Density Functional Theory (DFT): Literature Review

Density Functional Theory (DFT): Literature Review Theoretical Background and Literature Review 2.1 Density Functional Theory This section covers basics about Density Functional Theory (DFT), which is the theoretical method behind our investigations. For those who are interested in a much more deep knowledge about the DFT we refer to textbooks such as [29] and [30]. 2.1.1 History of Density Functional Theory To get precise and accurate results from both theoretical and computational methods, the scale of physical phenomena must be well defined. In physics and material science the relevant scales of matter are time and size. In computational material science, for the multiscale understanding in both time and size scale the smallest relevant scale of atomic interactions are best described by ab initio techniques. These techniques are based on the determination of electronic structure of the considered materials and an intelligent transfer of its characteristics to higher-order scales using multidisciplinary schemes. More specifically, if the interaction of electrons is solely described using universal principles such as the fundamental laws of quantum mechanics condensed in the Schrodinger equation, these simulations are called firstprinciples, or ab initio methods. One can also separate those methods as Hartree-Fock and post-HF techniques that mainly uses by quantum chemistry field and De nsity Functional Theory (DFT) which is typically used in of material science. Ab initio simulations are becoming remarkably popular in scientific research fields. For example in DFT case, in a simple search at Web Of Science [31] or any other publication search tool, one can easily see that number of publications that include †Density Functional Theory† in their title or abstract is over 15000 in 2013. Therefore, it can be concluded that, ab initio based research already an important third discipline that makes the connection between experimental approaches and theoretical knowledge. Figure 2.1: Usage trend of DFT over years Within ab initio simulations quantum mechanical equations for any system that may be ordered or disordered are solved. That actually gives one drawback which is, solving that kind of equations is generally only possible for simple systems, because of the expensive electron-electron interaction term. So, in general, the ab initio simulations are restricted to 150-200 atoms calculations with most powerful computer clusters. Due to the that severe limitation, better techniques and methods are developed and implemented to bring the real materials into realm of ab initio simulations. The major development of ab initio methods with practical applications took place when many electron interactions in a system was possible to be approximated using a set of one electron equations (Hartree-Fock method) or using density functional theory In 1927, Thomas [32] and Fermi [33] introduce a statistical model to compute the energy of atoms by approximate the distribution of electrons in an atom. Their concept was quite similar to modern DFT but less rigorous because of the crucial manybody electronic interaction was not taken into account. The idea of the Thomas and Fermi was that, at the starting point for simplicity that electrons do not interact with each other and using classic terms, therefore, one can describe the kinetic energy as a functional of electron density of non-interacting electrons in a homogeneous electron gas. 3 years later, in 1930, Dirac [34] succeeded to include the many-body exchange and correlation terms of the electrons and actually he formulated the local density approximation (LDA), that is still used in our days. However, the Thomas-Fermi and Dirac model that are based on homogeneous electron gas do not cover the accuracy demand in current applications. In same the years as Thomas and Fermi, Hartree [35] also introduce a procedure to calculate approximate wavefunctions and energies for atoms and that was called Hartree function. Some years later, to deal with antisymmetry of the electron system, his students Fock [36] and Slater[37], separately published self-consistent functions taking into account Pauli exclusion principals and they expressed the multi-electron wavefunction in the form of single-particle orbitals namely Slater-determinants. Since the calculations within the Hartree-Fock model are complicated it was not popular until 1950s. The fundamental concepts of density functional theory were proposed by Hohenberg and Kohn in their very well known paper in the year 1964 [38]. The main idea was trying to use the electron density instead of complex and complicated wavefunction. A wavefunction contains 3N variables, where N is the number of electrons and each electron has 3 spatial degrees of freedom. In contrast to that electron density contains only 3 variables. Therefore, the implementation of the electron density with 3 variables will be more easy to handle than 3N wavefunction variables. In their work, Hohenberg and Kohn proved that all ground state properties of a quantum system, in particular the ground state total energy, are unique functionals of the ground state density. However, the Hohenberg-Kohn (HK) formulation is not useful for actual calculations of ground state