Hello Dr Trent, first thank you for this beautifully taught course. I did well on Quantum chem 1 because of the previous playlist. However, my question is what exactly are atomic coordinates. I googled this term & i saw that its basically like locating an atom in a unit cell & hence obtaining x y z coordinates. But whats a unit cell and who chose those numbers displayed for the coordinates and what are they relative to. This is really a big transition from Quantum Chem 1. please reach back. Thanks!
Hi Abdalla. The Cartesian coordinates here are not located within a unit cell, but are locations in infinite 3-dimensional space relative to some arbitrary origin. The term "unit cell" implies an infinite repeating unit which extends forever in all dimensions. The unit cell contains the minimum amount of space necessary to describe how the atoms repeat throughout a system over all space. This is typically used in condensed phase systems (solids / crystals and liquids / solutions). The Cartesian coordinates given here are intended to imply a gas phase by default which takes place in some infinite container. It doesn't matter what we choose the origin to be, just that we choose one, as only interatomic distances have any meaning. Similarly we can rotate the axes in any direction we like without affecting the properties of the system. These attributes are called translational invariance and rotational invariance.
I'm not sure I really understood the section on degrees of freedom. If I have a system with 10 atoms (N=10), then there are 30 coordinates (3N=30). But what does it mean to say these coordinates have only 24 unique coordinates? If I only give you 24 values I haven't fully described the system... I also sometimes see it stated that degrees of freedom is the number of ways the coordinates can move. So surely a molecule has only 6 degrees of freedom - the three translations and the three rotations. So I don't know if degrees of freedom refers to the minimum number of values needed to describe a system (in which case here it would be 3N, not 3N - 6), or whether it refers to the number of independent ways it can move (in which case here it would be 6 not 3N - 6). Can anyone help? I feel like I am close to understanding since I can work out where 3N and 6 come from individually, but not why one is subtracted from the other.
A molecule has an x, y, and z coordinate for all N atoms. This gives 3N coordinates. If we translate the molecule, none of the *internal* degrees of freedom change (all atoms still have the same interatomic distance to all other atoms as they did before translation). The same is true of rotation. All molecules have 3 translations. Non-linear molecules have 3 rotations. This leaves 3N-6 *internal* degrees of freedom which will change the interatomic distances between atoms. It is completely arbitrary where we define the origin, and what directions we choose for the x, y, and z axes. No matter our choice, we have the same molecule (the same set of *internal* degrees of freedom). Thus the 3 translations (choice of origin) and the 3 rotations (choice of x, y, and z axes) are redundant coordinates. They do not provide new information about the structure of the molecule, only information about our arbitrary choices of origin and axes. The remaining 3N-6 non-redundant coordinates are the *internal* degrees of freedom, which affect the molecular structure. These can be represented by the vibrational normal modes of the molecule. A non-linear polyatomic molecule has 3N-6 vibrational modes which are independent / orthogonal, just as we need to describe our *internal* degrees of freedom, and thus form an ideal basis set for describing these *internal* degrees of freedom, which actually give us information about the structure of the molecule. This concept is expanded on later in the chapter, specifically in video 1.10 on Z-matrices.
I had a hard time understanding this part too. Does it mean that these coordinates can be stored in some more efficient way, with less numbers stored in memory, or something? I don't quite get how, because even if we stored RELATIVE displacements of atoms with respect to each other as vectors, these would still require 3 coordinates, whether we store them as Cartesian x,y,z coordinates, or polar theta,phi,r coordinates.
Hi Adam, A PDB file contains more information than an XYZ file, and is a superset of the XYZ file's information, so converting PDB --> XYZ is straightforward. Count the total number of atoms, and put that on the first line. Second line is an arbitrary comment or empty line. Third to N+2nd line each contain four columns: Atomic symbol, X coordinate, Y coordinate, Z coordinate. All 4 of those are contained within the PDB file, but which column they are varies. Just match each column to to appropriate column for the format. Going backwards (XYZ --> PDB) would be more challenging, as PDB files contain more columns / information, so for each atom you would need more info than exists in the XYZ file (residue, residue index, chain, etc.).
Hi Mario. Great question. We don't know exactly what the bonds are from an xyz file. We can do a pretty good job of inferring what they are, but it isn't guaranteed. There are other file formats that explicitly specify what atoms are bonded to one another. XYZ files are typically used for quantum chemistry methods where we don't have to specify where the bonds are, because it's a somewhat fuzzy, qualitative subject and what is or isn't a bond exists on a continuum. What is sometimes done is to look at all of the interatomic distances and count those within some fraction of the sum of the covalent radii as bonded atom pairs. This is what is done in the example problems in this chapter.
