$\mathrm{with}\left(\mathrm{QuantumChemistry}\right)\;$

$\left[\mathrm{AOLabels}\,\mathrm{ActiveSpaceCI}\,\mathrm{ActiveSpaceSCF}\,\mathrm{AtomicData}\,\mathrm{BondAngles}\,\mathrm{BondDistances}\,\mathrm{Charges}\,\mathrm{ChargesPlot}\,\mathrm{Chat}\,\mathrm{ContractedSchrodinger}\,\mathrm{CorrelationEnergy}\,\mathrm{CoupledCluster}\,\mathrm{DensityFunctional}\,\mathrm{DensityPlot3D}\,\mathrm{Dipole}\,\mathrm{DipolePlot}\,\mathrm{Energy}\,\mathrm{ExcitationEnergies}\,\mathrm{ExcitationSpectra}\,\mathrm{ExcitationSpectraPlot}\,\mathrm{ExcitedStateEnergies}\,\mathrm{ExcitedStateSpins}\,\mathrm{ExcitonDensityPlot}\,\mathrm{ExcitonPopulations}\,\mathrm{ExcitonPopulationsPlot}\,\mathrm{FullCI}\,\mathrm{GeometryOptimization}\,\mathrm{HartreeFock}\,\mathrm{Interactive}\,\mathrm{Isotopes}\,\mathrm{LiteratureSearch}\,\mathrm{MOCoefficients}\,\mathrm{MODiagram}\,\mathrm{MOEnergies}\,\mathrm{MOIntegrals}\,\mathrm{MOOccupations}\,\mathrm{MOOccupationsPlot}\,\mathrm{MOSymmetries}\,\mathrm{MP2}\,\mathrm{MolecularData}\,\mathrm{MolecularDictionary}\,\mathrm{MolecularGeometry}\,\mathrm{NuclearEnergy}\,\mathrm{NuclearGradient}\,\mathrm{OscillatorStrengths}\,\mathrm{Parametric2RDM}\,\mathrm{PlotMolecule}\,\mathrm{Populations}\,\mathrm{Purify2RDM}\,\mathrm{QuantumComputing}\,\mathrm{RDM1}\,\mathrm{RDM2}\,\mathrm{RDMFunctional}\,\mathrm{RTM1}\,\mathrm{ReadXYZ}\,\mathrm{Restore}\,\mathrm{Save}\,\mathrm{SaveXYZ}\,\mathrm{SearchBasisSets}\,\mathrm{SearchFunctionals}\,\mathrm{SkeletalStructure}\,\mathrm{SolventDatabase}\,\mathrm{Thermodynamics}\,\mathrm{TransitionDipolePlot}\,\mathrm{TransitionDipoles}\,\mathrm{TransitionOrbitalPlot}\,\mathrm{TransitionOrbitals}\,\mathrm{Variational2RDM}\,\mathrm{VibrationalModeAnimation}\,\mathrm{VibrationalModes}\,\mathrm{Video}\right]$

$\mathrm{bond\_distances} ≔ \mathrm{map}\left(x \to x\+2.0\, \left[\mathrm{fsolve}\left(\mathrm{expand}\left(\mathrm{ChebyshevT}\left(8\,x\right)\right)\right)\right]\right)\;$

$\mathrm{bond\_distances}≔\left[1.01921472\,1.16853039\,1.44442977\,1.80490968\,2.19509032\,2.55557023\,2.83146961\,2.98078528\right]$

$\mathrm{molecules} ≔ \left[\mathrm{seq}\left(\left[\left[''N''\,0\,0\,0\right]\,\left[''N''\,0\,0\,R\right]\right]\, R \mathbf{in} \mathrm{bond\_distances}\right)\right]\;$