properties with enough accuracy. A major improvement was achieved one year later, in 1965. Kohn and Sham [39] proposed a formulation by partially going back to a wavefunction description in terms of orbitals of independent quasi particles. The main idea was that the many-body problem can be mapped onto a system of non-interacting quasiparticles. This approach simplified the multi-electron problem into a problem of non-interacting electrons in an effective potential. This potential includes the external potential and the effects of the Coulomb interactions between the electrons, e.g., the exchange and correlation interactions. Since then up to now the Kohn-Sham equations are used in practically all calculations based on DFT. 2.1.2 Schr ¨odinger’s Equation In quantum mechanics, analogue to Newtons equations in classical mechanics, the Schr ¨odinger equation is used. This is a partial differential equation and used to describe the physical quantities at the quantum level. The Schr ¨odinger equation forms the basis of many ab initio approaches and its non-relativistic form is an eigenvalue equation of the form: HˆÎ ¨(ri,Rj)= EÃŽ ¨(ri,Rj) (2.1) where ÃŽ ¨(ri,Rj) is the wavefunction of the system depending on the electron coordinates ri,i =1N and the coordinates of all nuclei in the system Rj,j =1M. Hˆis the Hamiltonian of a system that contains M nuclei and N electrons. Therefore, the Schr ¨odinger equation that involves both nuclei and electrons has to be solved for the many-body eigenfunctions ÃŽ ¨(r1,r2, , rN ; R1,R2, , RM ). The many-body Hamiltonian can be written in the form: Hˆ= Tˆe + Tˆn + Vˆnn + Vˆen + Vˆee (2.2) ˆˆ where all of parts are operators. Te and Tn are the kinetic energies of the ˆˆ electrons and nuclei, respectively. Ven, Vee and Vˆnn represent the attractive electrostatic interaction between the electron and the nuclei and the repulsive potential due to the electron-electron and nucleus-nucleus interactions. One can also write them down explicitly: N f2 ˆ Te = − 2 i (2.3) 2me i=1 M 2Mn n=1 f2 ˆ Tn = − 2 n (2.4) 11 M ZnZme2 = (2.5) 4Ï€ 0 2 |Rn − Rm| =1;n,mn =m ˆ Vnn ˆ Ven = − 11 MN Zne2 (2.6) 4Ï€ 0 2 |ri − Rn| n=1 i=1 j= M e = (2.7) 4Ï€ 0 2 |ri − rj| i,j=1;i 2 11 ˆ Vee where me and Mn are the electron and nuclei masses, Zn is the nuclear number of the n-th atom, e is the electronic charge and f is the Planck constant. For simplicity one can also use atomic units. Then the Hamiltonian takes the form: NMM ZnZm in 22 |Rn − Rm| i=1 n=1 n,m=1;n =m 1 1 ˆ H = − 2 2 − + (2.8) j= MNMZn − + |ri − Rn||ri − rj| n=1 i=1 i,j=1;i 2.1.3 Born-Oppenheimer Approximation It is clear that forces on both electrons or nuclei is in the same order of magnitude because of their electric charge. Therefore, the expected momen 1 tum changes due to that forces must be the same. However electrons are much smaller than nuclei (e.g. even for Hydorgen case nuclei nearly 1500 times larger than an electron) they must have higher velocity than nuclei. One can conclude that electrons will very rapidly adjust themselves to reach the ground state configuration if the nuclei start moving. Born and Oppenheimer [40] published their work in 1927, they simply separated the nuclear motion from electronic motion which is now known as the Born-Oppenheimer approximation. Therefore, while solving the Hamiltonian Equation in (2.8) one can simply assume nuclei as stationary and solve the electronic ground state at first then calculate the energy of the system in that configuration and solve the nuclei motion. Then the separation of electronic and nuclear motion leads to an separation of the wavefunctions ÃŽ ¨ = ψφ of electrons and nuclei, respectively. Via the separation one can treat the nuclear motion externally by not in cluding the Hamiltonian and the â€Å"electronic† Hamiltonian can be written as: Hˆe = Tˆe + Vˆen + Vˆee (2.9) Solving the equation (2.9), one can get the total energy of the ground state of the system, which can be defined as: E0 = ψ0|He|ψ0 + Vnn (2.10) where E0 is the ground state total energy of the system and ψ0 is the eigenfunction of the electronic ground state. 2.1.4 Hohenberg-Kohn Theorem However, the Hamiltonian in Equation (2.9) is quite complicated to solve for realistic systems due to the high number of electrons and especially the term Vee makes it impossible to solve the problem exactly. Therefore, instead of solving the many-body wavefunctions, Hohenberg-Kohn deal with that problem by reducing it to the electron density Ï (r). This approach makes the fundamentals of DFT. According to Hohenberg and Kohn, the total energy of the system can be defined via the electron density as E = E[Ï (r)] and it will be the minimum for the ground state electron distribution, namely Ï 0(r). Therefore, the exact theory of many-body systems reduced to the electron density that can be defined as: Ï (r)= d3 r2d3 rN |ψ(r1, rN )|2 (2.11) and has to obey the relation: Ï (r)d3 r = N (2.12) where N is the total number of electrons in the system. One can also summarize the HK theorem in the form of the two main theorems, Theorem I : The external potential vext(r), which is the potential energy generated by the nuclei, can be determine from the ground state electron density Ï 0(r). Then Hamiltonian will be fully defined, also the wavefunction for the ground state will also be