Significant Energy Differences Research Articles

Studies on synthesis and influence of sterically driven Ni(II)-terpyridine (NNN) complexes on BSA/DNA binding and anticancer activity

The present work demonstrates the synthesis, structural diversity and coordination behavior of some selected new Ni(II)-Tpy complexes. The structural analysis revealed the coordination of the selected terpyridine ligands with the core metal atom in two different modes via dimeric species (1:1 fashion) through the Cl-bridging and a bis(Tpy)-Ni complex (2:1 fashion). Perhaps the most striking manifestations of these Ni(II)-Tpy complexes are BSA/DNA binding ability and anticancer activity. In addition, the cytotoxicity studies of Tpy ligand (4-([2,2′:6′,2″-terpyridin]-4′-yl)phenyl 5-methylthiophene-2-carboxylate) and the Ni(II) complexes were carried out using lung cancer cell line (A549), breast cancer cell line (MCF-7) and normal cell line (Vero cell). The cytotoxicity results were compared with the cisplatin control group. Notably, bis-terpyridyl complex 3C (R = 4-([2,2′:6′,2″-terpyridin]-4′-yl)phenyl 4-isopropoxybenzoate) demonstrates better activity with the IC50 value of 23.13 ± 3 μm for A549 and 22.7 ± 3 for MCF-7. The DFT calculations reveal the significant energy differences of HOMO and LUMO for the ligands and their corresponding Ni(II) complexes. The Tpy ligands and Ni(II)-Tpy complexes were investigated for BSA binding and further all the Ni(II) complexes were analyzed for DNA binding studies.

The Role of the CuCl Active Complex in the Stereoselectivity of the Salt-Induced Peptide Formation Reaction: Insights from Density Functional Theory Calculations.

The salt-induced peptide formation (SIPF) reaction is a prebiotically plausible mechanism for the spontaneous polymerization of amino acids into peptides on early Earth. Experimental investigations of the SIPF reaction have found that in certain conditions, the l enantiomer is more reactive than the d enantiomer, indicating its potential role in the rise of biohomochirality. Previous work hypothesized that the distortion of the CuCl active complex toward a tetrahedral-like structure increases the central chirality on the Cu ion, which amplifies the inherent parity-violating energy differences between l- and d-amino acid enantiomers, leading to stereoselectivity. Computational evaluations of this theory have been limited to the protonated-neutral l + l forms of the CuCl active complex. Here, density functional theory methods were used to compare the energies and geometries of the homochiral (l + l and d + d) and heterochiral (l + d) CuCl-amino acid complexes for both the positive-neutral and neutral-neutral forms for alanine, valine, and proline. Significant energy differences were not observed between different chiral active complexes (i.e., d + d, l + l vs. l + d), and the distortions of active complexes between stereoselective systems and non-selective systems were not consistent, indicating that the geometry of the active complex is not the primary driver of the observed stereoselectivity of the SIPF reaction.

Diastereoselective Rotaxane Synthesis with Pillar[5]arenes via Co-crystallization and Solid-State Mechanochemical Processes.

Chiral rotaxanes have attracted much attention in recent decades for their unique chirality based on their interlocked structures. Thus, selective synthesis methods of chiral rotaxanes have been developed. The introduction of substituents with chiral centers to produce diastereomers is a powerful strategy for the construction of chiral rotaxanes. However, in case of a small energy difference between the diastereomers, diastereoselective synthesis is extremely difficult. Herein, we report a new diastereoselective rotaxane synthesis method using solid-phase diastereoselective [3]pseudorotaxane formation and mechanochemical solid-phase end-capping reactions of the [3]pseudorotaxanes. By co-crystallization of stereodynamic planar chiral pillar[5]arene with stereogenic carbons at both rims and axles with suitable end groups and lengths, the [3]pseudorotaxane with a high diastereomeric excess (ca. 92% de) was generated in the solid state because of higher effective molarity with aid by packing effects and significant energy differences between [3]pseudorotaxane diastereomers. In contrast, the de of the pillar[5]arene was low in solution (ca. 10% de) because of a small energy difference between diastereomers. Subsequent end-capping reactions of the polycrystalline [3]pseudorotaxane with high de in solvent-free conditions successfully yielded rotaxanes while maintaining the high de generated by the co-crystallization.