TMP Chem I see. I ended up answering the question myself by finding the relevant part on the code related to this, but the insight into XYZ files for Quantum ab-initio simulations is really interesting, so thanks! I have another related question though, should you reprocess the bonds as the trajectory evolves? This would make reactions possible, but I'm not sure it's a sound way to implement it.
That's typically not done, as the required energy functions are much more complicated and computationally expensive. For a typical MD simulation, once defined the bonds (and other internal degrees of freedom) are immutable. In those which are not (such as ReaxFF, it's not really dynamically redefining the bonds so much as using an energy function which smoothly transitions from bond to non-bond.
TMP Chem That makes total sense. Simply put, one of the first things taught in chemical kinetics is that you need the right velocities and relative orientations fo a reaction to occur, which would be inline to what you explain. I was wondering cause as you mention reaction dynamics are not just limited to quantum simulations, and I was wondering how you would emulate it with force fields. PS: Is the chapter on Hartree-Fock still gonna happen? If so, how's development coming along?
Yes. Still happening. I give a weekly update on Facebook of progress. All of the background image slides are complete. Writing code for additional demos / simulations now. Filming will occur after that. ~30 videos. Estimating mid-April for upload at the moment.
I was looking in your github and I noticed that you have methyl formate which is a huge wind fall, I've been trying to get a set of position vectors with respect to a common origin for about a week. I was able to describe the planar nuclei with pretty basic trigonometry, but the other nuclei that have a third spacial component were really really difficult to describe with a position vector. For instance, the sp2 carbon has a plane associated with its nearest neighbors. The sp2 carbon and both oxygens form another plane, but I couldn't figure out a good way to find the angle between the two planes. If I had this angle it would be a piece of cake to find a position vector to the hydrogen on the sp2 carbon. So my question is; is there a good reliable method for finding position vectors that point to each nucleus in the atom or is this something that must be done using some sort of geometry optimization algorithm?
See the video on drawing molecules. You shouldn't be deriving atomic coordinates by hand for anything except the very simplest molecules. Draw it in a program, optimize the coordinates, and take the result for your application.
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Great job ! We need more tutors like you. ❤
Hello Dr Trent, first thank you for this beautifully taught course. I did well on Quantum chem 1 because of the previous playlist. However, my question is what exactly are atomic coordinates. I googled this term & i saw that its basically like locating an atom in a unit cell & hence obtaining x y z coordinates. But whats a unit cell and who chose those numbers displayed for the coordinates and what are they relative to. This is really a big transition from Quantum Chem 1. please reach back. Thanks!
Hi Abdalla. The Cartesian coordinates here are not located within a unit cell, but are locations in infinite 3-dimensional space relative to some arbitrary origin. The term "unit cell" implies an infinite repeating unit which extends forever in all dimensions. The unit cell contains the minimum amount of space necessary to describe how the atoms repeat throughout a system over all space. This is typically used in condensed phase systems (solids / crystals and liquids / solutions). The Cartesian coordinates given here are intended to imply a gas phase by default which takes place in some infinite container. It doesn't matter what we choose the origin to be, just that we choose one, as only interatomic distances have any meaning. Similarly we can rotate the axes in any direction we like without affecting the properties of the system. These attributes are called translational invariance and rotational invariance.
I'm not sure I really understood the section on degrees of freedom. If I have a system with 10 atoms (N=10), then there are 30 coordinates (3N=30). But what does it mean to say these coordinates have only 24 unique coordinates? If I only give you 24 values I haven't fully described the system...
I also sometimes see it stated that degrees of freedom is the number of ways the coordinates can move. So surely a molecule has only 6 degrees of freedom - the three translations and the three rotations.
So I don't know if degrees of freedom refers to the minimum number of values needed to describe a system (in which case here it would be 3N, not 3N - 6), or whether it refers to the number of independent ways it can move (in which case here it would be 6 not 3N - 6). Can anyone help? I feel like I am close to understanding since I can work out where 3N and 6 come from individually, but not why one is subtracted from the other.
A molecule has an x, y, and z coordinate for all N atoms. This gives 3N coordinates. If we translate the molecule, none of the *internal* degrees of freedom change (all atoms still have the same interatomic distance to all other atoms as they did before translation). The same is true of rotation. All molecules have 3 translations. Non-linear molecules have 3 rotations. This leaves 3N-6 *internal* degrees of freedom which will change the interatomic distances between atoms.
It is completely arbitrary where we define the origin, and what directions we choose for the x, y, and z axes. No matter our choice, we have the same molecule (the same set of *internal* degrees of freedom). Thus the 3 translations (choice of origin) and the 3 rotations (choice of x, y, and z axes) are redundant coordinates. They do not provide new information about the structure of the molecule, only information about our arbitrary choices of origin and axes.
