Computational Chemistry

Computational Chemistry http://vitalii.chemicalblogs.com/2_computational_chemistry Applying power of computers to solve chemical problems Vitalii 2008-07-17T11:37:07Z Review: Are orbitals real?! http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/480_review_are_orbitals_real.html Review is based on critical analysis of the paper "Tomographic imaging of molecular orbitals" by J. Itatani et al. <div align="justify"> </div><h1 align="center">Introduction</h1> The paper "Tomographic imaging of molecular orbitals" by J. Itatani et al. published in 2004 in Nature is the initial work in the field of tomographic reconstruction of molecular orbitals. The authors proposed a technique to image a single orbital by probing molecules aligned in different directions with a femtosecond laser pulse. The paper describes an experimental application of the proposed tomography to the highest occupied molecular orbital (HOMO) of the N2 molecule and compares it with an ab initio orbital. Using a simple theoretical model the authors demonstrate that with an attosecond laser one can observe how orbitals change during chemical reactions - that is to observe the very foundations of chemistry. The paper has significant scientific importance because it started a new field of research - tomographic imaging. The work has brought a lot of attention from both theoreticians and experimentalists and presently (Fall 2007) has been cited 147 times. However the paper presents an oversimplified interpretation of the results and has some shortcomings in the theoretical part. <a title="Review: Are orbitals real?!" target="_blank" href="http://www.chemicalblogs.com/downloads/review_are_orbitals_real.pdf" style="font-size: x-large;">Read full text review (pdf)</a> General 2007-11-25T15:14:36Z Vitalii Aharonov-Bohm Effect (solution) http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/463_aharonov-bohm_effect_solution.html Solution of the <a href="http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/417_aharonov-bohm_effect.html" title="Aharanov Bohm effect">previously posted problem</a> on Aharonov-Bohm effect. <style type="text/css"> </style> The physical model described in the question is illustrated on Fig. 1. <img width="348" border="0" align="left" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_7d59867b.png" name="graphics1" /> Fig. 1: Electron in the spherical shell confined to a circular track around an infinite solenoid. Two types of motion could be distinguished in the model: motion of the electron inside the spherical shell and motion of the spherical shell on the circular track. Therefore it is convenient to describe the system using angle<img width="17" hspace="8" height="19" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_404632b2.gif" name="Object7" />to define the position of the spherical shell center on the circular track and spherical coordinates<img width="66" hspace="8" height="19" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_78e89002.gif" name="Object8" />to describe the point inside the spherical shell. Given that the solenoid is ideal, the electric and magnetic field vectors equal zero outside of the solenoid, while inside of the solenoid there is a constant magnetic filed <img width="58" hspace="8" height="22" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_688d6d5.gif" name="Object9" />. This makes two types of motion mentioned above topologically inequivalent: trajectories of the electron inside of the spherical shell do not encompass any regions containing the field and therefore are simply connected, in contrary, the trajectory of the sphere on the track encompasses section of the solenoid with a magnetic field and therefore is not simply connected. A charged particle traversing through the latter type of trajectory is known to be subject to Aharonov-Bohm effect, which is an example of non-local interaction between the field and a charged particle. In the case of the magnetic field the effect is called magnetic Aharonov-Bohm effect. It arises from the fact that even if magnetic field (B) equals zero along a trajectory, but the trajectory encompasses an area containing magnetic field (with a non zero flux) the vector field potential (A) along the trajectory is not zero and therefore affects motion of a charged particles. By the definition magnetic field and vector field potential are related through the following equation: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="76" hspace="8" height="21" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_468c3618.gif" name="Object10" />. </td> <td width="11%"> (1) </td> </tr> </thead> </table> Taking the surface integral of the both sides we