known. Theorem II : E0,the ground state total energy of the system with a particular vext will be the global minimum when Ï  = Ï 0. From the perspective of these two theorems one can write down the total electronic energy as: E[Ï ]= Te[Ï (r)] + Ï (r)vext[Ï (r)] + EH [Ï (r)] + Exc[Ï (r)]d3 r (2.13) One can also add the kinetic energy of the electrons T − e[Ï (r)], the classical Coulomb interaction (or Hartree interaction) between electrons EH [Ï (r)] and the remaining complex non-classical electron exchange correlations Exc[Ï (r)] into an universal functional FHK [Ï (r)]: E[Ï ]= FHK [Ï ]+ Ï (r)vext[Ï (r)]d3 r (2.14) The remaining will be to apply the variational principle to extract the ground state energy ÃŽ ´E[Ï (r)] |Ï =Ï 0 = 0 (2.15) ÃŽ ´Ã (r) 2.2 Kohn-Sham Equations However, the Equation (2.14) does not give an accurate solution. In that point, Kohn and Sham reformulated the current approach and introduced a new scheme by considering the orbitals by mapping the fully interacting electronic system onto a fictitious system of non-interacting quasi particles moving in an effective potential.The Kohn-Sham equations solution can be written as: ˆ HKSψi = iψi (2.16) where the Hamiltonian is HˆKS =[− 1 2 + Veff (r)] (2.17) 2 Therefore, the problem of finding the many-body Schr ¨odinger equation is now replaced by solving single particle equations. Since the KS Hamiltonian is a functional of just one electron at the point r then the electron density can be defined according to HK theorem: occ. Ï (r)= |ψi(r)|2 (2.18) i=1 Besides, kinetic energy term and the classical Coulomb interaction energy of the electrons can be define as: N 1 d3 Te = − r|ψi(r)|2 (2.19) 2 i=1 1 Ï (r)Ï (r ) EH [Ï ]= d3rd3 r(2.20) 2 |r − r | Then the Hohenberg-Kohn ground state energy cn be written according to Kohn-Sham approach: N ÃŽ ´Exc EKS = i − EH [Ï ]+ Exc − (2.21) ÃŽ ´Ã (r) i i are the one electron energies and are coming from the results of KS equations results, however it has low physical meaning. The most significant term in the Equation (2.20) is the last term. which is the exchange correlation term that contains all the many-body interactions of exchange and interactions of the electrons. One can also write down it as in the form of Hohenberg-Kohn universal functional from the equation: Exc[Ï ]= FHK [Ï ] − (Te[Ï ]+ EH [Ï ]) (2.22) The total ground state energy can be obtained from EKS in Equation (2.21). Since it contains only the electronic energy, the total ground state energy of the system is calculated by adding the nuclei-nuclei repulsion term: E0(R1, , RM )= i − EH [Ï 0]+ Exc[Ï 0] − vxcÏ 0dr + Vnn(R1, , RM ) (2.23) where E0 is the total ground state energy for a given atomic configuration (R1, , R2). Therefore, the total energy depend on ionic positions that is actually depends on the volume and cell shape, so one can easily compute the ground state structure by minimizing the total energy. Also one can find the force acting on the particular atom, say atom A, by taking the derivative of the energy with respect to ionic position of A: ÃŽ ´E0(R1, .., RM ) FA(RA) = (2.24) ÃŽ ´RA which also shows the total energy dependence on atomic positions. 2.3 Calculating the Exchange-Correlation Energy The derived and brieà ¯Ã‚ ¬Ã¢â‚¬Å¡y explained KS equations from the fundamentals of all modern DFT calculations today. The most important point in the solution of KS equations are the exchange-correlation functional Exc which also determines the quality of the calculation. There are two well known approximation methods to get the exchange correlations: local density approximation (LDA)[39] and generalized gradient approximation (GGA)[41, 42]. 2.3.1 Local Density Approximation The local density approximation starts with a very simple approximation that, for regions of material where the charge density is slowly varying, the exchange-correlation energy at that point can be considered as the same as for a local uniform electron gas of the same charge density. In that case one can write the Exc as: Exc = Ï (r) xc(r) (2.25) where xc(r) is the exchange correlation energy per electron in an homogenous electron gas of density Ï (r). Even though the approximation is seemingly simple it is suprisingly accurate. However, it also has some drawbacks such as under-predict on of ground state energies and ionisation, while overpredicting binding energies as well as slightly favouring the high spin state structures and does not work fine for some systems where the charge density is rapidly changing. 2.3.2 Generalized Gradient Approximation Knowing the drawbacks of LDA the most logical step to go beyond LDA is not to limit oneself to the information about the charge densitiy Ï (r) at a particular point r, but also adding the information about the gradient of the charge density Ï (r) to be able to take into account the unhomogeneous density in the system. Then one can write the exchange correlation energy as : Exc[Ï ]= f(Ï , Ï )dr (2.26) That way of description leads to an improvement over LDA, nevertheless in some systems LDA still works better. There also several different parameterizations of GGA while in LDA its only one. In GGA some of these parameterizations are semi-emprical, in that experimental data (e.g. atomization energies) is used in their derivation. Others are found entirely from first principles. A commonly used functional is the PW91 functional, due to Perdew and Yang [43, 44] and most commonly used today is PBE [45, 46] by Perdew, Burke and Ernzerhof. 2.4 Ultra-Soft Pseudopotentials and the Projector-Augmented Wave Method In the previous section, the calculation of Exc is described. Nevertheless this is not the single sensitive point of DFT calculations. The other point is the treatment of the electron-nuclei interaction. There are several available methods that describes the electron-nuclei interaction, but the most effective

