10
Number of
Doubly-Occupied Levels = 5
Charge on the
System = 0
Total Orbitals
(Basis Functions) = 7
Primitive Gaussians
= 21
Starting HyperGauss
calculation with 7 basis functions and 21 primitive Gaussians.
Energy=-47041.816388
Gradient=0.025078 Symmetry=C2V
ENERGIES AND
GRADIENT
Total Energy = -47041.8163879 (kcal/mol)
Total Energy = -74.965896965 (a.u.)
Electronic Kinetic
Energy = 46761.1623307 (kcal/mol)
Electronic Kinetic
Energy = 74.518646311 (a.u.)
The Virial
(-V/T) = 2.0060
eK, ee and eN
Energy = -52630.8235810 (kcal/mol)
Nuclear Repulsion
Energy = 5589.0071931 (kcal/mol)
RMS Gradient = 0.0250783 (kcal/mol/Ang)
MOLECULAR POINT
GROUP
C2V
III) Use the Semi-emperical computational
method
Semi-empirical quantum chemistry methods are based on the Hartree–Fock formalism, but
make many approximations and obtain some parameters from empirical data. They
are very important in computational chemistry for treating large molecules
where the full Hartree–Fock method without the approximations is too expensive.
The use of empirical parameters appears to allow some inclusion of electron
correlation effects into the methods.
The other NDO methods, MINDO/3, MNDO, AM1,
and PM3 replace nuclear repulsion terms in the potential energy by
parameterized, core-repulsion terms. The terms compensate for considering only
valence electrons in the electronic Schrödinger equation, and they incorporate
effects of electron correlation.
PM3 is a reparameterization of AM1, which is based on the neglect of diatomic differential overlap (NDDO)
approximation. NDDO retains all one-center differential overlap terms when
Coulomb and exchange integrals are computed. PM3 differs from AM1 only in the
values of the parameters. The parameters for PM3 were derived by comparing a
much larger number and wider variety of experimental versus computed molecular
properties. Typically, nonbonded interactions are less repulsive in PM3 than in
AM1. PM3 is primarily used for organic molecules, but is also parameterized for
many main group elements.
PM3
PolakRibiere optimizer
Convergence limit = 0.0100000
Iteration limit = 50
Accelerate convergence = YES
Optimization algorithm = Polak-Ribiere
Criterion of RMS gradient = 0.1000 kcal/(A mol) Maximum cycles = 45
RHF Calculation:
RHF calculation in computational physics and
chemistry, the Hartree–Fock (HF) method is a method of approximation for the
determination of the wave function and the energy of a quantum many-body system
in a stationary state.
Singlet state calculation
Number of electrons = 8
Number of Double Occupied Levels = 4
Charge on the System = 0
Total Orbitals = 6
Starting PM3 calculation with 6 orbitals
E=-217.2215 Grad=0.014 Conv=YES(3 cycles 9 points) [Iter=1 Diff=0.00000]
ENERGIES AND GRADIENT
Total Energy
= -7492.6904720 (kcal/mol)
Total Energy
= -11.940123906 (a.u.)
Binding Energy
= -217.2217040 (kcal/mol)
Isolated Atomic Energy
= -7275.4687680 (kcal/mol)
Electronic Energy
= -10937.8397201 (kcal/mol)
Core-Core Interaction
= 3445.1492481 (kcal/mol)
Heat of Formation
= -53.4587040 (kcal/mol)
Gradient
= 0.0125341 (kcal/mol/Ang)
MOLECULAR POINT GROUP
C2V
Single Point, SemiEmpirical,
molecule = C:\Users\Lisa-Alisa\Desktop\H2O\water.hin.
PM3
Convergence limit = 0.0100000
Iteration limit = 50
Accelerate convergence = YES
RHF Calculation:
RHF calculation in computational physics and
chemistry, the Hartree–Fock (HF) method is a method of approximation for the
determination of the wave function and the energy of a quantum many-body system
in a stationary state.
Singlet state calculation
Number of electrons = 8
Number of Double Occupied Levels = 4
Charge on the System = 0
Total Orbitals = 6
Starting PM3 calculation with 6 orbitals
Iteration = 1 Difference = 1086.48757
Iteration = 2 Difference = 15.32661
Iteration = 3 Difference = 6.16280
Iteration = 4 Difference = 2.80484
Iteration = 5 Difference = 0.00230
Energy=-217.221704 Gradient=0.013250 Symmetry=C2V
ENERGIES AND GRADIENT
Total Energy =
-7492.6904717 (kcal/mol)
Total Energy
= -11.940123906 (a.u.)