obtain: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="168" hspace="8" height="34" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m373fb5ce.gif" name="Object11" />, </td> <td width="11%"> (2) </td> </tr> </thead> </table> where<img width="21" hspace="8" height="19" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_5153a3eb.gif" name="Object12" />is the surface encompassed by the trajectory. Applying Stokes' theorem to the right hand side gives: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="131" hspace="8" height="36" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m60e6fc79.gif" name="Object13" />, </td> <td width="11%"> (3) </td> </tr> </thead> </table> where L is the trajectory. Due to the symmetry of the problem <img width="21" hspace="8" height="21" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_7e5c9fa0.gif" name="Object14" /> is constant along the trajectory therefore: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="123" hspace="8" height="36" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_5635b05.gif" name="Object15" />, </td> <td width="11%"> (4) </td> </tr> </thead> </table> Where A is the component of the vector potential tangent to the trajectory (the component parallel to the magnetic filed is zero due to the symmetry of the problem and another component could be made 0 by a gauge transformation). Taking into account that the trajectory is a circle with radius R we obtain: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="125" hspace="8" height="36" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_9144a94.gif" name="Object16" /> </td> <td width="11%"> (5) </td> </tr> </thead> </table> Combining equations 3-5 we obtain an expression for the vector filed potential<img width="21" hspace="8" height="19" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m5f92fc61.gif" name="Object17" />: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="96" hspace="8" height="55" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m27310b81.gif" name="Object18" /> </td> <td width="11%"> (6) </td> </tr> </thead> </table> The numerator of the ratio in the equation (6) is the flux of the magnetic field through the encompassed surface. Since B is not zero only inside of the solenoid and is constant: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="125" hspace="8" height="56" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_d865dab.gif" name="Object19" /> </td> <td width="11%"> (7) </td> </tr> </thead> </table> The remaining surface integral is just the area of the surface enclosed by the solenoid with radius a: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="117" hspace="8" height="35" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m5ef333d1.gif" name="Object20" /> </td> <td width="11%"> (8) </td> </tr> </thead> </table> Combining equations (7) and (8) results in an explicit expression for <img width="21" hspace="8" height="19" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m5f92fc61.gif" name="Object21" />: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="73" hspace="8" height="44" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_7e5b4137.gif" name="Object22" /> </td> <td width="11%"> (9) </td> </tr> </thead> </table> Since the radius of the circular track (R0 = 50 Å) is by an order of magnitude bigger then the radius of the spherical shell (r0 = 5 Å) the value of<img width="21" hspace="8" height="19" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m5f92fc61.gif" name="Object23" />inside the shell may be assumed to be equal to the value in the center of the shell: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="79" hspace="8" height="47" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_7ab87b0b.gif" name="Object24" /> </td> <td width="11%"> (10) </td> </tr> </thead> </table> Also the timescale of motion of the sphere on the track is slower then that for an electron in the sphere. Therefore we may assume that electron moving in the sphere experiences constant in time<img width="21" hspace="8" height="19" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m5f92fc61.gif" name="Object25" />. Within these assumptions we may now separate two types of motion: <ol> <li> Motion of the sphere on the track becomes motion of a particle in a ring with a non-zero magnetic flux. </li> <li> Motion of the electron in the sphere becomes motion of a particle in a sphere with an infinite square potential. </li> </ol> Now we solve these two problems independently and then combine their solutions. <ol> Particle in a ring with a non-zero magnetic flux. The Hamiltonian describing the motion of a charged particle in the presence of the non-zero magnetic vector potential is given by [1]: </ol> <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="131" hspace="8" height="40" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_317cc241.gif" name="Object26" />. </td> <td width="11%"> (11) </td> </tr> </thead> </table> Taking into account the specifics of the problem: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="60" hspace="8" height="20" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_e31d16a.gif" name="Object27" />, </td> <td width="11%"> (12) </td> </tr> </thead> </table> where <img width="17" hspace="8" height="19" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_404632b2.gif" name="Object28" />is the angle describing the position on the ring. Then in spherical coordinates using atomic units (m=1, q=-1) and the fact that A is tangent to the trajectory, the equation of motion is: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="245" hspace="8" height="49" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m65f4b9e4.gif" name="Objekt4" /> </td> <td width="11%"> (13) </td> </tr> </thead> </table> Applying a substitution<img width="56" hspace="8" height="21" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m659863de.gif" name="Object29" />to this differential equation leads to a quadratic equation: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="247" hspace="8" height="23" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m5d1ec8d9.gif" name="Object30" /> </td> <td width="11%"> (14) </td> </tr> </thead> </table> From which x could be found: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="140" hspace="8" height="24" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_2664b885.gif" name="Object31" /> </td> <td width="11%"> (15) </td> </tr> </thead> </table> Due to the boundary condition of the particle on a ring problem: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="74" hspace="8" height="21" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m668632a9.gif" name="Object32" /> </td> <td width="11%"> (16) </td> </tr> </thead> </table> the value of x must satisfy: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="53" hspace="8" height="19" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_1ee4c2e5.gif" name="Object34" /> </td> <td width="11%"> (17) </td> </tr> </thead> </table> where N must be an integer. Therefore levels of energy are quantized as follows: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="157" hspace="8" height="44" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_4c24c4c0.gif" name="Object33" /> </td> <td width="11%"> (18) </td> </tr> </thead> </table> As one can notice presence of the magnetic vector potential has removed the degeneracy of the states with N=k and N=-k quantum numbers. Combining equations (15) with (18) and recalling the substitution gives the eigenstates of the system: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="64" hspace="8" height="21" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_6b56e793.gif" name="Object35" />, </td> <td width="11%"> (19) </td> </tr> </thead> </table> and <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="104" hspace="8" height="22" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m62eade3.gif" name="Object36" />. </td> <td width="11%"> (20) </td> </tr> </thead> </table> <ol> Particle in sphere with an infinite square potential. Motion of the electron in a spherically symmetric potential given by [2,3]: </ol> <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="101" hspace="8" height="20" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_63373b86.gif" name="Object37" />and<img width="108" hspace="8" height="20" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m8943b96.gif" name="Object41" /> </td> <td width="11%"> (21) </td> </tr> </thead> </table> is described by the following Hamiltonian: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="108" hspace="8" height="38" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m15006e02.gif" name="Object38" /> </td> <td width="11%"> (22) </td> </tr> </thead> </table> Due to symmetry of the problem in spherical coordinates radial and angular variables are separable and solutions are described in terms of the free spherical waves: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="270" hspace="8" height="20" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_19454341.gif" name="Object39" />and<img width="138" hspace="8" height="20" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_5267a572.gif" name="Object40" /> </td> <td width="11%"> (23) </td> </tr> </thead> </table> Where <img width="27" hspace="8" height="20" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_617270b7.gif" name="Object42" />is a normalization coefficient, <img