We are pleased to provide institutions and individuals with top-quality modern courses on the hot topics of computational chemistry and general chemical disciplines. The research-related topics are taught by active researchers having numerous international publications and substantial citation indices. The participation of established scientists in the teaching process makes a difference in the services that your institution delivers. Apart from computational chemistry topics, we support high-school students in passing university-entry exams, such as the SAT, A-level, and accepted analogs. Should you feel interested in the teaching-centered collaboration, contact us at vvchaban@gmail.com to discuss the goals, means, and terms.
Educational Courses
SAT on Mathematics;
Subject SATs on Chemistry and Physics ;
General Chemistry;
Physical Chemistry;
Molecular Dynamics Simulations;
Chemical Interactions and Bonding;
Introduction to Scientific Research in Chemistry;
Professional Communication and Scientific Ethics;
R&D in Silico;
Popular Lectures
Herein, provided are the annotations of popular educational lectures that are immediately available for carrying out. The search over this webpage using the keywords must be helpful to find what we normally teach and research. Should you be in demand of any of those educational materials, drop a message declaring your interest to vvchaban@gmail.com so that we could start discussing a collaboration.
Molecular Wave Function
In quantum mechanics, a molecular wavefunction is a mathematical function that describes the quantum state of a simulated molecule. It is a complex-valued function of the positions of all the electrons and atomic nuclei in the simulated molecule. Specifically, the molecular wavefunction is used to calculate the probability of finding an electron in a particular region of space. The square of the absolute value of the wave function at a particular point in space is the probability density of finding an electron at that point. Note that all electrons are identical structures. The only difference between electrons in a molecule is their potential energies, which are in inverse proportion to their distances to the closest atomic nuclei.
The molecular wavefunction represents a solution to the Schrödinger equation, which is a fundamental equation in quantum mechanics. The Schrödinger equation describes the time evolution of a quantum system. In the case of a molecule and molecular ensembles, the Schrödinger equation is very complex. It is impossible to find an exact (analytical) solution for most molecules. However, several approximate methods can be used to solve the Schrödinger equation for molecules, crystals, and materials.
One of the most common methods for solving the Schrödinger equation for molecules is the Hartree-Fock method. The Hartree-Fock method is also known as a self-consistent field (SCF) method. The so-called SCF approximation means that the electrons in a molecule exist independently of each other. This assumption is not entirely accurate, but it is a proper approximation for many molecules. The Hartree-Fock method produces a set of one-electron wavefunctions, which we call molecular orbitals. These molecular orbitals are combined to construct the molecular wavefunction.
Another common method for solving the Schrödinger equation for molecules is the density functional theory (DFT). Modern implementations of the idea beyond DFT are more accurate than the Hartree-Fock method, but they can be more computationally expensive. DFT does not use molecular orbitals but instead uses the electron density of the molecule. The electron density is a function of the positions of all the electrons in the molecule. It is used to calculate the energy of the molecule.
Molecular wavefunctions can be used to calculate a wide range of molecular properties:
(1) The energy of a molecule is its total potential energy. The immediate potential energy of a molecule is determined by the positions of the electrons and atomic nuclei in the molecule.
(2) The structure of a molecule is an arrangement of its atoms in space. The structure of a molecule is characterized by the positions of the atomic nuclei in the molecule.
(3) The bonding in a molecule is the chemical force that holds the atoms in the molecule together. The bonding in a molecule is determined by the interactions between the electrons and nuclei in the molecule.
(4) The reactivity of a molecule is its ability to undergo chemical reactions. The reactivity of a molecule is determined by its electronic structure.
Molecular wavefunctions are used in a wide variety of applications:
Molecular wavefunctions are used to design new drugs by predicting their binding affinity to target proteins (molecular design).
Molecular wavefunctions are used to design new materials with desired properties, such as strength, elasticity, and conductivity (materials design).
Molecular wavefunctions are used to study a wide range of biochemical processes, such as enzyme catalysis and protein folding (biochemistry).
Molecular wavefunctions are used to develop quantum algorithms that can solve complex problems in chemistry and materials science (quantum computing).
Professor Vitaly V. Chaban and affiliates widely employ wave function-based calculations to understand chemical phenomena.