Binding Energy
= -217.2217037 (kcal/mol)
Isolated Atomic Energy
= -7275.4687680 (kcal/mol)
Electronic Energy =
-10937.8397555 (kcal/mol)
Core-Core Interaction
= 3445.1492838 (kcal/mol)
Heat of Formation
= -53.4587037 (kcal/mol)
Gradient
= 0.0132503 (kcal/mol/Ang)
MOLECULAR POINT GROUP
C2V
IR Spectrum
Transition State Search
As mentioned earlier, a potential
energy surface may contain saddle points; that is, stationary points where
there are one or more directions in which the energy is at a maximum. A saddle
point with one negative eigenvalue (Собственное значение)
corresponds to a transition structure for a chemical reaction of changing
isomeric form. Transition structures also exist for reactions involving
separated species, for
example, in a bimolecular reaction
A + B → C + D.
Activation energy, i.e., the energy of the transition structure relative to reactants,
can be observed experimentally. However, the only way that the geometries of
transition structures can be evaluated is from theory. Theory also can give
energetics and geometry parameters of short-lived reaction intermediates.
Transition state search algorithms
rather climb up the potential energy surface, unlike geometry optimization
routines where an energy minimum is searched for. The characterization of even
a simple reaction potential surface may result in location of more than one
transition structure, and is likely to require many more individual
calculations than are necessary to obtain equilibrium geometries for either
reactant or product.
EIGENVALUES
- собственное значение
The
transitional state spectrum
Transition State Search: Eigenvector Following, SemiEmpirical, molecule = C:\Users\Lisa-Alisa\Desktop\H2O\water.hin.
PM3
Convergence limit = 0.0100000 Iteration limit = 50
Accelerate convergence = YES
RHF Calculation:
RHF calculation in computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.
Singlet state calculation
Number of electrons = 8
Number of Double Occupied Levels = 4
Charge on the System = 0
Total Orbitals = 6
Starting PM3 calculation with 6 orbitals
Computing the Hessian is required.
Computing the Hessian using Cartesian coordinates.
Iteration = 1 Difference = 1086.48757
Iteration = 2 Difference = 15.32661
Iteration = 3 Difference = 6.16280
Iteration = 4 Difference = 2.80484
Iteration = 5 Difference = 0.00230
Computing the initial Hessian: done 30%.
Computing the initial Hessian: done 60%.
Computing the initial Hessian: done 100%.
ENERGIES AND GRADIENT
Total Energy = -7492.6899994 (kcal/mol)
Total Energy = -11.940123153 (a.u.)
Binding Energy = -217.2212314 (kcal/mol)
Isolated Atomic Energy = -7275.4687680 (kcal/mol)
Electronic Energy = -10937.8392833 (kcal/mol)
Core-Core Interaction = 3445.1492838 (kcal/mol)
Heat of Formation = -53.4582314 (kcal/mol)
Gradient = 0.1503936 (kcal/mol/Ang)
MOLECULAR POINT GROUP
C2V
IV) Density Functional method
Density functional theory (DFT) is a computational quantum mechanical
modelling method used in physics, chemistry and materials science to
investigate the electronic structure (principally the ground state) of
many-body systems, in particular atoms, molecules, and the condensed phases.
Using this theory, the properties of a many-electron system can be determined
by using functionals, i.e. functions of another function, which in this case is
the spatially dependent electron density. Hence the name density functional
theory comes from the use of functionals of the electron density. DFT is among
the most popular and versatile methods available in condensed-matter physics,
computational physics, and computational chemistry.
Vibrational Analysis, DFT,
molecule = C:\Users\Lisa-Alisa\Desktop\H2O\water.hin.
Exchange-Correlation=B3-LYP
B3-LYP
Convergence limit = 0.0000100
Iteration limit = 50
Accelerate convergence = YES
The initial guess of the MO coefficients is from eigenvectors of the
core Hamiltonian.
Shell Types: S, S=P.
RHF Calculation:
RHF calculation in computational physics and
chemistry, the Hartree–Fock (HF) method is a method of approximation for the
determination of the wave function and the energy of a quantum many-body system
in a stationary state.
Singlet state calculation
Number of electrons = 10
Number of Doubly-Occupied Levels = 5
Charge on the System = 0
Total Orbitals (Basis Functions) = 7
Primitive Gaussians = 21
Starting HyperDFT calculation with 7 basis functions and 21 primitive
Gaussians.
2-electron Integral buffers will be 32000 words (double precision) long.
Two electron integrals will use a cutoff of 1.00000e-010
Regular integral format is used.
306 integrals have been produced.
Starting the SCF procedure...
Iteration = 1 Difference = 25.3750037271
Iteration = 2 Difference = 14.9830152138
Iteration = 3 Difference = 0.0339600050
Iteration = 4 Difference = 0.0006392639
Iteration = 5 Difference = 0.0000082136
ENERGIES AND GRADIENT
Total Energy
= -47233.6385858 (kcal/mol)
Total Energy
= -75.271585057 (a.u.)
