From Wikipedia, the free encyclopedia
Qian Xuesen (: 钱学森; : 錢學森; : Qián Xuésēn; : Ch'ien Hsüeh-sên) (11 December 1911 – 31 October 2009) was a
who made important contributions to the
and space programs of both the
and . The name he used while in the United States was Hsue-Shen Tsien or H.S. Tsien.
During the 1940s Qian was one of the founders of the
at the . During the
of the 1950s, the
government accused Qian of having
sympathies, and he was stripped of his security clearance in 1950. Qian then decided to return to China, but instead was detained at
near . After spending 5 years under virtual house arrest, Qian was released in 1955, in exchange for the repatriation of American pilots captured during the . Notified by U.S. authorities that he was free to go, Qian immediately arranged his departure, leaving for China in September 1955, on the passenger liner SS President Cleveland of , via Hong Kong. He returned to lead the Chinese rocket program, and became known as the "Father of Chinese Rocketry" (or "King of Rocketry").
He is the cousin of the mechanical engineer , and his nephew is the 2008 Nobel Prize in chemistry winner . Asteroid
and the ill-fated space ship Tsien in the
are named after him.
Qian Xuesen (: Ch'ien Hsüeh-sên) was born in , the capital of
province, 180 km southwest of . He left Hangzhou at the age of three, when his father obtained a post in the Ministry of Education in . Qian graduated from , then graduated from
(now spelled Jiao Tong) in
in 1934 and received a degree in mechanical engineering, with an emphasis on rai he then spent an internship at Nanchang Air Force Base. In August 1935 Qian left China on a
to study mechanical engineering at the
and earned a
degree from MIT a year later.
While at MIT he was influenced by the methods of American engineering education, and its focus on experimentation. Qian's experiments included the plotting of plot pressures, using mercury filled manometers. (By contrast, most engineers in China at this time were not the "hands on" instead, theoretical studies were preferred.) Qian sought a school where his mathematical skills would be appreciated, and went to the
to pursue his studies under . Qian earned his doctorate from Caltech in 1939 with a thesis on slender body theory at high speeds. He would remain on the Caltech faculty until his departure for China in 1955, becoming the Robert H. Goddard Professor of Jet Propulsion in 1949, and establishing a reputation as one of the leading rocket scientists in the United States.
It was shortly after arriving at Caltech in 1936 that Qian was attracted to the rocketry ideas of , other students of von Kármán, and their associates, including . Around Caltech the dangerous and explosive nature of their work earned them the nickname "Suicide Squad."
Left to right:
(German scientist), Qian Xuesen, . Prandtl served G von Kármán and Qian served the United S after 1956, Qian served China. Qian's overseas cap displays his temporary
rank of colonel. Interestingly, Prandtl was von Kármán' von Kármán in turn was Qian's.
In 1943, Qian and two others in the Caltech rocketry group drafted the first docum it was a proposal to the Army for developing missiles in response to Germany's . This led to the , which flew in 1944, and later the , the , and other designs.
he served under
as a consultant to the , and commissioned with the assimilated rank of . Von Kármán and Tsien both were sent by the Army to
to investigate the progress of wartime aerodynamics research. Qian investigated research facilities and interviewed German scientists including
and Rudolph Hermann. Von Kármán wrote of Qian, “At the age of 36, he was an undisputed genius whose work was providing an enormous impetus to advances in high-speed aerodynamics and jet propulsion.” The American journal
would name Qian its Person of the Year in 2007, and comment on his interrogation of von Braun, "No one then knew that the father of the future U.S. space program was being quizzed by the father of the future Chinese space program."
During this time, Colonel Qian worked on designing an intercontinental space plane. His work would inspire the , which itself would later influence the development of the American .
Qian Xuesen married
(蒋英), a famed opera singer and the daughter of
(蒋百里) and his wife, Japanese nurse Sat? Yato. The elder Jiang was a military strategist and adviser to
leader . The Qians were married on September 14, 1947 in , and wou their son Qian Yonggang was born in
on October 13, 1948, while their daughter Qian Yungjen was born in early 1950, when the family was residing in .