Ancient Mesopotamia and Greek inventions Essay

Our world today wasn’t entirely created from recent achievements. We have collected knowledge from ancient civilizations such as Mesopotamia and Greece by studying their history and improving their accomplishments. These cultures have had a major impact on the daily lives of the people in the modern world. Although Ancient Mesopotamia and Greece were some of the earliest civilized cultures, they differ greatly in their achievements and innovations that played important roles for future humans. As the world’s earliest civilization, Ancient Mesopotamia’s innovations continue to affect the world. It made vital contributions in fields like science, mathematics and astronomy; they even developed a writing system. The early Mesopotamian civilization was known for inventing the first 30-day lunar calendar. Using the phases of the Moon, they counted 12 lunar months as a year. Moreover, Mesopotamians first observed a seven-day week. The invention of the calendar was a rem arkable contribution that later had a major influence on our modern calendar. The Mesopotamians also developed mathematics to a very advanced level and created the sexagesimal system for the calculation of time and angles. This system is still practical, because of the multiply divisibility of the number 60. For example, in modern times we still use 60-minute hours, 24-hour days and the 360-degree circle. The Mesopotamians developed theories to measure the area of solids and shapes, and the circumference of circles. The Mesopotamian’ s achievements laid many of the foundations for modern mathematics. One of the most remarkable contributions was the development of the first historically significant writing system of the Middle East known as cuneiform. They wrote with a stylus on special tablets of soft, wet clay, because it was the perfect surface on which to leave marks. The fact that people started to use soft clay not only for bricks and jars, but also for the writing, implied their intellect and potential future progress. Cuneiform was not a language ; however, it was the most widespread writing system in the ancient Middle East, which helped us to learn more about the Mesopotamian history and culture. Another civilization that made numerous influential contributions was Ancient Greece. The Greek civilization was famous for many admirable scholars who were recognized for remarkable achievements in the areas of math and science, medicine and architecture, which gave a rise to further discoveries by following generations. The Greeks were engaged in  mathematical study of logic; they provided one of the first proofs in mathematics and discovered irrational numbers. Even today, people still use the Pythagorean theorem, to understand and measure triangles. Greeks achieved such great progress in mathematics by using deductive reasoning, which also helped in every other discipline. Hippocrates made one of the most prominent achievements that expanded humankind’s understanding of medicine. He was the â€Å"father of medicine†, who determined the natural causes of diseases rather than blaming them on the gods punishments, and then established procedures for medical treatment. Hippocrates’ modern concepts like diet, rest, and a clean environment were be lieved to be beneficial for the human body to heal itself. Also, doctors were responsible for the patient’s well being and privacy in ancient Greece, and they strictly followed a number of professional ethical standards, later called, the Hippocratic oath. The modern version of this oath is still used today; it confides the ideas that the doctor is responsible for his/her actions in case problems arise. The ancient Greeks created the most impressive and highly distinctive architectural styles that influenced the architecture of the past two millennia. Greek architecture developed three distinct orders, the Doric, Ionic, and Corinthian; their parts and proportions were ordered and coordinated. The design, arrangement and decoration of the columns were remarkable and unique with a pure aesthetic effect. The style of Greek architecture provided the finest and the most magnificent buildings, with constant symmetry, proportion and harmony. Greek architecture can still be seen today. For example, the United States Capitol building and other federal monuments in Washington DC have notable similarities in the design, decoration of the columns with the classic Greek architecture. The ancient Mesopotamia was the first civilized territory on the globe that â€Å"began the history† by inventing a form of writing. The inventions and innovations of this civilization contributed to the evolution of humankind. The ability to write made a great impact on people’s intellectual