Electronic Kinetic Energy
= 46816.5680366 (kcal/mol)
Electronic Kinetic Energy
= 74.606940913 (a.u.)
The Virial (-V/T)
= 2.0089
eK, ee and eN Energy
= -53036.9116931 (kcal/mol)
Nuclear Repulsion Energy
= 5803.2731073 (kcal/mol)
RMS Gradient = 66.3487826 (kcal/mol/Ang)
MOLECULAR POINT GROUP
C2V
IV) Molecular Dynamic method
Molecular Dynamics
A molecular dynamics simulation
samples phase space (the region defined by atomic positions and velocities) by
integrating numerically Newton’s equations of motion. Unlike single point and geometry
optimization calculations, molecular dynamics calculation account for thermal
motion. Molecules may contain enough thermal energy to cross potential
barriers. Molecular dynamics calculations provide information about possible
conformations, thermodynamic properties, and dynamic behavior of molecules.
Molecular dynamics, DFT, molecule =
C:\Users\Lisa-Alisa\Desktop\H2O\water.hin.
Exchange-Correlation=B3-LYP
Density Functional
Convergence limit = 0.0000100
Iteration limit = 50
Accelerate convergence = YES
Heat time = 0.0000 ps Run time =
1.0000 ps
Cool time = 0.0000 ps Time step =
0.0010 ps
Starting temperature = 0.0000 K
Simulation temperature = 300.0000 K
Final temperature = 0.0000 K
Temperature step = 0.0000 K
The initial guess of the MO coefficients is from eigenvectors of the
core Hamiltonian.
Shell Types: S, S=P.
RHF Calculation:
RHF calculation in computational physics and
chemistry, the Hartree–Fock (HF) method is a method of approximation for the
determination of the wave function and the energy of a quantum many-body system
in a stationary state.
Singlet state calculation
Number of electrons = 10
Number of Doubly-Occupied Levels = 5
Charge on the System = 0
Total Orbitals (Basis Functions) = 7
Primitive Gaussians = 21
ENERGIES AND GRADIENT
Potential Energy
= -47239.9774387 (kcal/mol)
Potential Energy = -75.281686661 (a.u.)
Electronic Kinetic Energy
= 46734.6537795 (kcal/mol)
Electronic Kinetic Energy
= 74.476402251 (a.u.)
The Virial (-V/T)
= 2.0108
eK, ee and eN Energy
= -52597.6653235 (kcal/mol)
Nuclear Repulsion Energy
= 5357.6878848 (kcal/mol)
RMS Gradient
= 20.3828990 (kcal/mol/Ang)
MOLECULAR POINT GROUP
CS
Time = 1.0000 ps
Kinetic Energy = 12.0096 kcal/mol
Total Energy = -47227.9688
kcal/mol
Temperature = 1342.99 K
Time=1.0000 ps TotalEnergy=-47227.9688 kcal/mol T=1342.99 K [final]
V) Langevin Dynamics
Molecules in solution undergo
collisions with other molecules and experience frictional forces as they move
through the solvent. Using Langevin dynamics, you can model these effects and study the
dynamical behavior of a molecular system in a liquid environment. These
simulations can be much faster than molecular dynamics. Instead of explicitly
including solvent molecules, the Langevin method models their effect through
random forces applied to the molecule of interest to simulate collisions, and
frictional forces are added to model the energy losses associated with these
collisions.
Langevin dynamics simulations can be used to study the same kinds of
problems as molecular dynamics: time dependent properties of solvated systems
at non-zero temperatures. Because of the implicit treatment of the solvent, this method is
particularly wellsuited for studying large molecules in solution. It is
possible to decouple the time scales of molecular motion and focus on just the slow
modes associated with conformational changes, for example, or to follow the
rapid bond stretching motions leading to chemical
reaction, while incorporating the
influence of molecular collisions. Langevin dynamics has been use to study
solvent effects on the structural dynamics of the active site of the enzyme
lysozyme, conformational equilibria and the dynamics of conformational transitions
in liquid alkanes, and temperature effects on a system of interacting quantum
harmonic oscillators.
Langevin dynamics, DFT,
molecule = C:\Users\Lisa-Alisa\Desktop\H2O\water.hin.
Exchange-Correlation=B3-LYP
Density Functional
Convergence limit = 0.0000100
Iteration limit = 50
Accelerate convergence = YES
Heat time = 0.0000 ps Run time =
1.0000 ps
Cool time = 0.0000 ps Time step =
0.0010 ps
Starting temperature = 0.0000 K
Simulation temperature = 300.0000 K
Final temperature = 0.0000 K
Temperature step = 0.0000 K
Friction coefficient =
0.0000000
The initial guess of the MO coefficients is from eigenvectors of the
core Hamiltonian.