width="60" hspace="8" height="20" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m32ee984.gif" name="Object43" />is spherical Bessel function, <img width="70" hspace="8" height="20" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m57c05716.gif" name="Object44" />is a spherical harmonics, <img width="25" hspace="8" height="20" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_1d2cc040.gif" name="Object45" />is n-th root of equation <img width="86" hspace="8" height="20" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_638aadd1.gif" name="Object46" /> and n, l, m are quantum numbers. The energy eigenvalues of these wavefunctions are: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="68" hspace="8" height="47" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m48811c32.gif" name="Object47" /> </td> <td width="11%"> (24) </td> </tr> </thead> </table> Now we can combine solutions for two types of motions together and describe the overall eigenstates of the system as: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="280" hspace="8" height="22" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m7675c066.gif" name="Object48" />and </td> <td width="11%"> (25) </td> </tr> </thead> </table> <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="317" hspace="8" height="24" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_mc92bd94.gif" name="Object49" /> </td> <td width="11%"> (26) </td> </tr> </thead> </table> with energies: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="209" hspace="8" height="49" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_3e537cd5.gif" name="Object50" /> </td> <td width="11%"> (27) </td> </tr> </thead> </table> Squares of the wavefunctions given by equations 25 and 26 are the probabilities of finding center of the sphere in a point of track defined by angle<img width="17" hspace="8" height="18" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_6a9c3a65.gif" name="Object3" />with an electron inside of the sphere in the point defined by<img width="63" hspace="8" height="18" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m1e9e8c6a.gif" name="Object4" />. Wavefunction 25 is a combination of the free standing spherical wave for the electron inside of the sphere and a plane wave circling around the track with the speed defined by the wave vector N. Wavefunction 26 has similar interpretation, with an exception that electron moves in different direction with the speed defined by the wave vector N + AR0. For a given set of quantum numbers (N, n, m, l ) the general wavefunction is a linear combination of 25 and 26: <table width="100%" cellspacing="0" cellpadding="4" border="0"> <col width="228*" /> <col width="28*" /> <thead> <tr> <td width="89%"> <img width="367" hspace="8" height="26" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_m592c4898.gif" name="Object5" /> </td> <td width="11%"> (28) </td> </tr> </thead> </table> By substitution the magnitude of A from equation 10 we obtain: <img width="376" hspace="8" height="42" align="absmiddle" src="http://www.chemicalblogs.com/downloads/ab2/aharanov-bohm_html_55e6fe7.gif" name="Object6" /> A more precise solution will require to take into account the fact values of the magnetic vector potential are different for different points inside of the spherical shell and also take into consideration coupling between motion of the sphere and motion of the electron inside of it (analogous to the corrections to the Born-Oppenheimer approximation). [1] C. Wittig, Molecular Dynamics lectures (2006). [2] G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists, Academic Press, 1995. [3] G. Salvador, Phys. Rev. 67, 12102 (2003) General 2007-10-31T20:03:16Z Vitalii Aharonov-Bohm Effect http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/417_aharonov-bohm_effect.html Aharonov-Bohm effect is one of the most fascinating discoveries of the 20th century. Here is a typical problem where Aharonov-Bohm effect appear: <img src="http://www.chemicalblogs.com/downloads/aharanov-bohm.jpg" /> An electron is inside of a sphere with radius 5 Å. Mass and thickness of the sphere are negligible. However, electromagnetic fields freely pass through the sphere without reflection or attenuation. The shell is confined to a circular track of radius 50 Å. A solenoid of radius 1 Å is perpendicular to the track, passing through its center. A magnetic filed inside of the solenoid is B and 0 outside. Describe the eigenstates of the system. At first glance it seems simple. But how would you solve it? The solution will be provided in the next post - stay tuned! General 2007-09-25T08:04:14Z Vitalii Are Orbitals Real?! http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/335_are_orbitals_real.html