capacities and potential future success in exploring and studying major concepts that later became fundamental for the future development of the whole humankind. Even though the Mesopotamians were the first who pioneered in mathematical studies, the Greeks’ logical approach to the mathematical problems helped them to excel in this discipline. Moreover they applied this knowledge into other areas of  science and technology, which shaped the foundation of Western civilization. Ancient Mesopotamia and Greece civilizations played a key role in the development and progress of our modern world. Without their astounding inventions we wouldn’t be able to succeed in many imp ortant spheres of science, mathematics, astronomy and technology. They say there is nothing new under the sun, which means that anything new that we create is merely an improvement on another invention from a previous inventor.

How to Remember Your Dreams

An Essay on Various Management Styles - Free Essay Example

Sample details Pages: 5 Words: 1490 Downloads: 5 Date added: 2017/06/26 Category Management Essay Type Narrative essay Did you like this example? Each organization and company has a different styles in their management but the principles of it is to underline the methods, abilities and techniques on how the superior or manager use in handling the situations and express their leadership in within an organization. Different sources stated different type of definition and types of managerial style. According to HR Zone, managerial styles are polarised in between autocratic and permissive (Anon., u.d.). Whereas according to The Times 100, there are four types of management style which are autocratic, paternalistic, democratic and laissez-faire (100, 1995-2014). It is important and needs for the manager to learn to adapt their management style in order to ensure the employees respond. The most commonly used by companies and organisation management style are democratic or participative management, Laissez-faire management, bureaucratic management, and autocratic management (style, 2014). Autocratic managers, origin fr om the word autocrat, do not make their decisions with any participation from the other stakeholders nor are any interactions with the others based on communicating these decisions. It is more like a dictatorial style as well. In autocratic management style, the superior tends to retain control and there is no consultations provided. They like to tell their employees or those who work under them what to do and they expect that their subordinates will obey to their instructions. Autocratic management tend to practice on one-way communication rather than two way communications. In this type of management style, it can help the productivity in a company or organisations because urgent tasks that need doing quickly can be completed or there is an element of risk about the work can be done on time. In this style, it might works well to those people who does not have any own decisions making or who love to follow as what they are told to do (style, 2014). However, this type of management may lead to lack of creativity of the company or it may resist if employee have no input because it is may helps a company productivity through commitment or ideas provide by the employee and have a sense of belonging to the company (100, 1995-2014). Usually directive autocratic manager supervise their subordinates closely while permissive autocrats will give their employees some degree of freedom as in how they work towards in achieving their goal. Persuasive managers are deeply different from autocratic style; however, they do put in the effort in convincing the employees of the benefits on their decision making (Anon., u.d.). As for consultative managers, it is slightly different from autocratic managers because they try to male decision which will take into account of the employee needs but employees are not allowed to provide any feedback and the flow of information is almost exclusively top-down. As permissive managers, they are also known as democratic managers in certain sources where they allow feedback from staff to provide some form of input into the decision making process and it is taken into consideration when making decisions but to a verifying degrees (Anon., u.d.). As for Laissez-faire management style, it is different from autocratic style because there is no direction or instructions or little from the managers or superior and their subordinates and employees are free to make the decisions. In certain resources, it is also known as hand off approach where the superior or employer will leave their subordinates to get on their job by themselves (style, 2014). Usually Laissez-faire practices two way communications where they will regularly get their feedback from the employee for this approach to work. However, chaos may take place because there is no centralised control and things might go wrong. This type of management gives the impact towards those who are highly skilled, trained or expert teams (100, 1995-2014). According to The Ti mes 100 (100, 1995-2014), paternalistic management style is as with autocratic but with a slightly different from autocratic where it is more sensitive towards employees feedback (Touchpoint, 2014) and it takes much responsibility for decision making