Total Energy of a System

If the increase in the total energy of a system of N conduction electrons when heated from zero to T is denoted by AU, then... 

The force constants in the equations are adjusted empirically to repro duce experimental observations. The net result is a model which relates the "mechanical" forces within a stmcture to its properties. Force fields are made up of sets of equations each of which represents an element of the decomposition of the total energy of a system (not a quantum mechanical energy, but a classical mechanical one). The sum of the components is called the force field energy, or steric energy, which also routinely includes the electrostatic energy components. Typically, the steric energy is expressed as... 

Filler particle si2e distribution (psd) and shape affect rheology and loading limits of filled compositions and generally are the primary selection criteria. On a theoretical level the influence of particle si2e is understood by contribution to the total energy of a system (2) which can be expressed on a unit volume basis as ... 

Real research studies with Gaussian involve not only larger molecules than the ones we ve generally looked at so far, but also multiple calculations to thoroughly investigate systems of interest. Here is an example procedure that might be used to predict the total energy of a system ... 

The total energy of a system with a given set of positions and velocities is given as the sum of the kinetic and potential energy. 

The Finnis-Sinclair type potentials (Finnis and Sinclair 1984) are central-force potentials but have a many-body character in that the energy of a system of particles is not merely a sum of pair interactions between individual atoms. In this scheme, modified for binary alloys by Ackland and Vitek (1990), the total energy of a system of N atoms is written as... 

Total energy of a system is considered simply as a sum of occupied orbital energies. 

However, from the practical standpoint it appears expedient to use the so-called free energy which, in contrast to entropy, is amenable to measurement in the course of a reaction. The free energy defines a portion of the total energy of a system that can be converted to work at pressure and temperature kept constant. The free energy is... 

The molecular mechanics method, often likened to a ball and spring model of the molecule, represents the total energy of a system of molecules with a set of simple analytical functions representing different interactions between bonded and non-bonded atoms, as shown schematically in Figure 1. 

The total energy of a system involves both enthalpy and entropy. Thus, whichever causes the greater change in overall energy during the reaction will be the one controlling the reaction and determining whether it is exothermic, endothermic, spontaneous, or not spontaneous [11]. 

In thermodynamics, the total energy of a system is given by the sum of the total kinetic and potential energies of the molecules in the system. 

Cohesive energies are defined as the difference between the total energy of a system and the sum of the energies of its components. If there is a rearrangement of the separate component densities when the components are brought together, this distortion must be taken into account. 

The finite lifetime of each excited state is the reflection of a fundamental law of nature - tendency towards minimum total energy of a system. The quantum mechanical system tends to occupy the state in which its total energy would be minimal. However, the transition of an atom to the lowest (ground) state depends on many circumstances (first of all, on the sort of excited configuration, on the presence of external fields, on the character of the matter itself - density of gas, vapours or plasma, etc.). There are two main channels of decay of the excited states radiative and radiationless. In the first case the electronic transition from the higher to the lower state is connected with the radiation of one or several quanta of... 

We cannot measure the total energy of a system all we can do is measure changes in energy. If a system does 15 J of work, it has used up some of its store of energy, and we say that its internal energy has fallen by 15 J. To denote this change, we write AU = —15 J. Throughout thermodynamics, the symbol AX means a difference in a property X ... 

The first law of thermodynamics states that in any process, the total energy of a system and its surroundings remains constant. The second law of thermodynamics says that in any spontaneous process, the total entropy of a system and its surroundings (AStotal = ASSyS + ASsurr) always... 

When the total energy of a system is the sum of the energies from the different degrees of freedom, for example, translation, rotation, vibration, and electronic, then the partition function for a combination of the energy levels is the product of the partition functions for each type. Thus,... 

The total energy of a system is a difficult quantity to measure directly. It is much easier to measure energy changes dE/dT—for example, the number of joules necessary to raise the temperature of one mole of gas by one degree Kelvin. If the gas is kept in a constant volume container, this is called the constant-volume molar heat capacity cv, and equals 3R/2 (independent of temperature) for a monatomic gas. Each possible direction of motion (x,y, or z) contributes RT / 2 to the total energy per mole, or R/2 to the heat capacity. 

In thermodynamics, a system is the matter within a defined region. The matter in the rest of the universe is called the surroundings. The first law of thermodynamics, a mathematical statement of the law of conservation of energy, states that the total energy of a system and its surroundings is a constant ... 

In the early 1990s, Brenner and coworkers [163] developed interaction potentials for model explosives that include realistic chemical reaction steps (i.e., endothermic bond rupture and exothermic product formation) and many-body effects. This potential, called the Reactive Empirical Bond Order (REBO) potential, has been used in molecular dynamics simulations by numerous groups to explore atomic-level details of self-sustained reaction waves propagating through a crystal [163-171], The potential is based on ideas first proposed by Abell [172] and implemented for covalent solids by Tersoff [173]. It introduces many-body effects through modification of the pair-additive attractive term by an empirical bond-order function whose value is dependent on the local atomic environment. The form that has been used in the detonation simulations assumes that the total energy of a system of N atoms is ... 

In classic mechanics, the total energy of a system (Etot) is the sum of its kinetic (Fkln) and potential energy (Epot) ... 

Recall that the canonical equations of classical mechanics can be used to derive the Hamiltonian expression for the total energy of a system from the momenta pk and positional coordinates qk ... 

The first law of thermodynamics states that energy cannot be created or destroyed (i.e., the total energy of a system is always constant). This means that if the internal energy of a reaction increases then there must be a concomitant uptake of energy usually in the form of heat. Enthalpy (H) is a parameter used to describe the energy of a system as heat... 

DFT is based on the proof of Hohenberg and Kohn that the total energy of a system is a function of the electron density only. In order to obtain the ground-state energy of a system one has to determine the ground-state electron distribution. Unfortunately, this is far from trivial. 

The electronic Hamiltonian, equation (6), does not include relativistic effects and hence cannot yield the true total energy of a system. Thus, its contribution to the energy is accounted for in the definition of the correlation error.85... 

The total energy of a system in a QM/MM calculation can be written as the sum of four contributions ... 

Here we derive the theorem for classical systems. The classical laws of motion can be formulated in terms of the Hamiltonian function for the particles in a system, which is defined in terms of the particle positions scalar quantities pt and qi be the entries of the vectors p and q. For a collection of N particles p e 9t3N and q e 9t3N are the collective positions and momenta vectors listing all 3/V entries. The Hamiltonian function is an expression of the total energy of a system ... 

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