Shortly after his wedding, Qian returned to America, to take up a teaching position at MIT; Jiang Ying would join him in December 1947. In 1949, upon the recommendation of von Kármán, Qian became the first director of the Daniel and Florence Guggenheim Jet Propulsion Center at Caltech.
In 1947 Qian was granted a permanent resident permit, and in 1949 Qian applied for naturalization. Years later, his wife Jiang Ying would say that he could not raise the necessary funds.
In the early 1940s, Army Intelligence was already aware of allegations that Qian was a Communist but his security clearance was not suspended. On June 6, 1950, however, his security clearance was revoked and Qian was questioned by the FBI. Two weeks later Qian announced that he would be resigning from Caltech and returning to China, which had come under the government of Communist leader . Qian had a conversation with the then
, whom Qian knew on a personal basis, in August. After Qian told him of the allegations Kimball said, "Hell, I don't think you're a Communist" at which point Qian indicated that he intended to leave the country, saying "I'm Chinese. I don't want to build weapons to kill my countrymen. It's that simple." Kimball then said "I won't let you out of the country."
After the firm in charge of arranging Qian's move back to China tipped off U.S. Customs that some of the papers encountered while packing Qian's things were marked "Secret" or "Confidential," U.S. officials went to the Pasadena warehouse where the materials were located and seized them. U.S. Immigration issued a warrant for Qian's arrest on August 25. Qian said that the documents that had security stamps were mostly written by himself and had outdated classifications, adding that "There were some drawings and logarithm tables, etc., which someone might have mistaken for codes." Included in the material was a scrapbook with news clippings about the trials of those charged with atomic espionage, such as . Subsequent examination of the documents showed they contained no classified material.
While at Caltech Qian had secretly attended meetings also attended by J. Robert Oppenheimer's brother , , and
that were organized by the Russian-born Jewish chemist Sidney Weinbaum and called Professional Unit 122 of the Pasadena Communist Party. Weinbaum's trial commenced on August 30 and both Frank Oppenheimer and Parsons testified against him. Weinbaum was convicted of perjury and sentenced to four years. Qian was taken into custody on September 6, 1950 for questioning and for two weeks detained at , a low-security United States federal prison near the ports of Los Angeles and .
When Qian had returned from China with his new bride in 1947 he had answered "no" on an immigration questionnaire that asked if he ever had been a member of an organization advocating overthrow of the U.S. Government by force and this, together with an American
document from 1938 with Qian's name on it, was used to argue that Qian was a national security threat. Prosecutors also cited a cross-examination session where Qian said "I owe allegiance to the people of China" and would "certainly not" let the Government of the United States make his decision for him as to whom he would owe allegiance to in the event of a conflict between the U.S. and Red China. On April 26, 1951 Qian was declared subject to deportation and forbidden from leaving
without permission.
Qian became the subject of five years of secret diplomacy and negotiation between the U.S. and China. During this time he lived under constant surveillance with the permission to teach without any research (classified) duties. During his incarceration, Qian received support from his colleagues at Caltech, including the institute's president , who flew to Washington to argue Qian's case. Caltech appointed attorney
to defend Qian.
The ban on Qian's leaving was lifted on 4 August 1955 and Qian resigned from Caltech shortly thereafter. Qian departed from Los Angeles aboard the Grover Cleveland in September 1955 amidst rumors that this was a swap for 11 U.S. airmen held captive by China since the end of the Korean War.
Under Secretary Kimball, who had tried to keep Qian in the U.S., commented on the affair to say:
"It was the stupidest thing this country ever did. He was no more a Communist than I was, and we forced him to go."