Shell Types: S, S=P.
RHF Calculation:
RHF calculation in computational physics and
chemistry, the Hartree–Fock (HF) method is a method of approximation for the
determination of the wave function and the energy of a quantum many-body system
in a stationary state.
Singlet state calculation
Number of electrons = 10
Number of Doubly-Occupied Levels = 5
Charge on the System = 0
Total Orbitals (Basis Functions) = 7
Primitive Gaussians = 21
Starting HyperDFT calculation with 7 basis functions and 21 primitive
Gaussians.
2-electron Integral buffers will be 32000 words (double precision) long.
Two electron integrals will use a cutoff of 1.00000e-010
Regular integral format is used.
319 integrals have been produced.
ENERGIES AND GRADIENT
Potential Energy
= -47238.6785911 (kcal/mol)
Potential Energy
= -75.279616816 (a.u.)
Electronic Kinetic Energy
= 46734.6401218 (kcal/mol)
Electronic Kinetic Energy
= 74.476380486 (a.u.)
The Virial (-V/T)
= 2.0108
eK, ee and eN Energy
= -52643.1736746 (kcal/mol)
Nuclear Repulsion Energy
= 5404.4950836 (kcal/mol)
RMS Gradient =
24.5004701 (kcal/mol/Ang)
MOLECULAR POINT GROUP
CS
EIGENVALUES(eV)
Symmetry: 1 A' 2 A' 3 A' 4 A' 1 A"
Eigenvalue: -512.483093
-24.481548 -11.503771 -5.930172
-3.671524
Symmetry: 5 A' 6 A'
Eigenvalue: 8.049422 11.473605
Time = 1.0000 ps
Kinetic Energy = 1.4270 kcal/mol
Total Energy = -47237.2500
kcal/mol
Temperature = 159.58 K
Time=1.0000 ps TotalEnergy=-47237.2500 kcal/mol T=159.58 K [final]
IV) Method Monte Carlo
Monte Carlo Simulations
The Monte Carlo method samples phase
space by generating random configurations from a Boltzmann distribution at a
given temperature. Averages computed from a properly equilibrated Monte Carlo
simulation correspond to thermodynamic ensemble averages. Thus, the Monte Carlo
method can be used to find average energies and equilibrium structural
properties of complex interacting systems.
A sequence of successive
configurations from a Monte Carlo simulation constitutes a trajectory in phase
space; with HyperChem, this trajectory may be saved and played back in the same
way as a dynamics trajectory. With appropriate choices of setup parameters, the
Monte Carlo method may achieve equilibration more rapidly than molecular
dynamics. For some systems, then, Monte Carlo provides a more direct route to
equilibrium structural and thermodynamic properties. However, these
calculations can be quite long, depending upon the system studied. Monte Carlo
simulations provide an alternate approach to the generation of stable conformations.
As with HyperChem’s other simulation methods, the effects of temperature
changes and solvation are easily incorporated into the calculations.
Monte Carlo, DFT, molecule =
C:\Users\Lisa-Alisa\Desktop\H2O\water.hin.
Exchange-Correlation=B3-LYP
Density Functional
Convergence limit = 0.0000100
Iteration limit = 50
Accelerate convergence = YES
Heat steps = 0 Run steps = 100
Cool steps = 0 Maximum delta =
0.0500 ps
Starting temperature = 0.0000 K
Simulation temperature = 300.0000 K
Final temperature = 0.0000 K
Temperature step = 0.0000 K
The initial guess of the MO coefficients is from eigenvectors of the
core Hamiltonian.
Shell Types: S, S=P.
RHF Calculation:
Singlet state calculation
Number of electrons = 10
Number of Doubly-Occupied Levels = 5
Charge on the System = 0
Total Orbitals (Basis Functions) = 7
Primitive Gaussians = 21
Total Energy = -47238.7813 kcal/mol
Temperature = 300.00 K
Steps=100.0000 TotalEnergy=-47238.7813 kcal/mol T=300.00 K [final]
Starting the SCF procedure...
Steps=100 Total Energy=-47238.7813 kcal/mol T=300.00 K [Iter=1
Diff=0.00000]
ENERGIES AND GRADIENT
Potential Energy
= -47241.4656307 (kcal/mol)
Potential Energy
= -75.284058246 (a.u.)
Electronic Kinetic Energy
= 46755.1090032 (kcal/mol)
Electronic Kinetic Energy
= 74.508999721 (a.u.)
The Virial (-V/T)
= 2.0104
eK, ee and eN Energy
= -52751.3071619 (kcal/mol)
Nuclear Repulsion Energy
= 5509.8415313 (kcal/mol)
RMS Gradient
= 21.6762023 (kcal/mol/Ang)
MOLECULAR POINT GROUP
CS
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