Molecular Physics

We review the current status of quantum chemistry as a predictive tool of chemistry and molecular physics, capable of providing highly accurate, quantitative data about molecular systems. We begin by reviewing wave-function based electronic-structure theory, emphasizing the N-electron hierarchy of coupled-cluster theory and the one-electron hierarchy of correlation-consistent basis sets. Following a discussion of the slow basis-set convergence of dynamical correlation and basis-set extrapolations, we consider the methods of explicit correlation, from the early work of Hylleraas in the 1920s to the latest developments in such methods, capable of yielding high-accuracy results in medium-sized basis sets. Next, we consider the small corrections to the electronic energy (high-order virtual excitations, vibrational, relativistic, and diagonal Born-Oppenheimer corrections) needed for high accuracy and conclude with a review of the composite methods and computational protocols of electronic-structure theory.

Phenylhydrazine (PHZ), a potent chemical causes toxicity on various tissues at various levels. Administration of phenylhydrazine mainly causes haematotoxicity which leads to the haemolytic anemia. In mammals PHZ induced anemia increased the iron absorption in spleen, liver and duodenum and finally iron metabolism was altered. Local demand and supply of Fe would increase erythropoeitic activity of the spleen so the size of spleen was increased that create the splenomegaly. PHZ induced anemia activate immune response which triggers phagocytosis in the spleen and liver. Apart from this administration of PHZ interfere the binding of erythropoietin (EPO) with erythropoietin receptors (EPOR) so that JAK-STAT would be affected.PHZ also showed genotoxic effect by creating single strand DNA damage.

In this paper we write down equations of motion (following the approach pioneered by Hoover) for an exact isothermal-isobaric molecular dynamics simulation, and we extend them to multiple thermostating rates, to a shape-vary-ing cell and to molecular systems, ...

Magnetic insulators have proved to be fertile ground for studying new types of quantum many body states, and I survey recent experimental and theoretical examples. The insights and methods transfer also to novel superconducting and metallic states. Of particular interest are critical quantum states, sometimes found at quantum phase transitions, which have gapless excitations with no particle-or wave-like interpretation, and control a significant portion of the finite temperature phase diagram. Remarkably, their theory is connected to holographic descriptions of Hawking radiation from black holes.

Theories based on the coupling between spin fluctuations and fermionic quasiparticles are among the leading contenders to explain the origin of high-temperature superconductivity, but estimates of the strength of this interaction differ widely. Here we analyze the charge- and spin-excitation spectra determined by angle-resolved photoemission and inelastic neutron scattering, respectively, on the same crystals of the high-temperature superconductor YBa2Cu3O6.6. We show that a self-consistent description of both spectra can be obtained by adjusting a single parameter, the spin-fermion coupling constant. In particular, we find a quantitative link between two spectral features that have been established as universal for the cuprates, namely high-energy spin excitations and "kinks" in the fermionic band dispersions along the nodal direction. The superconducting transition temperature computed with this coupling constant exceeds 150 K, demonstrating that spin fluctuations have sufficient strength to mediate high-temperature superconductivity.

It is shown that the nonlinear equations governing the dynamics of the large amplitude waves in a self-gravitating unmagnetized collisionless dust-electron-ion plasma admit stationary dust-acoustic shock solutions. Owing to the adiabaticity of dust-charge variation, inclusion of self-gravitation, and to the departure from the so-called Botzmannian electrons and ions to the trapped electrons and nonthermal ions, the dynamics of the nonlinear wave is found to be governed by a new energy-like integral equation.

Vapour-liquid equilibria (VLE) of the Lennard-Jones potential, truncated and shifted at 2.5σ are studied with molecular dynamics simulation, which is an attractive potential for studying inhomogeneous systems. Comprehensive simulation data is reported for three cases: no interface, planar interface, or spherical interface between the coexisting phases, covering a wide range of temperatures. Spherical droplets are studied also for a range of radii between 5 and 16σ. The size dependence of surface tension and other properties is quantified for spherical interfaces.