Basis Sets
Atomic basis sets are a set of mathematical functions used to represent the atomic orbitals of an atom, i.e., the positions of electrons belonging to an atom. They are used in quantum chemistry calculations to approximate the electronic structures of molecules.
There are two main types of atomic basis sets:
(1) Slater-type orbitals (STOs) are based on the hydrogen-like atom wave functions. They are the most accurate type of atomic basis set. Unfortunately, the mathematical properties of STOs prevent their efficient usage in computers.
(2) Gaussian-type orbitals (GTOs) are based on Gaussian functions. They are less accurate than STOs, but they are much more computationally efficient. GTOs are widely used in modern computational chemistry software to simulate molecules.
Atomic basis sets are typically characterized by the following parameters:
(1) The number of basis functions used to represent each atomic orbital (cardinality).
(2) The type of basis function used (STO or GTO).
(3) The number of Gaussian functions used to represent a single STO (contraction).
(4) The inclusion of a higher angular momentum basis function (polarizing behavior).
(5) The inclusion of basis functions with larger exponents (diffuse behavior).
The choice of a basis set is up to a researcher (quantum chemist). The choice depends on the desired accuracy of the calculation and the available computational resources. For high-accuracy calculations, STOs or highly contracted GTOs are typically used. For less accurate (preparatory) calculations, smaller GTOs can be used. A common recipe is to detect a new phenomenon using a small basis set and repeat the desired set of calculations using a publication-quality level of theory.
Here are some of the most common atomic basis sets:
(1) STO-3G is a small basis set with three Gaussian functions per STO.
(3) 6-31G is a medium-sized basis set with six Gaussian functions per occupied orbital and three Gaussian functions per unoccupied orbital. The 6‑31G basis set supplemented by a few polarization functions is typically used in routine calculations to identify this or that forecasted phenomenon.
6-311G is a relatively large basis set with six Gaussian functions per occupied orbital and three Gaussian functions per unoccupied orbital with the third layer of valence electron functions.
cc-pVDZ is a correlation-consistent basis set with double zeta polarization functions.
cc-pVTZ is a correlation-consistent basis set with triple zeta polarization functions.
Many more basis sets cover essentially the entire Periodic Table of Elements. Atomic basis sets allow us to approximate the electronic structure of molecules with a high degree of accuracy, which is essential for understanding and predicting the properties of molecules.
Professor Vitaly Chaban extensively uses 6-31G(d) and TZVP basis sets in their numerous simulations within materials science.
Plane-Wave Basis Sets
A plane-wave basis set is a set of mathematical functions used to represent the electronic wavefunctions of a molecule or solid. They are based on the idea that the electronic wavefunctions of a molecule or solid can be approximated as a superposition of plane waves. Plane waves are sinusoidal waves with infinite wavelengths that extend throughout three-dimensional space. They are represented by the equation: ψ(r) = exp(ik·r), where ψ(r) is the electronic wavefunction; k is the wavevector; r is the position vector. The energy of a plane wave is E = ħ²k²/2m, where ħ is the reduced Planck constant; m is the mass of the electron.
The plane-wave basis set must be truncated to include only plane waves with energies up to a certain energy. This maximum energy is called the cutoff energy. It is typically chosen to be several times the highest energy of the valence electrons in the molecule or crystal. Plane-wave basis sets have several advantages over traditional atomic basis sets:
(1) They are translationally invariant, which means that they are not affected by the periodic boundary conditions (PBCs). PBCs are routinely applied in solid-state calculations using DFT.
(2) They are complete, which means that they can represent any electronic wave function regardless of its energy or complexity.
(3) They are systematically improvable, which means that the accuracy of the calculations can be increased by increasing the cutoff energy.
(4) Plane-wave basis sets are also computationally efficient, especially for large systems. This is because the Fourier transform can be used to efficiently convert between real-space and reciprocal-space representations of the electronic wavefunction.
(5) Plane-wave basis sets are widely used in solid-state physics and quantum chemistry. They are particularly well-suited for studying the properties of materials with periodic structures, such as metals, semiconductors, and insulators.