Qian had a successful career in China, leading and becoming the father of the Chinese missile program with the construction of China's
Qian's reputation as a prominent scientist who, in effect, defected from the United States to China, gave him considerable influence in the China of
during the late 1950s. He provided intellectual support for the failed agricultural policies of the , based on falsified science, when he wrote the, "...efforts of peasants and agricultural scientists will bring about bumper crops that far exceed present levels".
Qian rose through Party ranks to become a
member. He became associated with the
in the 1970s by joining in its attacks on rivals: he dubbed
"the sworn enemy of all scientific workers" and also denounced his superior, . He supported the government's crushing of the
and condemned the
movement after the central government initiated a crackdown in 1999.[] Qian retired in 1991 and lived quietly in Beijing, refusing to speak to Westerners.
In 1979 Qian was awarded Caltech's Distinguished Alumni Award. In the early 1990s the filing cabinets containing Qian's research work were offered to him by Caltech. Most of these works became the foundation for the Qian Library at
while the rest went to the Institute of Mechanics. Qian eventually received his award from Caltech, and with the help of his friend Frank Marble brought it to his home in a widely covered ceremony. Qian was also invited to visit the US by AIAA after the normalization of Sino-US relationship, but he refused the invitation, having wanted a formal apology for his detention. In a 2002 published reminiscence, Marble stated that he believed that Qian had “lost faith in the American government” but that he had “always had very warm feelings for the American people.”
The PRC government launched its manned space program in 1992 (reportedly with some help from Russia due to their extended history in space) and used Qian's research as the basis for the
which successfully launched the
mission in October 2003. The elderly Qian was able to watch China's first manned space mission on television from his hospital bed.
author , in his novel , named a Chinese spaceship after him.
In his later years, since the 1980s, Qian advocated scientific investigation of ,
and "special human body functions". Some people claim that Qian actually did not spend his effort[] on qigong, but that he just expressed that people should consider the widely practiced qigong in a scientific manner. He particularly encouraged scientists to accumulate observational data on qigong for the establishment of future theories.
From the early 1980s he studied in a number of areas, and created , contributed on science and technology system and somatic science, , , , literature and art, , systems science, geography, social science, and education.
Advanced the concepts, theory and method on system science: open complex giant system, from qualitative to quantitative integration of Hall for Workshop of comprehensive and integrated system, and opened up a Chinese school of the Science of Complexity. Organizated scientific seminars and train successors.
In 2008, he was named
Person of the Year. This selection is not intended as an honour but is given to the person judged to have the greatest impact on aviation in the past year.
named Qian as one of the eleven most inspiring people in China. He died at the age of 97 on October 31, 2009 in Beijing.
In July 2009, the Omega Alpha Association named Qian (H. S. Tsien) one of four Honorary Members in the international systems engineering honor society.
A Chinese film production Qian Xue Sen, directed by Zhang Jianya, stars Chen Kun as Qian, was released on 11 December 2011 in both Asia and North America.
Tsien HS Two-dimensional subsonic flow of compressible fluids // Aeronaut. Sci. 1939
Von Karman T, Tsien HS. The buckling of thin cylindrical shells under axial compression. J Aeronaut Sci 1941
Tsien, HS 1943 Symmetrical Joukowsky Airfoils in shear flow. Q. Appl. Math.
Tsien, HS, "On the Design of the Contraction Cone for a Wind Tunnel," J. Aeronaut. Sci., 10, 68-70, 1943
Von Karman, T. and Tsien, HS, "Lifting- line Theory for a Wing in Nonuniform Flow," Quarterly of Applied Mathematics, Vol. 3, 1945
Tsien, HS: Similarity laws of hypersonic flows. J. Math. Phys. 25, 247-251, (1946).
Tsien, HS 1952 The transfer functions of rocket nozzles. J. Am. Rocket Soc
Tsien, HS, "Rockets and Other Thermal Jets Using Nuclear Energy", The Science and Engineering of Nuclear Power, Addison-Wesley Vol.11, 1949
Tsien, HS, “Take-Off from Satellite Orbit,” Journal of the American. Rocket Society, Vol. 23, No. 4, 1953
Tsien, HS 1956 The Poincaré-Lighthill-Kuo Method, Advances in Appl. Mech.