We introduce a representative database of 22 α,βto β,γ -enecarbonyl isomerisation energies (to be known as the EIE22 dataset). Accurate reaction energies are obtained at the complete basis-set limit CCSD(T) level by means of the high-level W1-F12 thermochemical protocol. The isomerisation reactions involve a migration of one double bond that breaks the conjugated πsystem. The considered enecarbonyls involve a range of common functional groups (e.g., Me, NH 2 , OMe, F, and CN). Apart from π -conjugation effects, the chemical environments are largely conserved on the two sides of the reactions and therefore the EIE22 data-set allows us to assess the performance of a variety of density functional theory (DFT) procedures for the calculation of π -conjugation stabilisation energies in enecarbonyls. We find that, with few exceptions (M05-2X, M06-2X, BMK, and BH&HLYP), all the conventional DFT procedures attain root mean square deviations (RMSDs) between 5.0 and 11.7 kJ mol −1 . The range-separated and double-hybrid DFT procedures, on the other hand, show good performance with RMSDs below the 'chemical accuracy' threshold. We also examine the performance of composite and standard ab initio procedures. Of these, SCS-MP2 offers the best performance-to-computational cost ratio with an RMSD of 0.8 kJ mol −1 .

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form φ(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v0. Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse-(shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.

Molecular dynamics simulations using classical force fields were carried out to study the structural and transport properties of clay mineral−water−CO 2 systems at pressure and temperature relevant to geological carbon storage. The simulations show that the degree of swelling caused by intercalation of CO 2 strongly depends on the initial water content in the interlayer space and that CO 2 intercalation stimulates inner-sphere adsorption of the positively charged interlayer ions on the internal clay surfaces, which modifies the wetting properties of the surfaces. DFT-based molecular dynamics simulations were used to interpret the origin of the observed shift in the asymmetric stretch vibration of CO 2 trapped in montmorillonite. The origin of the shift is attributed to the electric field effects on the CO 2 molecules induced by the water molecules.

High temperature superconductivity emerges in the cuprate compounds upon changing the electron density of an insulator in which the electron spins are antiferromagnetically ordered. A key characteristic of the superconductor is that electrons can be extracted from them at zero energy only if their momenta take one of four specific values (the `nodal points'). A central enigma has been the evolution of the zero energy electrons in the metallic state between the antiferromagnet and the superconductor, and recent experiments yield apparently contradictory results. The oscillation of the resistance in this metal as a function of magnetic field indicate that the zero energy electrons carry momenta which lie on elliptical `Fermi pockets', while ejection of electrons by high intensity light indicates that the zero energy electrons have momenta only along arc-like regions. We present a theory of new states of matter, which we call `algebraic charge liquids', which arise naturally between the antiferromagnet and the superconductor, and reconcile these observations. Our theory also explains a puzzling dependence of the density of superconducting electrons on the total electron density, and makes a number of unique predictions for future experiments.

Although the classical picture of crystallization depicts a simple and immediate transformation from an amorphous to a crystalline phase, it has been argued that, in selected systems, intermediate metastable phases exist before a stable state is finally reached. However, most experimental observations have been limited to colloids and proteins, for which the crystallization kinetics are fairly slow and the size is comparatively large. Here, we demonstrate for the first time in an inorganic compound at an atomic scale that an amorphous phase transforms into a stable crystalline state via intermediate crystalline phases, thus directly proving Ostwald's rule of stages. Through in situ high-resolution electron microscopy in real time at a high temperature, we show the presence of metastable transient phases at an atomic scale during the crystallization of an olivine-type metal phosphate. These results suggest a new description for the kinetic pathway of crystallization in complex inorganic systems.

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form $\phi(r)$ and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v 0. Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.

In the present work, we have studied the spatial evolution of the aluminum plasma produced by the fundamental (1064 nm), second (532 nm) and third (355 nm) harmonics of a Q-switched pulsed Nd:YAG laser. The experimentally observed line profiles of neutral aluminum have been used to extract the excitation temperature using Boltzmann plot method whereas the electron number density has been determined from the Stark broadened profiles. Besides we have studied the variation of excitation temperature and electron number density as a function of laser irradiance at atmospheric pressure. In addition, we have performed quantitative analysis of photon absorption and vapor ionization mechanism at three laser wavelengths and estimated the inverse bremsstrahlung (IB) absorption and photoionization (PI) coefficients. The validity of the assumption of local thermodynamic equilibrium is discussed in the light of the experimental results.