Pne waves are used to calculate the electronic structures of solids. This includes the calculation of electronic energy levels, band gaps, and Fermi surfaces. Furthermore, plane-wave basis sets are used to calculate the optical properties of molecules and solids. This includes the calculation of absorption spectra, emission spectra, and refractive indices. Plane-wave basis sets are necessary to calculate the phonon dispersion curves of molecules and solids. Phonons represent quantized vibrations of the atoms in crystalline structures. Their properties are important for understanding the thermal properties of materials.
Plane-wave basis sets can be used to perform molecular dynamics (MD) simulations. These are known as ab initio MD or first-principles MD simulations. The MD simulations allow us to study the motion of atoms in a system over time. Phase transitions, chemical reactions, and diffusion phenomena can be quantified in this way.
Vitaly Chaban and affiliates apply plane-wave DFT calculations toshed light on the peculiarities of the periodic systems,. which may exist in both solid and liquid states.
Ultraviolet-visible (UV-Vis) Spectroscopy
UV-Vis spectroscopy represents an indispensable analytical technique that utilizes the interaction of light with matter in the ultraviolet (UV) and visible (Vis) regions of the electromagnetic spectrum. It has become an integral tool in various scientific disciplines, including chemistry, biology, materials science, and environmental science, owing to its ability to provide insights into the electronic transitions and molecular structures of materials.
The fundamental principle underlying UV-Vis spectroscopy lies in the interaction between light and molecules. When a sample is irradiated with UV or Vis light, molecules absorb specific wavelengths of light corresponding to the excitation of electrons from their ground state to higher energy levels. The amount of light absorbed at each wavelength is measured and plotted as an absorbance spectrum, which serves as a unique fingerprint of the sample's electronic structure and molecular composition.
UV-Vis spectroscopy has gained widespread adoption due to its numerous advantages:
(1) Simplicity and ease of use. UV-Vis spectrometers are relatively simple instruments, making them accessible to a wide range of users with varying levels of expertise. Data acquisition and analysis are straightforward, and the technique can be applied to a diverse array of sample types.
(2) High sensitivity. UV-Vis spectroscopy exhibits exceptional sensitivity, enabling the detection of minute concentrations of analytes. This makes it suitable for analyzing trace amounts of substances in various matrices, particularly in environmental and biological samples.
(3) Non-destructive nature. UV-Vis spectroscopy is a non-destructive technique. This ensures the preservation of the sample's composition and structure. This allows for repeated analysis of the same sample without any damage, conserving valuable materials.
(4) Quantitative analysis capabilities. UV-Vis spectroscopy serves as a powerful tool for quantitative analysis by establishing a calibration curve between absorbance and concentration. This enables the accurate determination of the concentration of an analyte in a sample, making it invaluable for various applications.
(5) Rapid data acquisition. UV-Vis spectrometers can acquire data rapidly, providing real-time analysis capabilities. This is particularly valuable for monitoring dynamic processes, such as chemical reactions, and time-sensitive applications.
UV-Vis spectroscopy plays a crucial role in the identification and characterization of organic compounds, including dyes, pigments, and pharmaceuticals. The unique absorbance patterns of these compounds allow for their unambiguous identification and structural analysis. UV-Vis spectroscopy is widely used to determine the concentration of a substance in a solution. By comparing the absorbance of the sample to a calibration curve constructed using known concentrations, the concentration of the analyte can be accurately determined. UV-Vis spectroscopy provides valuable insights into the electronic transitions of molecules, helping to elucidate their energy levels, bonding properties, and reactivity. This information is essential for understanding the properties of materials and designing new compounds. UV-Vis spectroscopy can be employed to monitor the progress of chemical reactions, tracking the disappearance of reactants and the formation of products. This technique is particularly useful for studying reaction kinetics and mechanisms. UV-Vis spectroscopy plays a significant role in environmental monitoring, enabling the detection and quantification of pollutants, contaminants, and other environmental toxins in water, soil, and air samples. Its sensitivity and versatility make it an invaluable tool for assessing environmental quality.
Valence Bond Theory (VBT)
VBT is a chemical bonding theory that explains the formation of chemical bonds in terms of the interaction of localized electron pairs. It remains one of the two primary bonding theories, along with the molecular orbital theory. VBT has been widely used to explain the bonding in molecules since its development in the early 20th century.