How the Choice of Force-Field Affects the Stability and Self-Assembly Process of Supramolecular CTA Fibers.

In recent years, computational methods have become an essential element of studies focusing on the self-assembly process. Although they provide unique insights, they face challenges, from which two are the most often mentioned in the literature: the temporal and spatial scale of the self-assembly. A less often mentioned issue, but not less important, is the choice of the force-field. The repetitive nature of the supramolecular structure results in many similar interactions. Consequently, even a small deviation in these interactions can lead to significant energy differences in the whole structure. However, studies comparing different force-fields for self-assembling systems are scarce. In this article, we compare molecular dynamics simulations for trifold hydrogen-bonded fibers performed with different force-fields, namely GROMOS, CHARMM General Force Field (CGenFF), CHARMM Drude, General Amber Force-Field (GAFF), Martini, and polarized Martini. Briefly, we tested the force-fields by simulating: (i) spontaneous self-assembly (none form a fiber within 500 ns), (ii) stability of the fiber (observed for CHARMM Drude, GAFF, MartiniP), (iii) dimerization (observed for GROMOS, GAFF, and MartiniP), and (iv) oligomerization (observed for CHARMM Drude and MartiniP). This system shows that knowledge of the force-field behavior regarding interactions in oligomer and larger self-assembled structures is crucial for designing efficient simulation protocols for self-assembling systems.

Importance of thorough conformational analysis in modelling transition metal-mediated reactions: Case studies on pincer complexes containing phosphine groups

Advances in processing capabilities of computer clusters have allowed for the full modeling of organometallic complexes that previously would have been simplified to reduce computational cost. Increased feasibility of computational modeling offers new challenges, not only in terms of limitations of methods and theory, but attention should be paid to complexes that can exist in many conformations, as the appropriate choice of conformer may be easily overlooked. In this work a series of pincer complexes with isopropyl and cyclopentyl substituents have been chosen as examples to demonstrate the importance of conformational analysis. The complexes examined contain four isopropyl or cyclopentyl groups on phosphor atoms generating between 27 and 324 possible rotamers. The importance of conformational search in a mechanistic investigation is demonstrated with the CO2 insertion into a nickel hydride bond of POCOP iPr nickel hydride complex. Results show that the reaction energy profile can be both exergonic and endergonic depending on rotamer choice. Specifically, the POCOPiPr Ni-formato complex product of the CO2 insertion reaction had an energy difference between the lowest and highest energy rotamer as high as 16.8 kcal/mol. The significant energy differences between rotamers highlight the importance of thorough conformational analysis and should be taken into consideration when evaluating the energy profile of related reactions.

Chirality selective spin interactions mediated by the moving superconducting condensate

We show that superconducting correlations in the presence of non-zero condensate velocity can mediate the peculiar interaction between localized spins that breaks the global inversion symmetry of magnetic moments. The proposed interaction mechanism is capable of removing fundamental degeneracies between topologically distinct magnetic textures. For the generic system of three magnetic impurities in the current-carrying superconductor we find the energy term proportional to spin chirality. In realistic superconductor/ferromagnetic/superconductor setups we reveal significant energy differences between various magnetic textures with opposite chiralities. We calculate Josephson energies of junctions through left and right-handed magnetic helices as well as through the magnetic skyrmions with opposite topological charges. Relative energy shifts between otherwise degenerate magnetic textures in these setups are regulated by the externally controlled Josephson phase difference. The suggested low-dissipative manipulation with the skyrmion position in a racetrack geometry can be used for the advanced spintronics applications.

The Effects of Heel Height on Head Position, Long-Term Average Spectra, and Perceptions of Female Singers

Female singers often wear high heels for auditions and performances. Heel height research in non-singing contexts indicates that wearing heels can affect body alignment and head position. Studies in orthodontics, sleep apnea, and voice science suggest that head and neck positioning can alter the vocal tract. The purpose of this study was to assess the effects, if any, of heel height (barefoot, 10.16-cm stilettos) on three angles of singer head position (calculated from C7-tragus-nasion), long-term average spectra data, and perceptual data (questionnaire) acquired from female (N = 30) soloists during alternating periods of silence and singing. Results indicated that all participants (100%) significantly decreased head position angle measurements (inferior and posterior head and neck movement) when singing in high heels compared with singing barefoot. Participants, on average, significantly increased head position angle measurements (superior and anterior head and neck movement) when singing compared with standing silently, and did so to a greater degree when transitioning from silent heels to singing heels compared with transitioning from silent barefoot to singing barefoot. Long-term average spectra data indicated significant spectral energy differences between barefoot and high heel singing conditions across participants. Most participants (n= 21, 70.00%) indicated they felt comfortable and sang their best while barefoot. Results of this study, the second in a series of experiments addressing the effects of shoe heel height on female singers' vocal production, were discussed in terms of application to vocal pedagogy and directions for future research.