Entanglement-based technologies, such as quantum information processing, quantum simulations, and quantum-enhanced metrology, have the potential to revolutionise our way of computing and measuring and help clarifying the puzzling concept of entanglement itself. Ultracold atoms on atom chips are attractive for their implementation, as they provide control over quantum systems in compact, robust, and scalable setups. An important tool in this system is a potential depending on the internal atomic state. Coherent dynamics in this potential combined with collisional interactions allows entanglement generation both for individual atoms and ensembles. Here, we demonstrate coherent manipulation of Bose-condensed atoms in such a potential, generated in a novel way with microwave near-fields on an atom chip. We reversibly entangle atomic internal and motional states, realizing a trapped-atom interferometer with internal-state labelling. Our system provides control over collisions in mesoscopic condensates, paving the way for on-chip generation of many-particle entanglement and quantum-enhanced metrology with spin-squeezed states.

In this research paper, the authors have studied the properties of ion-acoustic solitons and double-layers in a plasma consisting of warm positive and negative ions with different concentration of masses, charged states and non-thermal electrons using small amplitude approximation. Reductive perturbation method is used to derive KdV and m-KdV equations. Existence of ion-acoustic solitons and double-layer is explored over a wide range of parameter space. The role of non-thermal electrons characterized by finite $\beta$ is investigated. It is observed that for a particular value of $\beta$ , there is a transition from compressive to rarefactive solitons. However, when $\beta$ is increased beyond a critical value, no double-layers are obtained. The significance of relative ion masses is also investigated.

Quantum computation promises to solve fundamental, yet otherwise intractable, problems across a range of active fields of research. Recently, universal quantum logic-gate sets-the elemental building blocks for a quantum computer-have been demonstrated in several physical architectures. A serious obstacle to a full-scale implementation is the large number of these gates required to build even small quantum circuits. Here, we present and demonstrate a general technique that harnesses multi-level information carriers to significantly reduce this number, enabling the construction of key quantum circuits with existing technology. We present implementations of two key quantum circuits: the three-qubit Toffoli gate and the general two-qubit controlled-unitary gate. Although our experiment is carried out in a photonic architecture, the technique is independent of the particular physical encoding of quantum information, and has the potential for wider application.

The elastic energy for many biopolymer systems is comparable to the thermal energy at room temperature. Therefore, biopolymers and their networks are constantly under thermal fluctuations. From the point of view of thermodynamics, this suggests that entropy plays a crucial role in determining the mechanical behaviors of these filamentous biopolymers. One of the main goals of this thesis is to understand how thermal fluctuations affect the mechanical properties and behaviors of filamentous networks, and also how stress affects the thermal fluctuations.

A force field has been developed to describe the phase behaviour, interfacial, and transport properties of nitrogen and hydrocarbon mixtures under conditions relevant to those found in the high pressure extraction of oil from underground reservoirs. A Gibbs ensemble Monte Carlo method is used to parametrize intermolecular potentials for the pure components by matching experimental and simulated liquid and vapour coexisting densities. Also the surface tension, diffusion coefficient and shear viscosity of nitrogen and its mixtures with butane have been determined. The latter properties were obtained by canonical molecular dynamics simulations. The diffusion coefficient and shear viscosity were calculated by a Green-Kubo method. Results for pure nitrogen are given for temperatures ranging from 70K to llOK.

We illustrate the capability of the complete active space self-consistent field method by Roos and co-workers for calculations of triplet state properties. We report phosphorescence lifetimes, zero-field splitting parameters, and nuclear quadrupole coupling constants for the lowest triplet state of a variety of benzene derivatives.