$\mathrm{molecules}≔\left[\left[\left[''N''\,0\,0\,0\right]\,\left[''N''\,0\,0\,1.01921472\right]\right]\,\left[\left[''N''\,0\,0\,0\right]\,\left[''N''\,0\,0\,1.16853039\right]\right]\,\left[\left[''N''\,0\,0\,0\right]\,\left[''N''\,0\,0\,1.44442977\right]\right]\,\left[\left[''N''\,0\,0\,0\right]\,\left[''N''\,0\,0\,1.80490968\right]\right]\,\left[\left[''N''\,0\,0\,0\right]\,\left[''N''\,0\,0\,2.19509032\right]\right]\,\left[\left[''N''\,0\,0\,0\right]\,\left[''N''\,0\,0\,2.55557023\right]\right]\,\left[\left[''N''\,0\,0\,0\right]\,\left[''N''\,0\,0\,2.83146961\right]\right]\,\left[\left[''N''\,0\,0\,0\right]\,\left[''N''\,0\,0\,2.98078528\right]\right]\right]$

$\mathrm{energies\_dft}≔ \left[\mathrm{seq}\left(\mathrm{Energy}\left(\mathrm{molecule}\,\mathrm{method}\=\mathrm{DensityFunctional}\, \mathrm{basis}\=''cc-pVDZ''\, \mathrm{xc}\=''B3LYP''\right)\, \mathrm{molecule} \mathbf{in} \mathrm{molecules}\right)\right]\;$

$\mathrm{energies\_dft}≔\left[\mathrm{-109.50786339}\,\mathrm{-109.52331040}\,\mathrm{-109.37588586}\,\mathrm{-109.17741963}\,\mathrm{-109.03358249}\,\mathrm{-108.95146495}\,\mathrm{-108.90997138}\,\mathrm{-108.89291096}\right]$

$\mathrm{pes\_dft} ≔ \mathrm{interp}\left(\mathrm{bond\_distances}\,\mathrm{energies\_dft}\,R\right)\;$

$\mathrm{pes\_dft}≔-0.14339035R^7+2.20942302R^6-14.44738600R^5+51.96535307R^4-110.97891955R^3+140.38786698R^2-96.50876625R-81.97856683$

$\mathrm{energies\_rdm}≔ \left[\mathrm{seq}\left(\mathrm{Energy}\left(\mathrm{molecule}\,\mathrm{method}\=\mathrm{RDMFunctional}\, \mathrm{basis}\=''cc-pVDZ''\, \mathrm{xc}\=''B3LYP''\right)\, \mathrm{molecule} \mathbf{in} \mathrm{molecules}\right)\right]\;$

$\mathrm{energies\_rdm}≔\left[\mathrm{-109.50786339}\,\mathrm{-109.52331040}\,\mathrm{-109.37588586}\,\mathrm{-109.18887170}\,\mathrm{-109.10062254}\,\mathrm{-109.06672079}\,\mathrm{-109.05806429}\,\mathrm{-109.05565802}\right]$

$\mathrm{pes\_rdm} ≔ \mathrm{interp}\left(\mathrm{bond\_distances}\,\mathrm{energies\_rdm}\,R\right)\;$

$\mathrm{pes\_rdm}≔0.00403016R^7+0.13029220R^6-2.19462464R^5+12.96198119R^4-38.72108443R^3+62.54064536R^2-51.32917602R-92.88749381$

$$\begin{gathered} \mathrm{p\_dft}≔ \mathrm{plot}\left(\mathrm{pes\_dft}\, R\=1.0..2.9\, \mathrm{axes}\=\mathrm{boxed}\, \mathrm{labels}\=\left[''Bond\; Distance\; (Ã\dots )''\,"Energy\left(\mathrm{hartree}\right)\"\right]\, \mathrm{color}\=\mathrm{red}\, \mathrm{thickness}\=3\, \mathrm{labeldirections}\=\left[\mathrm{horizontal}\,\mathrm{vertical}\right]\right)\: \\ \mathrm{p\_rdm} ≔ \mathrm{plot}\left(\mathrm{pes\_rdm}\, R\=1.0..2.9\, \mathrm{axes}\=\mathrm{boxed}\, \mathrm{labels}\=\left[''Bond\; Distance\; (Ã\dots )''\,"Energy\left(\mathrm{hartree}\right)\"\right]\, \mathrm{color}\=\mathrm{blue}\, \mathrm{thickness}\=3\right)\: \\ \mathrm{plots}:-\mathrm{display}\left(\left\{\mathrm{p\_dft}\,\mathrm{p\_rdm}\right\}\right)\; \end{gathered}$$