Tsien, HS, 1958, "The equations of gas dynamics."
Engineering Cybernetics, Tsien, H.S. McGraw Hill, 1954
Tsien, H.S. Technische Kybernetik. ?bersetzt von Dr. H. Kaltenecker. Berliner Union Stuttgart 1957
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钱学森：论系统工程(新世纪版)，上海交通大学出版社
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Computational chemistry is a branch of
to assist in solving chemical problems. It uses methods of , incorporated into efficient , to calculate the structures and properties of
and solids. Its necessity arises from the fact that — apart from relatively recent results concerning the
(see references therein for more details) — the quantum
cannot be solved analytically, much less in closed form. While computational results normally complement the information obtained by chemical , it can in some cases predict hitherto unobserved chemical . It is widely used in the design of new drugs and materials.
Examples of such properties are structure (i.e. the expected positions of the constituent atoms), absolute and
(interaction) ,
and higher , ,
quantities, and
with other particles.
The methods employed cover both static and dynamic situations. In all cases the computer time and other resources (such as memory and disk space) increase rapidly with the size of the system being studied. That system can be a single molecule, a group of molecules, or a solid. Computational chemistry methods range from highly accurate highly accurate methods are typically feasible only for small systems.
are based entirely on
and . Other methods are called empirical or
because they employ additional empirical parameters.
Both ab initio and semi-empirical approaches involve approximations. These range from simplified forms of the first-principles equations that are easier or faster to solve, to approximations limiting the size of the system (for example, ), to fundamental approximations to the underlying equations that are required to achieve any solution to them at all. For example, most ab initio calculations make the , which greatly simplifies the underlying
by assuming that the nuclei remain in place during the calculation. In principle,
eventually converge to the exact solution of the underlying equations as the number of approximations is reduced. In practice, however, it is impossible to eliminate all approximations, and residual error inevitably remains. The goal of computational chemistry is to minimize this residual error while keeping the calculations tractable.
In some cases, the details of electronic structure are less important than the long-time
behavior of molecules. This is the case in conformational studies of proteins and protein-ligand binding thermodynamics. Classical approximations to the
are employed, as they are computationally less intensive than electronic calculations, to enable longer simulations of . Furthermore,
uses even more empirical (and computationally cheaper) methods like
based on physicochemical properties. One typical problem in cheminformatics is to predict the binding affinity of drug molecules to a given target.
Building on the founding discoveries and theories in the , the first theoretical calculations in chemistry were those of
in 1927. The books that were influential in the early development of computational quantum chemistry include
and 's 1935 Introduction to Quantum Mechanics – with Applications to Chemistry, , Walter and Kimball's 1944 Quantum Chemistry, Heitler's 1945 Elementary Wave Mechanics – with Applications to Quantum Chemistry, and later 's 1952 textbook Valence, each of which served as primary references for chemists in the decades to follow.
With the development of efficient
technology in the 1940s, the solutions of elaborate
for complex
systems began to be a realizable objective. In the early 1950s, the first semi-empirical atomic orbital calculations were carried out. Theoretical chemists became extensive users of the early digital computers. A very detailed account of such use in the United Kingdom is given by Smith and Sutcliffe. The first ab initio
calculations on diatomic molecules were carried out in 1956 at MIT, using a
of . For diatomic molecules, a systematic study using a minimum basis set and the first calculation with a larger basis set were published by Ransil and Nesbet respectively in 1960. The first polyatomic calculations using Gaussian orbitals were carried out in the late 1950s. The first
calculations were carried out in Cambridge on the
computer in the 1950s using
and coworkers. By 1971, when a bibliography of ab initio calculations was published, the largest molecules included were
and . Abstracts of many earlier developments in ab initio theory have been published by Schaefer.
calculations (using a simple
(LCAO) method for the determination of electron energies of molecular orbitals of π electrons in conjugated hydrocarbon systems) of molecules ranging in complexity from
to , were generated on computers at Berkeley and Oxford. These empirical methods were replaced in the 1960s by
In the early 1970s, efficient ab initio computer programs such as ATMOL, , IBMOL, and POLYAYTOM, began to be used to speed up ab initio calculations of molecular orbitals. Of these four programs, only GAUSSIAN, now massively expanded, is still in use, but many other programs are now in use. At the same time, the methods of , such as , were developed, primarily by .
