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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
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<body>
<h1><pre>
#################################
# QUANTIFYING QUANTUM MECHANICS #
#################################
</pre></h1>
<div class="topnav">
<a href="./Index.html">Home</a>
<a href="./Main.html">Previous Page</a>
</div>
<center>
<pre>
<blockquote style="color:#33ff33;">
THE UNDERLYING PHYSICAL LAWS NECESSARY FOR THE
MATHEMATICAL THEORY OF A LARGE PART OF PHYSICS AND THE
WHOLE OF CHEMISTRY ARE THUS COMPLETELY KNOWN, AND THE
DIFFICULTY IS ONLY THAT THE EXACT APPLICATION OF THESE
LAWS LEADS TO EQUATIONS MUCH TOO COMPLICATED
TO BE SOLUBLE.
-- <a style="font-size:15px;" href="https://www.nobelprize.org/prizes/physics/1933/dirac/biographical/" style="color:#ffb000;">P. A. M. DIRAC, 1929</a>
</pre>
<p><a href="https://gaussian.com/">Gaussian</a>, a quantum chemistry tool controversial for its proprietary licensing, often interjects quotes at the end of output files.
</p>
</blockquote>
</p>
</center>
<h2><pre>
*******************
* DODGING THE WOO *
*******************
</pre></h2>
<p>~ Quantum mechanics is a dense, difficult to visualize, and difficult to teach branch of chemistry and physics, and is unfortunately abused by salespeople to market products and ideas</p>
<p>~ Chemicals, and by proxy, life, is made up of molecules, which are made up of small particles called atoms, which themselves are made up by even smaller particles known as <a href="https://en.wikipedia.org/wiki/Elementary_particle"> elementary particles</a></p>
<p>~ Quantum mechanics deals with the elementary particles that comprise atoms, known as protons, neutrons, and electrons.</p>
<p>~ These particles are incredibly small, a one liter water bottle will weigh one kilogram, but a single electron will has a <a href="https://physics.nist.gov/cgi-bin/cuu/Value?me">mass</a> of 9 millionth trillionth trillionths of a kilogram or:
</p>
<center>
<p> <i>0.000000000000000000000000000009 kilograms </i></p>
</center>
<p>
~ A series of conjectures, experiments, and mathematical models have lead to the conclusion that classical physics, as described by the likes of James Maxwell, Isaac Newton, and the philosophers of Arabia, Greece, and India, do not apply to these particles.
</p>
<p>~ Below is a video, originally aired by PBS, concerning how Max Planck's observations lead to the birth of quantum mechanics</p>
<center>
<iframe width="560" height="315" src="https://www.youtube.com/embed/FXfrncRey-4" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
</center>
<p>
~ This had lead to the birth of quantum mechanics, or the physics behind these particles, and how the lead to larger and larger particles, in an interaction known as bonding
</p>
<p>Bonding in molecules is described using probability density wavefunctions, known as orbitals, as described by Hank Green below</p>
<center>
<iframe width="560" height="315" src="https://www.youtube.com/embed/cPDptc0wUYI" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
</center>
<h2><pre>
**************************
* SOLVING THE UNSOLVABLE *
**************************
</pre></h2>
<p>~ Quantum mechanics is difficult for mathemeticians to solve with only one particle, and becomes completely impossible when evaluating two ore more particles </p>
<p>~ Because of this, high performance computing is used, but even the most powerful supercomputers have difficulty with quantum mechanical models</p>
<p>~ Because of this, with regards to structural biology, scientists will use quantum mechanics to probe specific features, such as tunnels within proteins, the shuttling of electrons throughout a region of a protein, or interactions between ligands and cofactors with the active site of a protein. </p>
<p>~ All biomolecules are constantly bombarded with water molecules, many need water to function to begin with. Therefore, it is of interest to quantum mechanically model water molecules at different states to determine their characteristics.</p>
<p>~ Below is an excerpt of the output file of <a href="https://www.faccts.de/">ORCA</a>, a free and open source quantum chemistry tool.</p>
<p>~ Specifically ORCA is using the Ahlrichs-Double Zeta Valence <a href="https://sites.google.com/site/orcainputlibrary/basis-sets">Basis Set</a> (equations to evaluate the energies of the molecule in question), in accordance with the principles of <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3928866/">Density Functional Theory</a> (an algorith to approximate the energy of the electrons of the water molecule, in their respective orbitals). This took 1 minute and 12 seconds for a single water molecule, computed in a HPC environment </p>