$\mathrm{mol} ≔ \mathrm{MolecularGeometry}\left(''1,3-difluorobenzene''\right)\;$

$\mathrm{mol}≔\left[\left[''F''\,2.36790000\,1.02540000\,\mathrm{-0.00020000}\right]\,\left[''F''\,\mathrm{-2.36810000}\,1.02530000\,0.00010000\right]\,\left[''C''\,\mathrm{-0.00030000}\,1.05310000\,0.00010000\right]\,\left[''C''\,1.20790000\,0.35580000\,0.00020000\right]\,\left[''C''\,\mathrm{-1.20810000}\,0.35540000\,\mathrm{-0.00020000}\right]\,\left[''C''\,1.20820000\,\mathrm{-1.03900000}\,0.00010000\right]\,\left[''C''\,\mathrm{-1.20790000}\,\mathrm{-1.03940000}\,\mathrm{-0.00010000}\right]\,\left[''C''\,0.00030000\,\mathrm{-1.73660000}\,0\right]\,\left[''H''\,\mathrm{-0.00040000}\,2.13890000\,0.00010000\right]\,\left[''H''\,2.14900000\,\mathrm{-1.58160000}\,0.00010000\right]\,\left[''H''\,\mathrm{-2.14840000}\,\mathrm{-1.58220000}\,\mathrm{-0.00010000}\right]\,\left[''H''\,0.00040000\,\mathrm{-2.82270000}\,0.00010000\right]\right]$

$\mathrm{PlotMolecule}\left(\mathrm{mol}\right)\;$

$\mathrm{data} ≔ \mathrm{CoupledCluster}\left(\mathrm{mol}\right)\;$

$\mathrm{grad} ≔ \mathrm{NuclearGradient}\left(\mathrm{mol}\, \mathrm{method}\=\mathrm{CoupledCluster}\right)\;$

$\mathrm{Chat}\left(''Buckminsterfullerene''\right)\;$

$''Buckminsterfullerene,\; also\; known\; as\; a\; buckyball,\; is\; a\; specific\; type\; of\; molecular\; formation\; that\; includes\; 60\; carbon\; atoms\; arranged\; in\; a\; spherical\; structure,\; similar\; in\; shape\; to\; a\; soccer\; ball.\; It\; was\; named\; after\; Richard\; Buckminster\; Fuller,\; a\; renowned\; architect\; known\; for\; designing\; structures\; similar\; to\; the\; shape\; of\; this\; molecule.\; This\; particular\; molecule\; is\; a\; type\; of\; fullerene,\; a\; category\; of\; carbon\; structures\; which\; also\; includes\; carbon\; nanotubes.\; Buckminsterfullerenes\; are\; significant\; in\; scientific\; research\; due\; to\; their\; unique\; physical\; and\; chemical\; properties.\; They\; are\; used\; in\; a\; variety\; of\; applications,\; ranging\; from\; conductors\; and\; superconductors\; to\; medical\; applications.\; The\; buckminsterfullerene\; was\; discovered\; in\; 1985\; by\; a\; team\; of\; scientists\; including\; Harry\; Kroto,\; Richard\; Smalley,\; and\; Robert\; Curl,\; for\; which\; they\; were\; awarded\; the\; Nobel\; Prize\; in\; Chemistry\; in\; 1996.''$