Paper "Tomographic imaging of molecular orbitals" by J. Itatani. in Nature challenges common QM (quantum mechanics) interpretation of orbitals as pure mathematical constructs. Authors goes as far as to say that they experimentally measured HOMO (highest occupied molecular orbital). Is that possible indeed or is it just a wrong interpretation of the experiment? The paper could be found at: <a href="http://spectroscopy.mps.ohio-state.edu/institute/2007/corkum/nature_Tomography.pdf" target="_blank">http://spectroscopy.mps.ohio-state.edu/institute/2007/corkum/nature_Tomography.pdf</a> <a href="http://spectroscopy.mps.ohio-state.edu/institute/2007/corkum/nature_Tomography.pdf" target="_blank"></a>I appreciate your comments on this issue.You can vote on this question here: <a href="http://www.webqc.org/chemicalforum/viewtopic.php?t=466">http://www.webqc.org/chemicalforum/viewtopic.php?t=466</a>[UPDATE] I've published critical review of this paper in another post: <a href="http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/480_review_are_orbitals_real.html">http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/480_review_are_orbitals_real.html</a> General 2007-07-26T14:56:15Z Vitalii Beautiful Fe2O3 deposits http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/326_beautiful_fe2o3_deposits.html I've recently returned from Hawaii. There I've made several shots of the ground colored with Fe2O3. Looks amazing ... <img src="http://www.chemicalblogs.com/downloads/Fe2O3/normal_100_2590.JPG" /> <img src="http://www.chemicalblogs.com/downloads/Fe2O3/normal_100_2592.JPG" /> <img src="http://www.chemicalblogs.com/downloads/Fe2O3/normal_100_2780.JPG" /> <img src="http://www.chemicalblogs.com/downloads/Fe2O3/normal_100_2787.JPG" /> <img src="http://www.chemicalblogs.com/downloads/Fe2O3/normal_100_2807.JPG" /> <img src="http://www.chemicalblogs.com/downloads/Fe2O3/normal_100_2889.JPG" /> <img src="http://www.chemicalblogs.com/downloads/Fe2O3/normal_100_2890.JPG" /> <img src="http://www.chemicalblogs.com/downloads/Fe2O3/normal_100_2895.JPG" /> <img src="http://www.chemicalblogs.com/downloads/Fe2O3/normal_100_2922.JPG" /> General 2007-07-21T00:08:34Z Vitalii Structure, vibrational frequencies, ionization energies, and photoelectron spectrum of the para-benzyne radical anion http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/203_structure_vibrational_frequencies_ionization_energies_and_photoelectron_spectrum_of_the_para-benzyne_radical_anion.html My article finally has been published in "Theoretical Chemistry Accounts"! Title: Structure, vibrational frequencies, ionization energies, and photoelectron spectrum of the para-benzyne radical anion Abstract: Equilibrium structure, vibrational frequencies, and ionization energies of the para-benzyne radical anion are characterized by coupled-cluster and equation-of-motion methods. Vibronic interactions with the low-lying excited state result in a flat potential energy surface along the coupling mode and even in a lower-symmetry C2v structures. Additional complications arise due to Hartree–Fock instabilities and near-instabilities. The magnitude of vibronic interactions was characterized by geometrical parameters, charge localization patterns and energy differences between the D2h and 2v structures. The observed trends suggest that the C2v minimum predicted by several theoretical methods is an artifact of incomplete correlation treatment. The comparison between the calculated and experimental spectrum confirmed D2h structure of the anion, as well as accuracy of the coupled-cluster and spin-flip structures, frequencies and normal modes of the anion and the diradical. Density functional calculations (B3LYP) yielded only a D2h minimum, however, the quality of the structure and vibrational frequencies is poor, as follows from the comparison to high-level wave function calculations and the calculated spectrum. The analysis of charge localization patterns and the performance of different functionals revealed that B3LYP underestimates the magnitude of vibronic interactions due to self-interaction error. Keywords: Para-benzyne radical anion, Photoelectron spectroscopy, Coupled-cluster methods, Density functional theory, Symmetry breaking. <a target="_blank" href="http://www.springerlink.com/content/93080662544021nv">Full text of the original pulication is available at http://www.springer.com</a> <a href="http://www.chemicalblogs.com/downloads/Structure, vibrational frequencies, ionization energies, and photoelectron spectrum of the para-benzyne radical anion.pdf" title="Structure, vibrational frequencies, ionization energies, and photoelectron spectrum of the para-benzyne radical