One of the first mentions of the term "computational chemistry" can be found in the 1970 book Computers and Their Role in the Physical Sciences by Sidney Fernbach and Abraham Haskell Taub, where they state "It seems, therefore, that 'computational chemistry' can finally be more and more of a reality." During the 1970s, widely different methods began to be seen as part of a new emerging discipline of computational chemistry. The
was first published in 1980.
Computational chemistry has featured in a number of Nobel Prize awards, most notably in 1998 and 2013. , "for his development of the density-functional theory", and , "for his development of computational methods in quantum chemistry", received the 1998
in Chemistry. ,
received the 2013
in Chemistry for "the development of multiscale models for complex chemical systems".
The term theoretical chemistry may be defined as a mathematical description of chemistry, whereas computational chemistry is usually used when a mathematical method is sufficiently well developed that it can be automated for implementation on a computer. In theoretical chemistry, chemists, physicists and mathematicians develop
and computer programs to predict atomic and molecular properties and reaction paths for . Computational chemists, in contrast, may simply apply existing computer programs and methodologies to specific chemical questions.
There are two different aspects to computational chemistry:
Computational studies can be carried out to find a starting point for a laboratory synthesis, or to assist in understanding experimental data, such as the position and source of spectroscopic peaks.
Computational studies can be used to predict the possibility of so far entirely unknown molecules or to explore reaction mechanisms that are not readily studied by experimental means.
Thus, computational chemistry can assist the experimental chemist or it can challenge the experimental chemist to find entirely new chemical objects.
Several major areas may be distinguished within computational chemistry:
The prediction of the molecular structure of molecules by the use of the simulation of forces, or more accurate quantum chemical methods, to find stationary points on the energy surface as the position of the nuclei is varied.
Storing and searching for data on chemical entities (see ).
Identifying
and properties (see
Computational approaches to help in the efficient synthesis of compounds.
Computational approaches to design molecules that interact in specific ways with other molecules (e.g.
The words exact and perfect do not appear here, as very few aspects of chemistry can be computed exactly. However, almost every aspect of chemistry can be described in a qualitative or approximate quantitative computational scheme.
Molecules consist of nuclei and electrons, so the methods of
apply. Computational chemists often attempt to solve the non-relativistic , with relativistic corrections added, although some progress has been made in solving the fully relativistic . In principle, it is possible to solve the Schr?dinger equation in either its time-dependent or time-independent form, as appropriate for in practice, this is not possible except for very small systems. Therefore, a great number of approximate methods strive to achieve the best trade-off between accuracy and computational cost.
Accuracy can always be improved with greater computational cost. Significant errors can present themselves in
models comprising many electrons, due to the computational expense of full relativistic-inclusive methods. This complicates the study of molecules interacting with high atomic mass unit atoms, such as transitional metals and their catalytic properties. Present algorithms in computational chemistry can routinely calculate the properties of molecules that contain up to about 40 electrons with sufficient accuracy. Errors for energies can be less than a few kJ/mol. For geometries, bond lengths can be predicted within a few picometres and bond angles within 0.5 degrees. The treatment of larger molecules that contain a few dozen electrons is computationally tractable by approximate methods such as
There is some dispute within the field whether or not the latter methods are sufficient to describe complex chemical reactions, such as those in biochemistry. Large molecules can be studied by semi-empirical approximate methods. Even larger molecules are treated by
methods that employ what are called . In QM/MM methods, small portions of large complexes are treated quantum mechanically (QM), and the remainder is treated approximately (MM).