VBT is based on a set of postulates, which are fundamental assumptions about the nature of chemical bonding. Any atom possesses a fixed number of valence electrons. The valence electrons are the outermost electrons in an atom's orbital. These electrons possess the highest potential energies (see the computed electronic structures). The valence electrons designate the electrons that are involved in chemical bonding. Electrons in a molecule occupy atomic orbitals. In VBT, for the sake of simplicity, electrons are assumed to occupy individual atomic orbitals, rather than the delocalized molecular orbitals in the molecular orbital theory. Chemical bonds are formed by the overlap of atomic orbitals. When the orbitals of two atoms overlap, a covalent bond is inherently formed. The overlap of orbitals means the sharing of electrons between the two adjacent atoms.
The electrons in a bond are localized in the bond region. The electrons in a covalent bond are not evenly distributed throughout the molecule. Instead, they are concentrated in the region between the bonded atoms. The strength of a bond is proportional to the overlap of the orbitals involved. The strength of a covalent bond is directly related to the degree of overlap between the orbitals of the bonded atoms. The more overlap there is, the stronger the bond is.
VBT distinguishes between two main types of covalent bonds: sigma bonds (σ bonds) and pi bonds (π bonds). The sigma bonds are formed by the head-to-head overlap of atomic orbitals. They are the strongest type of covalent bond and are responsible for the rotational rigidity of single bonds. The pi bonds are formed by the sideways overlap of atomic orbitals. They are weaker (less energetic) than sigma bonds. The pi bonds are responsible for the rotational flexibility of double and triple bonds.
VBT has been successfully applied to explain the geometries of molecules. The arrangement of atoms in a molecule is determined by the repulsion between electron pairs in the molecule's valence orbitals. VBT can be used to predict the geometry of many simple molecules. VBT predicts the reactivity of molecules, which is influenced by the strength and polarity of their bonds. VBT can be used to explain the reactivity of many organic and inorganic compounds. The properties of materials can be understood within the framework of VBT. The properties of materials, such as their strength, conductivity, and color, are determined by the bonding between their atoms. VBT can be used to explain the properties of many materials, including metals, semiconductors, and polymers.
Despite its many successes, VBT has the following limitations. VBT does not always accurately predict the bond angles in molecules. VBT sometimes predicts bond angles that differ from the experimentally determined values. VBT does not explain the existence of chemical bonding in some molecules, such as metals and ionic compounds.
VBT does not take into account electron delocalization: VBT assumes that electrons are localized in individual bonds, but this is not always the case. Nonetheless, in some molecules, electrons are delocalized over multiple atoms. Valence bond theory is an intuitive and valuable tool for understanding chemical bonding. in many molecules. VBT represents a reasonable starting point for understanding the nature of chemical bonds without performing quantum-chemical calculations.
Molecular Orbital Theory (MOT)
In the realm of chemistry, MOT stands as a cornerstone for comprehending chemical bonding. It delves into the quantum mechanical aspects of molecular formation, describing how electrons occupy molecular orbitals shaped by the interplay of atomic orbitals. This contrasts with the valence bond theory, which portrays electrons as inhabitants of localized atomic orbitals.
MOT posits that molecular orbitals arise from the mathematical combination of atomic orbitals, each capable of accommodating a maximum of two electrons with opposite spins. The energy of a molecular orbital is dictated by the degree of interaction between its constituent atomic orbitals. Molecular orbitals fall into two distinct categories: bonding orbitals and antibonding orbitals.
The bonding orbitals emerge from constructive overlap between atomic orbitals. This leads to an enhanced electron density in the region between the two atoms. Higher shared electron density fosters molecular stability. In turn, the antibonding orbitals arise from the destructive overlap between atomic orbitals. This results in a diminished electron density in the interatomic region. As a result, the molecule destabilizes once it contains a populated antibonding orbital.
The bond order of a molecule serves as a quantitative measure of the bonding strength between two atoms. It is calculated by subtracting the number of electrons occupying antibonding orbitals from the number of electrons occupying bonding orbitals. For instance, the bond order of three means a triple bond in the structural formula of the molecule (see acetylene). The bond order of one simply corresponds to a single covalent bond (see ethane).
MOT has garnered widespread recognition for its ability to elucidate a diverse array of chemical phenomena. MOT effectively explains the bonding patterns in homonuclear diatomic molecules, such as H2, O2, and N2. MOT also sheds light on the bonding mechanisms in heteronuclear diatomic molecules, including CO, HF, and HCl. Moreover, MOT successfully explains the bonding intricacies in polyatomic molecules, such as H2O, NH3, and CH4.