anion" target="_blank">Full text of the final draft "Structure, vibrational frequencies, ionization energies, and photoelectron spectrum of the para-benzyne radical anion"</a> General 2007-05-17T20:37:31Z Vitalii Quantum Chemistry Abbreviations http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/187_quantum_chemistry_abbreviations.html List of quantum chemistry abbreviations is very useful for starting theoreticians and especially for experimentalists who need to read a quantum chemistry paper. AO - atomic orbital CAS - complete active space CASSCF - complete active space self-consistent-field CCSD - coupled-cluster theory with single and double excitations CI - configuration interaction CISD - configuration interaction with single and double excitations CLSCF - closed-shell self-consistent-field CSF - configuration stat functionDFT - density functional theoryDIIS - Direct Inversion in the Iterative Subspace DM - Direct Minimization EOM - equation of motion EA - electron attachement GDM - geometric direct minimization GTO - Gaussian-type orbital GVB - generalized valence bond HF - Hartree-Fock HOMO - highest occupied molecular orbital IP - ionization potential LCAO - linear combination of atomic orbitals LUMO - lowest unoccupied molecular orbital MO - molecular orbital MOM - maximum overlap method MCSCF - multiconfiguration self-consitent-field MP2 - second-order Møller-Plesset perturbation theory NBO - natural bond orbital NBO - non-bonding orbital NVT - nuclear vibrational theory OO - optimized orbital PES - potential energy surface RHF - restricted Hartree-Fock ROHF - restricted open shell Hartree-Fock SCF - self-constistent-field SF - spin flip STO - Slater-type orbital TDDFT - time–dependent density functional theory TOSH - transition–optimized shifted Hermite TZ - triple zetaUHF - unrestricted Hartree-Fock VCI - vibrational configuration interaction VPT2 - second–order vibrational perturbation theory ZPE - zero point energy If you have any additions to this list please fill free to commnet on that. General 2007-04-26T15:29:45Z Vitalii Computational Chemistry Cluster http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/177_computational_chemistry_cluster.html I have just finished configuration of our new computational cluster (11 powerful computers) for quantum chemistry calculations. Here is how it looks like: <center> Computational Cluster: Front View <img src="http://www.chemicalblogs.com/resserver.php?blogId=2&resource=cluster-front.jpg" alt="Cluster front" style="margin: 5px;" class="res_image" /> Computational Cluster: Rear View<img class="res_image" style="margin: 5px;" alt="Cluster back" src="http://www.chemicalblogs.com/resserver.php?blogId=2&resource=cluster-back.jpg" /> </center> OS: Scientific Linux 4.4 Quantum chemistry packages: Gamess, Molpro, Q-ChemComputers: Server (CPU: 2 x Xeon 5160 3GHz, RAM: 8GB, HDD: 4 x 300GB)8 x Regular nodes (CPU: 2 x Xeon 5160 3GHz, RAM: 16GB, HDD: 4 x 300GB)2 x Heavy nodes (CPU: 2 x Xeon 5160 3GHz, RAM: 24GB, HDD: 6 x 300GB)The most interesting feature of this cluster is network boot - all nodes do not have OS installed, instead they boot from the server. This make configuration much more manageable. General 2007-04-22T10:11:46Z Vitalii Resolving the structure of the p-benzyne radical anion with photoionization spectroscopy http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/124_resolving_the_structure_of_the_p-benzyne_radical_anion_with_photoionization_spectroscopy.html Poster for the Western Spectroscopy conference (click to enlarge): <a href="http://www.chemicalblogs.com/downloads/BRA_WSA1.jpg"> <img src="http://www.chemicalblogs.com/downloads/BRA_WSA.jpg" /> </a> General 2007-02-11T00:32:05Z Vitalii DFT electron self-interaction error http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/100_dft_electron_self-interaction_error.html My recent studies of para-benzyne radical anion has shown that relative energy difference between C2v and D2h structures calculated at DFT level of theory are proportional to the electron self-interaction error included in DFT potential. The more HF exchange DFT potential has the smaller is the electron self-interaction error. Thus the most common B3LYP potential places D2h structure lower in energy mostly because of the electron self-interaction error. <a type="image/png" href="http://www.chemicalblogs.com/resserver.php?blogId=2&resource=dft-self-interaction-error.png" id="res_12" class="nodecoration"><img border="0" src="http://www.chemicalblogs.com/resserver.php?blogId=2&resource=dft-self-interaction-error.png&mode=medium" alt="DFT electron self interaction error" style="margin: 5px;" class="res_image_medium" /></a> General 2007-01-08T11:43:06Z Vitalii