A single molecular formula can represent a number of molecular isomers. Each isomer is a local minimum on the energy surface (called the ) created from the total energy (i.e., the electronic energy, plus the repulsion energy between the nuclei) as a function of the coordinates of all the nuclei. A stationary point is a geometry such that the derivative of the energy with respect to all displacements of the nuclei is zero. A local (energy) minimum is a stationary point where all such displacements lead to an increase in energy. The local minimum that is lowest is called the global minimum and corresponds to the most stable isomer. If there is one particular coordinate change that leads to a decrease in the total energy in both directions, the stationary point is a
and the coordinate is the . This process of determining stationary points is called .
The determination of molecular structure by
became routine only after efficient methods for calculating the first derivatives of the energy with respect to all atomic coordinates became available. Evaluation of the related second derivatives allows the prediction of vibrational frequencies if harmonic motion is estimated. More importantly, it allows for the characterization of stationary points. The frequencies are related to the eigenvalues of the , which contains second derivatives. If the eigenvalues are all positive, then the frequencies are all real and the stationary point is a local minimum. If one eigenvalue is negative (i.e., an imaginary frequency), then the stationary point is a transition structure. If more than one eigenvalue is negative, then the stationary point is a more complex one, and is usually of little interest. When one of these is found, it is necessary to move the search away from it if the experimenter is looking solely for local minima and transition structures.
The total energy is determined by approximate solutions of the time-dependent Schr?dinger equation, usually with no relativistic terms included, and by making use of the , which allows for the separation of electronic and nuclear motions, thereby simplifying the Schr?dinger equation. This leads to the evaluation of the total energy as a sum of the electronic energy at fixed nuclei positions and the repulsion energy of the nuclei. A notable exception are certain approaches called , which treat electrons and nuclei on a common footing. Density functional methods and semi-empirical methods are variants on the major theme. For very large systems, the relative total energies can be compared using molecular mechanics. The ways of determining the total energy to predict molecular structures are:
Main article:
The programs used in computational chemistry are based on many different
methods that solve the molecular
associated with the . Methods that do not include any empirical or semi-empirical parameters in their equations – being derived directly from theoretical principles, with no inclusion of experimental data – are called . This does not imply that the solu they are all approximate quantum mechanical calculations. It means that a particular approximation is rigorously defined on first principles (quantum theory) and then solved within an error margin that is qualitatively known beforehand. If numerical iterative methods have to be employed, the aim is to iterate until full machine accuracy is obtained (the best that is possible with a finite
on the computer, and within the mathematical and/or physical approximations made).
Diagram illustrating various ab initio electronic structure methods in terms of energy. Spacings are not to scale.
The simplest type of ab initio electronic structure calculation is the
(HF) scheme, an extension of , in which the correlated electron–electron repulsion is not specificall only its average effect is included in the calculation. As the basis set size is increased, the energy and wave function tend towards a limit called the Hartree–Fock limit. Many types of calculations (known as
methods) begin with a Hartree–Fock calculation and subsequently correct for electron–electron repulsion, referred to also as . As these methods are pushed to the limit, they approach the exact solution of the non-relativistic Schr?dinger equation. In order to obtain exact agreement with experiment, it is necessary to include relativistic and
terms, both of which are only really important for heavy atoms. In all of these approaches, in addition to the choice of method, it is necessary to choose a . This is a set of functions, usually centered on the different atoms in the molecule, which are used to expand the molecular orbitals with the
. Ab initio methods need to define a level of theory (the method) and a basis set.
The Hartree–Fock wave function is a single configuration or determinant. In some cases, particularly for bond breaking processes, this is quite inadequate, and several
need to be used. Here, the coefficients of the configurations and the coefficients of the basis functions are optimized together.