but with a caring attitude for the employees (100, 1995-2014). Superior or the managers who hold on this type of management style are concerned towards their employee’s feelings and wellbeing but they will not put any individual ahead the company or organisation success. Pros of using this management style is where the employee may feel being appreciated and valued, however the cons is that they will be frustrated because they have only a little scope of making decision (100, 1995-2014), which means even though they voices out their opinion, the last and final decision making is still on the hand of their superior. Democratic management style will seeks for all the stakeholders’ opinion into account and also achieve the consensus before reaching the final decision and also the superior encourage the participation of their employees. They will also share information within their own team members and also provide opportunities for the team to influence the decision making. In this management style, it will gain the commitment from the team members and particularly when changes need to be made (100, 1995-2014). This style of management encourages more trust, harmony, productivity and job satisfaction in the overall organization. It might be useful for a small business organization or company because the feedback from their employees has the chance to be taken up. Most of the company and organization are practicing this management style in order to achieve a better productivity level. However, this style of management can be frustrated slowly, having all different parties being involved in the decision making for an easy or more seamless implementation process, but they are more likely to buy or suppo rt the decisions anyhow (Touchpoint, 2014) and sometimes the employees does not know how to do make their own decisions and they want their superior to make the decisions (style, 2014). Besides, if too much consultation time is being used in decision making, thus it will affects the company or organization productivity and reduces in its outcome. According to Bank of America, active leadership management tends to lead their subordinates and employees by example or being a role model and a high standard was set for themselves and also their employees. Usually the employers or superior will not ask an employee to do on a task that they are unwilling to do themselves. In this management style they are involved highly in a day-to-day work and are fully aware of what is happening in the office or workplace (Touchpoint, 2014). As for directive leadership management style, it stands less than authoritative compare to autocratic management style but the leaders do not typically solici t the employee input. They will uses a short time frame, an unpredictable client or any of an emergency situation as a reason or excuse for acting unilaterally. It might be true for certain times but other times they will have a bit more difficulty of letting go of control (Touchpoint, 2014). There are another several types of management style such as participatory, servant and task-oriented management style. According to The Times 100 (100, 1995-2014), participatory management style based on a coaching philosophy and it focuses more on empowering the employees and seek for their own knowledge and make their own decision when it is appropriate (100, 1995-2014). Whereas servant management style is based on people come first philosophy where it is famous with the writer Robert Greenleaf. This is based on finding talented people in order to run the company or organization and thus give power to them to do what they can do the best. The leader can sees him or her as a ‘servantà ¢â‚¬â„¢ to the customers and to encourage the workers to adopt to the same attitudes (100, 1995-2014). The final style as stated in The Times 100 is task oriented management style where the employer or leader will use this style of management probably have been a project managers before. In this management, they are expert or professionals in planning projects, allocating resources, assigning roles, setting benchmarks and keeping to strict deadlines. In our workplace, democratic management style is being practice by our company. They practice a two way communications where they take up the opportunity for the employees to voice out their ideas and suggestions in company decision making. They will consult their team members first before they make any decisions while it still maintains overall results. This way of communication actually builds a good rapport in between the employer and employee because they not only open up to the stakeholders but also those who are working for the company to feel being appreciated and being valued. In this management style, they take in the respond from their subordinates and workers seriously in order to achieve a better workplace environment and productivity of their company. By practicing this management style, it not only improves the productivity of a company or organization but it will also help to identify the problem earlier and easier. And with a good communication with the staff, it can also improve the job satisfaction and benefits staff morale too. Don’t waste time! Our writers will create an original "An Essay on Various Management Styles" essay for you Create order