MOT provides insights into the color of molecules, which is determined by the energy levels of their molecular orbitals (around HOMO and LUMO). MOT offers a framework for understanding the electronic structure of metals, in which electrons are not confined to individual atomic orbitals but rather delocalized across the entire lattice of metal atoms.
Despite its many successes, MOT is not without limitations. MOT presents a more intricate theoretical framework compared to VBT, requiring a solid grasp of quantum mechanics for comprehensive understanding. MOT occasionally predicts bond lengths that substantially deviate from experimental values. MOT does not explicitly account for electron correlation, the interaction between electrons residing in different orbitals.
MOT is a more rigorous and sophisticated approach compared to VBT. While MOT has made significant contributions to our understanding of chemical phenomena, it is crucial to remember its limitations. Thus far, MOT remains an invaluable resource for comprehending the nature of chemical bonds without conducting expensive QM calculations.
Molecular Mechanics
Molecular mechanics (MM) is a computational method used to model the behavior of molecules. It is based on the principles of classical physics and uses force fields to calculate the potential energy of a molecule as a function of its geometric structure. Each force field is a collection of formulae and numerical constants therein, which determine the forces acting among the interaction centers. MM can be used to study a wide range of molecular properties:
(1) MM predicts the structure of a molecule, including its bond lengths, angles, and dihedral angles after a geometry optimization algorithm is applied to minimize the interatomic forces.
(2) MM is used to calculate the energy of a molecule, which can be used to study a variety of properties, such as conformational stability, reactivity, and thermodynamic potentials.
(3) MM empowers the studies of the dynamics of molecules, such as their vibrational and rotational motions.
MM is a relatively simple and computationally efficient method, which makes it well-suited for studying large molecules and systems without the need to compute the wave functions for these systems. Since all equations of MM are solved analytically, this group of methods is cheaper and more numerically stable compared to quantum chemistry.
The calculations employing molecular mechanics involve the following concepts. The Born-Oppenheimer approximation states that the motions of the electrons in a molecule are much faster than the motions of the atomic nuclei. This allows us to treat the electrons as if they were moving in an average field created by the nuclei. A force field is a set of mathematical functions that describe the potential energy of a molecule as a function of its geometric structure. Force fields are typically based on experimental data and quantum mechanical calculations. Practical MM calculations are carried out using a variety of computational methods. Some of the most common methods include energy minimization: Energy minimization, also known as geometry optimization, is a method for finding the structure of a molecule with the lowest potential energy. This is typically done by using one of the gradient-based optimization algorithms. Molecular dynamics is a method for simulating the motion of molecules over time. This is done by using Newton's laws of motion to update the positions and velocities of the atoms in the molecule. MD based on MM is probably the most powerful and developed method of modern computational chemistry. MM force fields have a wide range of applications:
Drug design: Molecular mechanics is used to design new drugs by predicting their binding affinity to target proteins.
Materials design: Molecular mechanics is used to design new materials with desired properties, such as strength, elasticity, and conductivity.
Biochemistry: Molecular mechanics is used to study a wide range of biochemical processes, such as enzyme catalysis and protein folding.
Large systems possessing sophiscicated structures and conformational diversities represent a matter of research by Dr. Vitaly Chaban and students.
Nuclear Magnetic Resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon, in which atomic nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field. The atomic nuclei respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance when the oscillation frequency matches the intrinsic frequency of the nuclei. The latter depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved. In practical applications with static magnetic fields up to ca. 20 tesla, the resonance frequencies fall into the megahertz range. The NMR results from specific magnetic properties of certain atomic nuclei.
Nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution. It studies molecular physics and crystals as well as non-crystalline materials. NMR is also routinely used in advanced medical imaging techniques, such as magnetic resonance imaging (MRI).
NMR spectroscopy is based on the principle that certain atomic nuclei possess a magnetic moment, which is a vector quantity. This quantity numerically describes the strength and direction of the magnetic field produced by the nucleus. When a nucleus is placed in an external magnetic field, it experiences a torque that tends to align its magnetic moment with the direction of the field. However, the nucleus also has a property called spin, which causes it to precess (wobble) about the direction of the field. The frequency of this precession, known as the Larmor frequency, is directly proportional to the strength of the magnetic field and the magnetic moment of the nucleus.