<blockquote style="color:#33ff33;">
<pre>
****************
* O R C A *
****************
--- An Ab Initio, DFT and Semiempirical electronic structure package ---
########################################################
# -***- #
# Developed by Frank Neese #
# Lehrstuhl fuer Theoretische Chemie #
# Institut fuer Physikalische und Theoretische Chemie #
# Universitaet Bonn #
# Germany #
# #
# All rights reserved #
# -***- #
########################################################
Program Version 2.6 - Revision 71 -
With contributions from (in alphabetic order):
Ute Becker : Parallelization
Dmitry Ganyushin : Spin-Orbit,Spin-Spin,Magnetic field MRCI
Dimitrios Liakos : RI-MP2 improvements
Simone Kossmann : meta GGA functionals
Taras Petrenko : Resonance Raman, ABS,fluorescence,NRVS
Christoph Riplinger : Improved optimizer, TS searches
Frank Wennmohs : Multiple parts of the code
We gratefully acknowledge several collegues who have allowed us to
interface, adapt or use parts of their codes:
Stefan Grimme : VdW corrections, initial TS optimization
and many helpful discussions :-)
Markus Reiher, Alexander Wolf and Bernd Hess : otool_dkh (higher order DKH)
Andreas Klamt, Michael Diedenhofen : otool_cosmo (COSMO solvation model)
Alain StAmant : redundant internal coordinate setup
Reinhart Ahlrichs : matrix diagonalization, basis sets
Frank Weinhold : gennbo (NPA and NBO analysis)
Your calculation utilizes the basis: Ahlrichs-VDZ
</pre>
</blockquote>
<p>~ ORCA outputs always summarize the input file, in this case, water, with each atom partitioned into a three dimensional grid</p>
<blockquote style="color:#33ff33;">
<pre>
================================================================================
INPUT FILE
================================================================================
NAME = H2O_xyz_opt_freq_compound_jobs.inp
| 1> #
| 2> # H2O opt ; all population analyses OFF
| 3> #
| 4> ! RKS RI BP86 SVP SV/J Opt TightSCF NOPOP
| 5> %base "temp"
| 6> * xyz 0 1
| 7> O -1.666704747 0.000000000 -2.277536320
| 8> H -1.666704747 0.759337000 -1.681493320
| 9> H -1.666704747 -0.759337000 -1.681493320
| 10> *
| 11>
| 12> #
| 13> # H2O freq ; all population analyses ON; coordinates and guess read from the previous job
| 14> #
| 15> $new_job
| 16>
| 17> ! RKS RI BP86 SVP SV/J TightSCF NumFreq ALLPOP MoRead
| 18> %moinp "temp.gbw"
| 19> * xyzfile 0 1
| 20>
| 21> ****END OF INPUT****
================================================================================
</pre>
</blockquote>
<p>~ Preprocessing is conducted to better comply with Density Functional Theory, once this optimization is complete, ORCA will determine which functions from the basis set to use</p>
<blockquote style="color:#33ff33;"><pre>
-------------------------------
AUXILIARY BASIS SET INFORMATION
-------------------------------
There are 2 groups of distinct atoms
Group 1 Type O : 8s3p3d1f contracted to 6s3p3d1f pattern {311111/111/111/1}
Group 2 Type H : 4s2p contracted to 2s1p pattern {31/2}
Atom 0O basis set group => 1
Atom 1H basis set group => 2
Atom 2H basis set group => 2
Checking for AutoStart:
The File: temp.gbw exists
Trying to determine its content:
... Fine, the file contains calculation information
... Fine, the calculation information was read
... The file does not contain a basis set - skipping AutoStart
------------------------------------------------------------------------------
ORCA GTO INTEGRAL CALCULATION
-- RI-GTO INTEGRALS CHOSEN --
------------------------------------------------------------------------------
BASIS SET STATISTICS AND STARTUP INFO
Gaussian basis set:
# of primitive gaussian shells ... 22
# of primitive gaussian functions ... 38
# of contracted shells ... 12
# of contracted basis functions ... 24
Highest angular momentum ... 2
Maximum contraction depth ... 5
Auxiliary gaussian basis set:
# of primitive gaussian shells ... 27
# of primitive gaussian functions ... 59
# of contracted shells ... 19
# of contracted aux-basis functions ... 47
Highest angular momentum ... 3
Maximum contraction depth ... 3
Ratio of auxiliary to basis functions ... 1.96
One Electron integrals ... done
Ordering auxiliary basis shells ... done
Integral threshhold Thresh ... 3.000e-011
Primitive cut-off TCut ... 3.000e-012
Pre-screening matrix ... done
Shell pair data ...