The output power of any laser system is limited by the power that any of its individual components can withstand without being destroyed. This increases the size, complexity and cost of next-generation lasers built using conventional optical-gain media. But by using a plasma, which is impervious to optical damage, as the gain medium, such limitations could be significantly surpassed. Here, we report the use of stimulated Raman backscattering in a millimetre-scale plasma to simultaneously amplify and compress an input pulse to increase its intensity by more than two orders of magnitude. Further amplification and compression of such a pulse was achieved by passing it twice through our system, an approach that could be readily extended in future with a cavity-like multipass design. Such an approach could enable the construction of a new generation of compact, low-cost ultrahigh-intensity laser systems.

A description of the ab initio quantum chemistry package GAMESS-UK is presented. The package offers a wide range of quantum mechanical wavefunctions, capable of treating systems ranging from closed-shell molecules through to the species involved in complex reaction mechanisms. The availability of a wide variety of correlation methods provides the necessary functionality to tackle a number of chemically important tasks, ranging from geometry optimization and transition-state location to the treatment of solvation effects and the prediction of excited state spectra. With the availability of relativistic ECPs and the development of ZORA, such calculations may be performed on the entire Periodic including the lanthanides. Emphasis is given to the DFT module, which has been extensively developed in recent years, and a number of other, novel features of the program. The parallelization strategy used in the program is outlined, and detailed speedup results are given. Applications of the code in the areas of enzyme and zeolite catalysis and in spectroscopy are described.

A new four-dimensional, hyperchaotic dynamic system, based on Lorenz dynamics, is presented. Besides, the most representative dynamics which may be found in this new system are located in the phase space and are analyzed here. The new system is especially designed to improve the complexity of Lorenz dynamics, which, despite being a paradigm to understand the chaotic dissipative flows, is a very simple example and shows great vulnerability when used in secure communications. Here, we demonstrate the vulnerability of the Lorenz system in a general way. The proposed 4D system increases the complexity of the Lorenz dynamics. The trajectories of the novel system include structures going from chaos to hyperchaos and chaotic-transient solutions. The symmetry and the stability of the proposed system are also studied. First return maps, Poincaré sections, and bifurcation diagrams allow characterizing the global system behavior and locating some coexisting structures. Numerical results about the first return maps, Poincaré cross sections, Lyapunov spectrum, and Kaplan-Yorke dimension demonstrate the complexity of the proposed equations.

Theoretical and numerical investigations are carried out for the amplitude modulation of dust-ion acoustic waves (DIAW) propagating in an unmagnetized weakly coupled collisionless fully ionized plasma consisting of isothermal electrons, warm ions and charged dust grains. Modulation oblique (by an angle $\theta$ ) to the carrier wave propagation direction is considered. The stability analysis, based on a nonlinear Schrödinger-type equation (NLSE), exhibits a sensitivity of the instability region to the modulation angle $\theta$ , the dust concentration and the ion temperature. It is found that the ion temperature may strongly modify the wave’s stability profile, in qualitative agreement with previous results, obtained for an electron-ion plasma. The effect of the ion temperature on the formation of DIAW envelope excitations (envelope solitons) is also discussed.

There is a need to develop alternate energy sources in the coming century because fossil fuels will become depleted and their use may lead to global climate change. Inertial fusion can become such an energy source, but significant progress must be made before its promise is realized. The high-density approach to inertial fusion suggested by Nuckolls et al. leads reaction chambers compatible with civilian power production. Methods to achieve the good control of hydrodynamic stability and implosion symmetry required to achieve these high fuel densities will be discussed. Fast Ignition, a technique that achieves fusion ignition by igniting fusion fuel after it is assembled, will be described along with its gain curves. Fusion costs of energy for conventional hotspot ignition will be compared with those of Fast Ignition and their capital costs compared with advanced fission plants. Finally, techniques that may improve possible Fast Ignition gains by an order of magnitude and reduce driver scales by an order of magnitude below conventional ignition requirements are described.