If a radiofrequency (RF) pulse is applied to the NMR-active atomic nucleus that is close to its Larmor frequency, it will absorb energy and transition to a higher energy state. This absorption of energy can be detected as a decrease in the intensity of the RF signal. The amount of energy absorbed depends on the strength of the applied RF pulse and the difference in energy between the two nuclear states.
The Larmor frequency of a nucleus is also affected by its chemical environment. This is because the electron clouds surrounding different atoms in a molecule create slightly different magnetic fields near the atomic nucleus. This effect is known as the chemical shift. It represents the basis for NMR spectroscopy.
NMR spectroscopy has a wide range of applications in chemistry, physics, and medicine. Some of the most important applications are as follows:
(1) Structure determination of organic molecules. NMR spectroscopy is the most powerful tool for determining the structure of organic molecules. The chemical shifts of the nuclei in a molecule can be used to identify the different types of atoms and to determine their positions relative to each other.
(2) Study of molecular physics and crystals. NMR spectroscopy can be used to study the structure and dynamics of molecules in solutions and solids. It can also be used to study the properties of crystals, such as their lattice structure and their electronic properties.
(3) Medical imaging. NMR spectroscopy is the basis for MRI, which is a powerful tool for medical diagnosis. MRI can be used to create detailed images of the internal human organs without the use of X-rays or other ionizing radiation.
NMR spectroscopy is a rapidly developing field. The new applications are being discovered all the time. Some of the areas of active research in NMR spectroscopy include the development of new NMR methods for studying the structure and dynamics of biological molecules; usage of NMR spectroscopy to study the properties of materials at the nanoscale; development of new NMR imaging techniques for medical diagnosis.
Overall, NMR spectroscopy represents a powerful and versatile tool that has revolutionized the way we presently use to study molecules and materials. It is a constantly evolving field. We can expect to see even more exciting developments in the years to come.
Professor Chaban maintains tight collaborations with the research groups which routinelt emply NMR to characterize their newly synthesized products.
Fourier-Transform Infrared (FTIR) Spectroscopy
FTIR represents a powerful analytical technique that utilizes the absorption or emission of infrared radiation to study the vibrational characteristics of molecules. It has emerged as a ubiquitous tool in various scientific disciplines due to its exceptional versatility, sensitivity, and ability to provide detailed information about molecular structures and interactions.
FTIR spectroscopy operates on the fundamental principle that molecules – when exposed to infrared radiation – absorb specific wavelengths corresponding to their unique vibrational modes. These vibrational modes arise from the stretching, bending, and rocking motions of atoms within a molecule. The absorption pattern, or infrared spectrum, is a fingerprint of the molecule, providing a wealth of information about its composition and structure.
The FTIR spectroscopy offers several distinctive advantages that have propelled its widespread adoption. The FTIR spectrometers can achieve exceptional resolution, enabling the detection of subtle variations in infrared spectra, which is crucial for distinguishing closely related molecules. The FTIR spectrometers can cover a broad range of infrared frequencies, encompassing the mid-infrared (MIR) and far-infrared (FIR) regions. This allows for the investigation of a wide spectrum of molecular vibrations, including those associated with functional groups and conformational changes. The FTIR spectrometers acquire vibrational data rapidly, providing real-time analysis capabilities. This is particularly valuable for dynamic processes and time-sensitive applications. The FTIR spectroscopy is a non-destructive technique, meaning it does not alter the sample's composition or structure. This makes it suitable for analyzing precious or delicate samples. FTIR spectroscopy analyzes a wide variety of samples in different forms, including solids, liquids, gases, and thin films. Its adaptability extends to various sample preparation methods, such as direct sampling, transmission, and attenuated total reflection (ATR).
The FTIR spectroscopy has permeated numerous scientific disciplines, serving as an essential tool for a wide range of applications:
(1) Material Identification and Characterization. FTIR spectroscopy is employed to identify and characterize a vast array of materials, including polymers, ceramics, minerals, and organic compounds. Its ability to reveal molecular structures and functional groups makes it invaluable for material science research and quality control.