The total molecular energy can be evaluated a in other words, the . Such a surface can be used for reaction dynamics. The stationary points of the surface lead to predictions of different
for conversion between isomers, but these can be determined without a full knowledge of the complete surface.
A particularly important objective, called computational , is to calculate thermochemical quantities such as the
to chemical accuracy. Chemical accuracy is the accuracy required to make realistic chemical predictions and is generally considered to be 1 kcal/mol or 4 kJ/mol. To reach that accuracy in an economic way it is necessary to use a series of post-Hartree–Fock methods and combine the results. These methods are called .
Main article:
Density functional theory (DFT) methods are often considered to be
for determining the molecular electronic structure, even though many of the most common
use parameters derived from empirical data, or from more complex calculations. In DFT, the total energy is expressed in terms of the total one- rather than the wave function. In this type of calculation, there is an approximate
and an approximate expression for the total electron density. DFT methods can be very accurate for little computational cost. Some methods combine the density functional exchange functional with the Hartree–Fock exchange term and are known as
Main article:
Semi-empirical
methods are based on the
formalism, but make many approximations and obtain some parameters from empirical data. They are very important in computational chemistry for treating large molecules where the full Hartree–Fock method without the approximations is too expensive. The use of empirical parameters appears to allow some inclusion of correlation effects into the methods.
Semi-empirical methods follow what are often called empirical methods, where the two-electron part of the
is not explicitly included. For π-electron systems, this was the
proposed by , and for all valence electron systems, the
proposed by .
Main article:
In many cases, large molecular systems can be modeled successfully while avoiding quantum mechanical calculations entirely.
simulations, for example, use a single classical expression for the energy of a compound, for instance the . All constants appearing in the equations must be obtained beforehand from experimental data or ab initio calculations.
The database of compounds used for parameterization, i.e., the resulting set of parameters and functions is called the , is crucial to the success of molecular mechanics calculations. A force field parameterized against a specific class of molecules, for instance proteins, would be expected to only have any relevance when describing other molecules of the same class.
These methods can be applied to proteins and other large biological molecules, and allow studies of the approach and interaction (docking) of potential drug molecules.
Main article:
Computational chemical methods can be applied to
problems. The electronic structure of a crystal is in general described by a , which defines the energies of electron orbitals for each point in the . Ab initio and semi-empirical calculations yi therefore, they can be applied to band structure calculations. Since it is time-consuming to calculate the energy for a molecule, it is even more time-consuming to calculate them for the entire list of points in the Brillouin zone.
Once the electronic and
variables are
(within the Born–Oppenheimer representation), in the time-dependent approach, the
corresponding to the nuclear
is propagated via the
associated to the time-dependent
(for the full ). In the
energy-dependent approach, the time-independent Schr?dinger equation is solved using the
formalism. The potential representing the interatomic interaction is given by the . In general, the
are coupled via the
The most popular methods for propagating the
associated to the
method (MCTDH),
the semiclassical method.
Main article:
Molecular dynamics (MD) use either ,
or a mixed model to examine the time-dependent behavior of systems, including vibrations or Brownian motion and reactions. MD combined with
leads to .
or QTAIM model of
was developed in order to effectively link the quantum mechanical picture of a molecule, as an electronic wavefunction, to chemically useful concepts such as atoms in molecules, functional groups, bonding, the theory of
and the . Bader has demonstrated that these empirically useful chemistry concepts can be related to the
of the observable charge density distribution, whether measured or calculated from a quantum mechanical wavefunction. QTAIM analysis of molecular wavefunctions is implemented, for example, in the
software package.
There are many self-sufficient
used by computational chemists. Some include many methods covering a wide range, while others concentrating on a very specific range or even a single method. Details of most of them can be found in:
modelling programs: , .
supporting several methods.
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- American Chemical Society Computers in Chemistry Division, resources for grants, awards, contacts and meetings.
Mathematical Research in Materials Science: Opportunities and Perspectives - CSTB Report
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