$\mathrm{Chat}\left(''penicillin''\right)\;$

$Penicillin is a group of antibiotics that are used to treat and prevent a wide variety of bacterial infections. These antibiotics were among the first medications to be effective against many previously serious diseases, such as tuberculosis and certain types of pneumonia. They are derived from a type of fungi called Penicillium fungi and are used in both human and veterinary medicine. Penicillin works by interfering with the ability of bacteria to form cell walls. The cell walls are vital for the bacteria's survival because they keep the contents of the bacteria together and protect the bacteria from its surroundings. When the cell wall is damaged, the contents of the bacteria leak out and this kills the bacteria. Penicillin is most effective against gram-positive bacteria, including Streptococcus pneumoniae, Staphylococcus aureus, and certain types of strep throat and skin infections. However, many types of bacteria have become resistant to penicillin due to widespread use, which has led to the development of other types of antibiotics. It's also important to note that some people can have an allergic reaction to penicillin, which can range from a rash to a severe anaphylactic reaction.$

$\mathrm{Chat}\left(\mathrm{more}\right)\;$

$Penicillin is a group of antibiotics that are commonly used to treat different types of infections caused by bacteria. It was the first antibiotic to be discovered and is one of the most widely used in medicine today. The medicine works by destroying the wall that surrounds the bacteria, stopping them from growing and multiplying, and ultimately killing them. Penicillin was discovered in 1928 by a Scottish scientist named Alexander Fleming. He realized that a type of mold, Penicillium notatum, produced a substance that could kill bacteria like streptococci and staphylococci. This discovery revolutionized medicine and has saved countless lives since its introduction. There are several types of penicillin, including penicillin G, penicillin V, amoxicillin, and ampicillin, among others. Each is used to treat different kinds of infections, some of which can be life-threatening, like pneumonia, meningitis, and sepsis. While penicillin is a very important antibiotic, not everyone can use it. Some people are allergic to penicillin or may experience side effects such as diarrhea, nausea, rash, or yeast infections. Additionally, overuse of antibiotics like penicillin has led to the development of antibiotic-resistant bacteria, which is a major concern in healthcare today.$

$\mathrm{Chat}\left(''entanglement''\right)\;$

$Entanglement is a phenomenon in quantum physics where two or more particles become linked and instantaneously affect each other’s states or properties, regardless of the distance between them. When particles become entangled, the state of one particle is directly related to the state of the other. Even when the particles are separated by large distances, a change in one of the particles results in an immediate change in the other. This concept is often illustrated through the example of a pair of gloves: if you put a pair of gloves in two boxes (one in each), and then sent the boxes to opposite sides of the universe, the moment you opened one box and found a left-handed glove, you would immediately know that the other box must contain a right-handed glove, despite not observing it. In real quantum entanglement, the particles do not have definite states until they are measured, and the measurement of one particle immediately and inevitably influences the state of the other particle, no matter the distance between the particles. This phenomenon was described by Albert Einstein as "spooky action at a distance" due to its baffling and counterintuitive nature. It forms one of the core principles of quantum mechanics, with broad implications for quantum computing and secure communications, among other things.$

$\mathrm{Chat}\left(''density\; functional\; theory''\right)\;$

$Density Functional Theory (DFT) is a computational technique used in physics and chemistry to investigate the electronic structure of many-body systems, particularly atoms, molecules, and the condensed phases. This method is based on the principle that the ground state properties of a many-electron system can be determined through an energy functional of the electron density. In simpler terms, DFT calculates the properties of a system by examining the behavior of its electron density rather than of its individual electrons. The advantage of using DFT in comparison to other methods is its better balance between accuracy and computational cost. While not as accurate as methods that treat every electron interaction explicitly, it is capable of making approximations that are in general accurate enough for many scientific applications, and much less computer-intensive. DFT has become a popular method for researchers, especially in the field of quantum chemistry and solid-state physics, to study the electronic properties of matter. It is widely used to study a variety of physical and chemical phenomena, including the properties of solids, the nature of chemical bonds, and the structures and reactions of molecules.$