(2) Chemical Reaction Monitoring. FTIR spectroscopy is extensively used to monitor chemical reactions in real time, providing insights into reaction mechanisms, product formation, and intermediate species. This capability is crucial for optimizing synthetic processes and understanding reaction dynamics.
(3) Environmental Analysis. FTIR spectroscopy plays a critical role in environmental monitoring, enabling the detection and quantification of pollutants, contaminants, and other environmental toxins. Its sensitivity and specificity make it a valuable tool for assessing air, water, and soil quality.
(4) Industrial Process Control. FTIR spectroscopy is integrated into industrial processes to ensure product quality, monitor reaction progress, and detect potential contaminants. Its real-time analysis capabilities facilitate process optimization and troubleshooting.
(5) Medical Diagnosis. FTIR spectroscopy is increasingly utilized in medical diagnostics, aiding in the identification and classification of diseases based on their molecular signatures. Its potential applications span from cancer detection to monitoring the progressions of the diseases.
FTIR spectra can be both simulated by Dr. Chaban and obtained experimentally in the course of the existing coworking setups.
The Scholastic Assessment Test (SAT)
SAT represents a standardized test widely used for college admissions in the United States. It is administered by the College Board. SAT was first introduced in 1926 and changed substantially since then. The SAT is designed to assess a student's readiness for college-level work and to provide colleges with a common (standardized) measure of student achievement.
The SAT is a multiple-choice, pencil-and-paper test. The SAT lasts for three hours. It is divided into three sections: “Reading”, “Writing and Language”, and “Math”. Each section is scored on a scale of 200-800, for a total possible score of 1600. The “Reading” section measures a student's ability to comprehend and analyze written passages. The “Writing and Language section” measures a student's ability to use grammar, mechanics, and rhetoric effectively. The “Math” section measures a student's knowledge of math concepts and skills. Apart from this major content of the SAT, there are SAT Subject Tests since certain colleges require them as well. These are one-hour, multiple-choice tests that measure a student's knowledge of a specific subject. There are twenty different SAT Subject Tests offered, covering a wide range of subjects, including science, history, and foreign languages.
SAT Subject TesSAT Subject Tests are optional, but many colleges and universities recommend or require them for applicants who are interested in majoring in a particular subject. For example, a student who is interested in majoring in biology might be required to take the Biology SAT Subject Test.
SAT Subject Tests are scored on a scale of 200-800. A score of 500 or above is generally considered to be a good score, while a score of 700 or above is considered to be an excellent score. If you are considering taking SAT Subject Tests, it is important to check with the colleges and universities you are interested in to see if they require or recommend them. You can also find more information about SAT Subject Tests on the College Board website.
Most colleges and universities in the United States require applicants to submit their SAT scores. However, the importance of SAT scores in the college admissions process varies from school to school. Some schools place a lot of emphasis on SAT scores, while others give them less weight. In addition to SAT scores, colleges also consider a variety of other factors in the admissions process, such as a student's high school GPA, extracurricular activities, letters of recommendation, and personal essays.
If you are planning to take the SAT in the near future, there are several things you can do to prepare. The College Board offers a variety of resources on its website, including practice tests, study guides, and online courses. You can also find commercial SAT preparation courses and books available. The SAT is a challenging test, but it is also an important means of evaluating your academic skills.
A-Level Tests
A-levels, which stands for Advanced Levels, are a series of subject-based qualifications conferred as part of the General Certificate of Education (GCE) in England, Wales, Northern Ireland, and the Channel Islands. They are typically taken by students aged 16-18 years old in their final two years of secondary education. The A-levels are considered to be the equivalent of the Baccalauréat in France, the Abitur in Germany, Vestibular in Brazil, Universal State Exams in Russia, and the Matura in Austria and Switzerland.
The primary purpose of A-levels is to prepare students for university study. A-level grades are used by universities as a key factor in admissions decisions. A-levels can also be useful for students who are not planning to go to university, as they can provide valuable skills and knowledge for a wide range of careers.
There are over 70 A-level subjects available to choose from, covering a wide range of academic disciplines: mathematics, science (physics, chemistry, biology), English literature, history, modern languages, art, business studies, computer science, etc.