Ordering of the shell pairs ... done ( 0.000 sec) 78 of 78 pairs
Determination of significant pairs ... done ( 0.000 sec)
Creation of shell pair data ... done ( 0.000 sec)
Storage of shell pair data ... done ( 0.015 sec)
Shell pair data done in ( 0.015 sec)
Computing two index integrals ... done
Choleksy decomposition of the V-matrix ... done
Timings:
Total evaluation time ... 0.093 sec ( 0.002 min)
One electron matrix time ... 0.000 sec ( 0.000 min) = 0.0%
Schwartz matrix evaluation time ... 0.000 sec ( 0.000 min) = 0.0%
Two index repulsion integral time ... 0.000 sec ( 0.000 min) = 0.0%
Cholesky decomposition of V ... 0.000 sec ( 0.000 min) = 0.0%
</pre></blockquote>
<p> ~ Once this step is complete, ORCA will run these functions through a multiple-cycle algorithm, which is often determined by the basis set and the theory the user wishes to comply to </p>
<blockquote style="color:#33ff33;"><pre>
------------------------------
INITIAL GUESS: MODEL POTENTIAL
------------------------------
Loading Hartree-Fock densities ... done
Calculating cut-offs ... done
Setting up the integral package ... done
Initializing the effective Hamiltonian ... done
Starting the Coulomb interaction ... done ( 0.0 sec)
Starting the XC term evaluation ... done ( 0.2 sec)
promolecular density results
# of electrons = 9.996459369
EX = -8.780328300
EC = -0.351951797
EX+EC = -9.132280097
Transforming the Hamiltonian ... done ( 0.0 sec)
Diagonalizing the Hamiltonian ... done ( 0.0 sec)
Back transforming the eigenvectors ... done ( 0.0 sec)
Now organizing SCF variables ... done
------------------
INITIAL GUESS DONE ( 0.2 sec)
------------------
--------------
SCF ITERATIONS
--------------
ITER Energy Delta-E Max-DP RMS-DP [F,P] Damp
*** Starting incremental Fock matrix formation ***
0 -76.2724914852 0.000000000000 0.09051623 0.00977659 0.2898489 0.7000
1 -76.3175597673 -0.045068282097 0.04873674 0.00519443 0.1042095 0.7000
***Turning on DIIS***
2 -76.3304238632 -0.012864095820 0.04273026 0.00493381 0.0134901 0.0000
3 -76.3561277248 -0.025703861661 0.02668155 0.00293696 0.0602411 0.0000
4 -76.3600567428 -0.003929017965 0.00511797 0.00068805 0.0078445 0.0000
5 -76.3601853451 -0.000128602321 0.00208858 0.00023155 0.0014283 0.0000
6 -76.3601937836 -0.000008438488 0.00168204 0.00014971 0.0004665 0.0000
7 -76.3601949625 -0.000001178891 0.00005987 0.00000561 0.0001045 0.0000
**** Energy Check signals convergence ****
*****************************************************
* SUCCESS *
* SCF CONVERGED AFTER 8 CYCLES *
*****************************************************
</pre></blockquote>
<p>~ At this overwhelming point, the excitation energies will be computed for the molecule</p>
<blockquote style="color:#33ff33;"><pre>
----------------
ORBITAL ENERGIES
----------------
NO OCC E(Eh) E(eV)
0 2.0000 -18.759048 -510.4596
1 2.0000 -0.893243 -24.3064
2 2.0000 -0.460766 -12.5381
3 2.0000 -0.310894 -8.4599
4 2.0000 -0.232594 -6.3292
5 0.0000 0.032823 0.8932
6 0.0000 0.108241 2.9454
7 0.0000 0.517077 14.0704
8 0.0000 0.575518 15.6606
9 0.0000 0.861473 23.4419
10 0.0000 0.863898 23.5079
11 0.0000 0.955354 25.9965
12 0.0000 1.040097 28.3025
13 0.0000 1.283914 34.9371
14 0.0000 1.346081 36.6287
15 0.0000 1.484061 40.3834
16 0.0000 1.719828 46.7989
17 0.0000 2.122974 57.7691
18 0.0000 2.168365 59.0042
19 0.0000 2.870370 78.1067
20 0.0000 2.909380 79.1682
21 0.0000 3.092822 84.1600
22 0.0000 3.396156 92.4141
23 0.0000 3.721685 101.2722
</pre></blockquote>
<p>~ ORCA will print a concluding summary showing the computer uptime to calculate, as well as a statement showing the program has terminated with no fatal errors (some tools will report this as having an error code of 0).</p>
<blockquote style="color:#33ff33;"><pre>
Timings for individual modules:
Sum of individual times ... 46.794 sec (= 0.780 min)
GTO integral calculation ... 9.155 sec (= 0.153 min) 19.6 %
SCF iterations ... 27.468 sec (= 0.458 min) 58.7 %
SCF Gradient evaluation ... 10.171 sec (= 0.170 min) 21.7 %
****ORCA TERMINATED NORMALLY****
TOTAL RUN TIME: 0 days 0 hours 1 minutes 12 seconds 48 msec
</pre></blockquote>
<p>~ Ultimately, quantum mechanical computations provide an accurate analysis of biomolecules, given that the scope of this analysis is realistic.</p>
<span style="background-color: #ffb000;color: black;font-size:20px;">(END)</span>
<p>
</p>
</body>
</html>