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water, as an example, the 2 hydrogen atoms are at a 104.45 Degree angle from each other. But how is that calculated? I'm assuming it has something to do with the ratios of the electrostatic forces between the 2 hydrogen and the oxygen.

- Thread starter Tclack
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- #1

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water, as an example, the 2 hydrogen atoms are at a 104.45 Degree angle from each other. But how is that calculated? I'm assuming it has something to do with the ratios of the electrostatic forces between the 2 hydrogen and the oxygen.

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alxm

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Well, first you must already know something about the shape, since geometry is just as much a part of what defines a compound as the elements its composed of. E.g. ethanol (CH_{3}CH_{2}OH) and dimethyl ether (CH_{3}OC_{3}) consist of the same atoms, but are completely different substances.

In practice, a chemist would just use empirical knowledge and simple models such as VSEPR. E.g. in the VSEPR picture, the oxygen atom in water has four electron pairs, two of which are bonding, so you would start with a tetrahedral angle of 109.47 degrees. Since free electron pairs repel more strongly than the ones involved in binding, this would be a bit shorter, so you'd expect 'a bit less than 109', which it indeed is. But these models are not quantiative, nor based on rigorous theory. If you want to calculate geometries from pure theory, then there's no way to do that other than an explicit quantum-mechanical calculation. (Even then, you still need a reasonable starting guess) Indeed, geometric parameters are often used to gauge the accuracy of quantum-chemical methods.

So, in short, you solve the Schrödinger equation within the Born-Oppenheimer approximation and get the energy in terms of nuclear coordinates, you can then calculate the derivatives with respect to those coordinates (analytically in many cases), and optimize the geometry w.r.t. energy using steepest-descent or some other numerical method. The basics are covered in pretty much any introductory book on computational chemistry. As I attempted to explain in another recent https://www.physicsforums.com/showthread.php?t=437978", chemical bonding or structure can't be understood in purely electrostatic terms. The only aspect of the system which is purely electrostatic are the forces on the nuclei, which is only of any use if you already know the electronic density, which you*can't* derive in terms of electrostatics.

In practice, a chemist would just use empirical knowledge and simple models such as VSEPR. E.g. in the VSEPR picture, the oxygen atom in water has four electron pairs, two of which are bonding, so you would start with a tetrahedral angle of 109.47 degrees. Since free electron pairs repel more strongly than the ones involved in binding, this would be a bit shorter, so you'd expect 'a bit less than 109', which it indeed is. But these models are not quantiative, nor based on rigorous theory. If you want to calculate geometries from pure theory, then there's no way to do that other than an explicit quantum-mechanical calculation. (Even then, you still need a reasonable starting guess) Indeed, geometric parameters are often used to gauge the accuracy of quantum-chemical methods.

So, in short, you solve the Schrödinger equation within the Born-Oppenheimer approximation and get the energy in terms of nuclear coordinates, you can then calculate the derivatives with respect to those coordinates (analytically in many cases), and optimize the geometry w.r.t. energy using steepest-descent or some other numerical method. The basics are covered in pretty much any introductory book on computational chemistry. As I attempted to explain in another recent https://www.physicsforums.com/showthread.php?t=437978", chemical bonding or structure can't be understood in purely electrostatic terms. The only aspect of the system which is purely electrostatic are the forces on the nuclei, which is only of any use if you already know the electronic density, which you

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