The remaining 3N-6 non-redundant coordinates are the *internal* degrees of freedom, which affect the molecular structure. These can be represented by the vibrational normal modes of the molecule. A non-linear polyatomic molecule has 3N-6 vibrational modes which are independent / orthogonal, just as we need to describe our *internal* degrees of freedom, and thus form an ideal basis set for describing these *internal* degrees of freedom, which actually give us information about the structure of the molecule.
This concept is expanded on later in the chapter, specifically in video 1.10 on Z-matrices.
Thanks a lot - I think I'm getting there. I'll wait until 1.10 before coming back to this. Great videos so far by the way.
I had a hard time understanding this part too. Does it mean that these coordinates can be stored in some more efficient way, with less numbers stored in memory, or something?
I don't quite get how, because even if we stored RELATIVE displacements of atoms with respect to each other as vectors, these would still require 3 coordinates, whether we store them as Cartesian x,y,z coordinates, or polar theta,phi,r coordinates.
Hi Dr. do you main the atoms coordinate it is not really value ?
excellent playlist
excellent comment.
Hi Dr. Trent, Could you please recommend me book for computational chemistry
great explain on the DOF
Thanks, Roshan.
How do i convert pdb file to xyz?
Hi Adam,
A PDB file contains more information than an XYZ file, and is a superset of the XYZ file's information, so converting PDB --> XYZ is straightforward. Count the total number of atoms, and put that on the first line. Second line is an arbitrary comment or empty line. Third to N+2nd line each contain four columns: Atomic symbol, X coordinate, Y coordinate, Z coordinate. All 4 of those are contained within the PDB file, but which column they are varies. Just match each column to to appropriate column for the format.
Going backwards (XYZ --> PDB) would be more challenging, as PDB files contain more columns / information, so for each atom you would need more info than exists in the XYZ file (residue, residue index, chain, etc.).
How are bonds determined from the .xyz and .xyzq file format?
Hi Mario. Great question. We don't know exactly what the bonds are from an xyz file. We can do a pretty good job of inferring what they are, but it isn't guaranteed. There are other file formats that explicitly specify what atoms are bonded to one another. XYZ files are typically used for quantum chemistry methods where we don't have to specify where the bonds are, because it's a somewhat fuzzy, qualitative subject and what is or isn't a bond exists on a continuum. What is sometimes done is to look at all of the interatomic distances and count those within some fraction of the sum of the covalent radii as bonded atom pairs. This is what is done in the example problems in this chapter.
TMP Chem I see. I ended up answering the question myself by finding the relevant part on the code related to this, but the insight into XYZ files for Quantum ab-initio simulations is really interesting, so thanks! I have another related question though, should you reprocess the bonds as the trajectory evolves? This would make reactions possible, but I'm not sure it's a sound way to implement it.
That's typically not done, as the required energy functions are much more complicated and computationally expensive. For a typical MD simulation, once defined the bonds (and other internal degrees of freedom) are immutable. In those which are not (such as ReaxFF, it's not really dynamically redefining the bonds so much as using an energy function which smoothly transitions from bond to non-bond.
TMP Chem That makes total sense. Simply put, one of the first things taught in chemical kinetics is that you need the right velocities and relative orientations fo a reaction to occur, which would be inline to what you explain. I was wondering cause as you mention reaction dynamics are not just limited to quantum simulations, and I was wondering how you would emulate it with force fields.
PS: Is the chapter on Hartree-Fock still gonna happen? If so, how's development coming along?
Yes. Still happening. I give a weekly update on Facebook of progress. All of the background image slides are complete. Writing code for additional demos / simulations now. Filming will occur after that. ~30 videos. Estimating mid-April for upload at the moment.
Thank you so much.
Hi, I was wondering if you knew how to convert a .xyz file to a .pdb file? Is there a program that automatically does it?
OpenBabel is a free, open source and excellent software for this task. It can convert almost any chemical format and works on Linux, Mac and Windows!
I was looking in your github and I noticed that you have methyl formate which is a huge wind fall, I've been trying to get a set of position vectors with respect to a common origin for about a week. I was able to describe the planar nuclei with pretty basic trigonometry, but the other nuclei that have a third spacial component were really really difficult to describe with a position vector. For instance, the sp2 carbon has a plane associated with its nearest neighbors. The sp2 carbon and both oxygens form another plane, but I couldn't figure out a good way to find the angle between the two planes. If I had this angle it would be a piece of cake to find a position vector to the hydrogen on the sp2 carbon.
So my question is; is there a good reliable method for finding position vectors that point to each nucleus in the atom or is this something that must be done using some sort of geometry optimization algorithm?
See the video on drawing molecules. You shouldn't be deriving atomic coordinates by hand for anything except the very simplest molecules. Draw it in a program, optimize the coordinates, and take the result for your application.
how should I load a .XYZ file into VMD?