We extend the osmotic ensemble Monte Carlo (OEMC) molecular simulation method (Moucǩa et al. J. Phys Chem. B 2011, 115, 7849−7861) for directly calculating the aqueous solubility of electrolytes and for calculating their chemical potentials as functions of concentration to cases involving electrolyte hydrates and mixed electrolytes, including invariant points involving simultaneous precipitation of several solutes. The method utilizes a particular semigrand canonical ensemble, which performs simulations of the solution at a fixed number of solvent molecules, pressure, temperature, and specified overall electrolyte chemical potential. It avoids calculations for the solid phase, incorporating available solid chemical potential data from thermochemical tables, which are based on well-defined reference states, or from other sources. We apply the method to a range of alkali halides in water and to selected examples involving LiCl monohydrate, mixed electrolyte solutions involving water and hydrochloric acid, and invariant points in these solvents. The method uses several existing force-field models from the literature, and the results are compared with experiment. The calculated results agree qualitatively well with the experimental trends and are of reasonable accuracy. The accuracy of the calculated solubility is highly dependent on the solid chemical potential value and also on the force-field model used. Our results indicate that pairwise additive effective force-field models developed for the solution phase are unlikely to also be good models for the corresponding crystalline solid. We find that, in our OEMC simulations, each ionic force-field model is characterized by a limiting value of the total solution chemical potential and a corresponding aqueous concentration. For higher values of the imposed chemical potential, the solid phase in the simulation grows in size without limit. t of the remaining species are fixed. An example is an aqueous solution of s ions with a fixed

A theory of 4-component direct SCF calculations is presented using a quaternion formulation of the Dirac±Fock equations. Screening of integral batches is supplemented with screening on individual integrals and with separate screening of Coulomb and exchange contributions to the Fock matrix. The direct SCF method is applied to study bonding in caesium auride. The caesium±gold bond is found to be highly ionic, with gold present as the anion. A relativistic bond contraction of 41 pm is observed.

The transfer of spin angular momentum from a spin-polarized current to a ferromagnet can generate sufficient torque to reorient the magnet’s moment. This torque could enable the development of efficient electrically actuated magnetic memories and nanoscale microwave oscillators. Yet difficulties in making quantitative measurements of the spin-torque vector have hampered understanding. Here we present direct measurements of both the magnitude

We report on a delayed-choice quantum eraser experiment based on a two-photon imaging scheme using entangled photon pairs. After the detection of a photon which passed through a double-slit, a random delayed choice is made to erase or not erase the which-path information by the measurement of its distant entangled twin; the particle-like and wave-like behavior of the photon are then recorded simultaneously and respectively by only one set of joint detection devices. The present eraser takes advantage of two-photon imaging. The complete which-path information of a photon is transferred to its distant entangled twin through a “ghost" image. The choice is made on the Fourier transform plane of the ghost image between reading “complete information" or “partial information" of the double-path.

The frequency-dependent interaction induced polarizabilities and second hyperpolarizabilities are calculated for He 2 at the coupled cluster singles and doubles and full configuration interaction levels and for Ar 2 at the coupled cluster singles and doubles level. The frequency-dependence is approximated by a power series to second-order in the frequency arguments using Cauchy moments and hyperpolarizability dispersion coefficients. Using large correlation consistent basis sets, results close to the basis set limit are obtained. The computed curves for the interaction induced ͑hyper-͒ polarizabilities are tabulated for a range of internuclear distances. The data are employed in a companion paper to make for the first time a direct comparison between the experimentally determined pressure dependence of an ESHG hyperpolarizability and ab initio calculated hyperpolarizability second virial coefficients.

Molecular Dynamics (MD) simulations were carried out to study the hydrate structure and diffusion of water and cations in the clay interlayer region. The goal of this work was to examine the mechanisms by which the clay counterions influence the swelling and dispersion of shale. Three series of MD simulations were performed to study Wyoming montmorillonites containing either Na + , K + or Li + counterions and 100, 200 or 300 mg of adsorbed water per gram of clay. Here the TIP4P interaction model for liquid water is used in the MD simulations. The TIP4P results are compared with simulations using the MCY interaction model, particularly for the K-clay hydrates.