The A-levels are assessed through a combination of coursework and examinations. The proportion of coursework varies by subject, but it is typically around 50%. Examinations are typically held at the end of each year of study. A-levels are graded on a scale of A* to E, with A* being the highest grade and E being the lowest. The grade a student receives reflects their overall performance in the subject, taking into account both coursework and examinations.
The A-levels are a highly regarded qualification and are essential for students who want to study at a university in the UK. They are also increasingly recognized by employers as a valuable qualification for a wide range of careers. The A-levels prepare students for university study, provide valuable skills and knowledge for a wide range of careers, and represent a highly regarded qualification that is recognized by employers.
If you are considering taking A-levels shortly, do your research and choose subjects that you are interested in and that are relevant to your future career goals.
Usage of Python in Chemical Research
Python is a powerful and versatile programming language that has become increasingly popular in the field of chemistry. Its ease of use, wide range of libraries, and ability to handle complex data structures make it an invaluable tool for theoretical chemists. Furthermore, Python can be used to analyze large amounts of experimental data, such as spectra and chromatograms. It can also be used to create beautiful and informative visualizations of data. Python can be used to perform complex computational calculations, such as quantum mechanical simulations and molecular dynamics simulations. These calculations can be used to study the properties of molecules and materials. Python is used to develop cheminformatics tools, which are used to manage, analyze, and visualize chemical data. These tools are essential for drug discovery and development.
We use numerous libraries of functions and procedures developed in Python or equipped with interfaces to be employed with programs in Python. Here are some examples of specific Python libraries that are used in chemistry:
(1) NumPy is a library for numerical computation. It provides a wide range of functions for working with arrays, matrices, and vectors.
(2) Matplotlib is a library for data visualization. It can be used to create a wide variety of plots, including line plots, bar charts, and scatter plots.
(3) SciPy is a library for scientific computing. It provides a wide range of functions for numerical analysis and optimization.
(4) RDKit is a cheminformatics toolkit. It can be used to read, write, and manipulate chemical data.
(5) OpenMM is a molecular dynamics simulation toolkit. It can be used to simulate the behavior of molecules and materials upon their thermal motion at finite temperatures.
The OpenMM Toolkit for Theoretical Chemists
OpenMM is a relatively new development in the field of molecular simulations being a collection of useful functions to design sophisticated in-silico experiments employing molecular mechanics. OpenMM allows users to perform a variety of simulations, including molecular dynamics (MD), Monte Carlo (MC), and Langevin dynamics (LD). The paramount value of OpenMM is in the offered flexibility to combine methods and protocols as applied to a single chemical composition. The library is written in C++ and Python and can be used to simulate a wide variety of systems, including proteins, nucleic acids, lipids, and ensembles of small molecules.
OpenMM uses a modular design that allows users to customize their simulations by choosing from a variety of force fields, integrators, and thermostats. It also provides many features that make it easy to analyze simulation results, such as the ability to calculate energy, forces, and virial coefficients.
Here is how OpenMM works. The user defines the system to be simulated by specifying the molecules that will be included, the force field, and the integrator. OpenMM creates a representation of the system in memory. OpenMM calculates the forces acting on each atom in the system. OpenMM updates the positions and velocities of the atoms according to the chosen integrator. OpenMM calculates the properties of the system, such as the energy, temperature, and pressure. The above steps are repeated the desired number of times.
The user can define the system to be simulated using a variety of methods, e.g., by loading the PDB file. However, the system can also be built from scratch to specify all details including connectivity. The molecules can be packed using PACKMOL and then deposited into OpenMM. Some force fields arrive with the OpenMM distribution, but you can load your own one.
OpenMM creates a representation of the system in memory. This representation includes information about the atoms in the system, their positions and velocities, and the force field parameters. Next, OpenMM calculates the forces acting on each atom in the system. The forces are calculated using the force field parameters and the immediate positions of the atoms. OpenMM updates the positions and velocities of the atoms according to the chosen integrator. An integrator is a numerical algorithm that is used to solve the equations of motion for a system of particles. There are several different integrators available in OpenMM, and the choice of integrator depends on the properties of the system being simulated. After the requested sequence of simulations is finished,
OpenMM is a powerful and versatile tool that can be used to perform a wide variety of robust molecular simulations. It is recommended to researchers working in chemistry, biochemistry, and materials science.