Magnetic reconnection releases energy explosively as field lines break and reconnect in plasmas ranging from the Earth's magnetosphere to solar eruptions and astrophysical applications. Collisionless kinetic simulations have shown that this process involves both ion and electron kinetic-scale features, with electron current layers forming nonlinearly during the onset phase and playing an important role in enabling field lines to break 1-4 . In larger two-dimensional studies, these electron current layers become highly extended, which can trigger the formation of secondary magnetic islands 5-10 , but the influence of realistic three-dimensional dynamics remains poorly understood. Here we show that, for the most common type of reconnection layer with a finite guide field, the three-dimensional evolution is dominated by the formation and interaction of helical magnetic structures known as flux ropes. In contrast to previous theories 11 , the majority of flux ropes are produced by secondary instabilities within the electron layers. New flux ropes spontaneously appear within these layers, leading to a turbulent evolution where electron physics plays a central role.

Q uantum teleportation 1 , a way to transfer the state of a quantum system from one location to another, is central to quantum communication 2 and plays an important role in a number of quantum computation protocols 3-5 . Previous experimental demonstrations have been implemented with single photonic 6-11 or ionic qubits 12,13 . However, teleportation of single qubits is insufficient for a large-scale realization of quantum communication and computation 2-5 . Here, we present the experimental realization of quantum teleportation of a twoqubit composite system. In the experiment, we develop and exploit a six-photon interferometer to teleport an arbitrary polarization state of two photons. The observed teleportation fidelities for different initial states are all well beyond the state estimation limit of 0.40 for a two-qubit system 14 . Not only does our six-photon interferometer provide an important step towards teleportation of a complex system, it will also enable future experimental investigations on a number of fundamental quantum communication and computation protocols 3,15-18 .

A new algorithm to compute the virial coe cients of multicomponent mixtures is proposed. The number of graphs that must be evaluated increases dramatically in a multicomponent mixture so that it becomes di cult to enumerate and compute all possible graphs. However, once all of them are known and evaluated, the virial coe cient of the mixture can be evaluated for any composition. If one is interested in the virial coe cient of a mixture of a certain composition, then a simpler approach can be followed. Starting from the graphs of a purē uid, we assign a random chemical identity to each of the molecules of the graph. The probability of assigning a given chemical identity is taken from the composition of the mixture. In this way composition is treated as a random variable within the Monte Carlo procedure which determines the virial coe cient. The algorithm is checked by comparison with the virial coe cients of binary hard spheres mixtures which are well known. Good agreement is found. The procedure is then extended to multicomponent mixtures of hard spheres. Finally the procedure is applied to the determination of the virial coe cients of a¯exible molecule. For¯exible molecules the possible con® gurations of the molecules are treated as di erent components of the mixture. In this way we present what appears to be the ® rst determination of the third and fourth virial coe cients of polymers in the continuum.

Relativistic energy corrections which arise from the use of the Dirac±Coulomb Hamiltonian, and the Gaunt and Breit interaction operators, plus Lamb-shift e ects have been determined for the global minima of the ground electronic states of C 2 H 6 , NH 3 , H 2 O, [H,C,N], HNCO, HCOOH, SiC 2 , SiH ¡ 3 , and H 2 S, and for barrier characteristics for these molecular systems (inversion barrier of NH 3 and SiH ¡ 3 , barrier to linearity of H 2 O, H 2 S, and HNCO, rotational barrier of C 2 H 6 , di erence between conformations of HCOOH (Z=E) and SiC 2 (linear/Tshaped), and isomerization barrier of HCN/HNC). The relativistic calculations performed at the Hartree±Fock and the highly correlated CCSD(T) levels employed a wide variety of basis sets. Comparison of the perturbational and the four-component fully variational results indicate that the Coulomb±Pauli Hamiltonian and the lowest order Hamiltonian of direct perturbation theory (DPT(2)) are highly successful for treating the relativistic energy e ects in light molecular systems both at a single point on the potential energy hypersurface and along the surface. Electron correlation contributions to the relativistic corrections are relatively small for the systems studied, and are comparable with the 2-electron Darwin correction. Corrections beyond the Dirac±Coulomb treatment are usually rather small, but may become important for high accuracy ab initio calculations.