Long-Range Order in [(SnSe)1.2]1[TiSe2]1 Prepared from Designed Precursors.

Self-assembly of designed precursors has enabled the synthesis of novel heterostructures that exhibit extensive rotational disorder between constituents. In (SnSe)1.2TiSe2 nanoscale regions of long-range order were observed in scanning transmission electron microscopy (STEM) cross sectional images. Here a combination of techniques are used to determine the structure of this compound, and the information is used to infer the origin of the order. In-plane X-ray diffraction indicates that the SnSe basal plane distorts to match TiSe2. This results in a rectangular unit cell that deviates from both the bulk structure and the square in-plane unit cell previously observed in heterostructures containing SnSe bilayers separated by layers of dichalcogenides. The distortion results from lattice matching of the two constituents, which occurs along the <100> SnSe and the <110> TiSe2 directions as √3 × aTiSe2 equals aSnSe. Fast Fourier transform analysis of the STEM images exhibits sharp maxima in hkl families where h,k ≠ 0. The period is the same as that observed for 00l reflections, indicating regions of long-range superlattice order in all directions. X-ray reciprocal space maps contain broad maxima in hkl families of TiSe2 and SnSe based reflections consistent with the superlattice period, indicating that long-range order is present throughout a significant fraction of the film. The STEM images show that <110> planes of TiSe2 are adjacent to <100> planes of SnSe. Density functional theory suggests the preferred orientation is due to favored directions of nucleation with significant energy differences between islands of SnSe with different orientation relative to TiSe2. The calculations suggest that the long-range order in (SnSe)1.2TiSe2 results from an accidental coincidence in the lattice parameters of SnSe and TiSe2. These findings support a layer by layer nucleation process for the self-assembly of heterostructures from designed precursors, which rationalizes how designed precursors enable compounds with different constituents, defined thicknesses, and specific layer sequences to be prepared.

What interactions can distort the orientational distribution of interfacial water molecules as probed by second harmonic and sum frequency generation?

Aqueous interfaces are omnipresent in nature. Nonlinear optical methods such as second harmonic and sum frequency generation (SHG/SFG) are valuable techniques to access molecular level information from these interfaces. In the interpretation of SHG and SFG data for both scattering and reflection mode experiments, the relation between the second-order hyperpolarizability tensor β(2), a molecular property, and the surface second-order susceptibility χ(2), a surface averaged property, plays a central role. To correctly describe the molecular details of the interface, it needs to be determined how molecules are oriented, and what the influence is of interfacial electrostatic fields and H-bonding on the orientational distribution. Here, we revisit the relations between β(2) and χ(2) and show, by means of a Boltzmann average, that significant energy differences are needed to generate measurable changes in the molecular orientational distribution at the interface. In practice, H-bonding and surface pressure such as applied in a Langmuir trough can be strong enough to alter the shape of the orientational distribution function of water. In contrast, electrostatic fields, such as those present in the Stern layer, will not have a significant impact on the shape of the orientational distribution function of water molecules.

Atomistic modeling of crystal structure of Ca1.67SiHx

The atomic structure of calcium-silicate-hydrate (C1.67-S-Hx) has been investigated by theoretical methods in order to establish a better insight into its structure. Three models for C-S-H all derived from tobermorite are proposed and a large number of structures were created within each model by making a random distribution of silica oligomers of different size within each structure. These structures were subjected to structural relaxation by geometry optimization and molecular dynamics steps. That resulted in a set of energies within each model. Despite an energy distribution between individual structures within each model, significant energy differences are observed between the three models. The C-S-H model related to the lowest energy is considered as the most probable. It turns out to be characterized by the distribution of dimeric and pentameric silicates and the absence of monomers. This model has mass density which is closest to the experimental one.

Pu@C24: A New Example Satisfying the 32-Electron Principle

A transition in point group symmetry from C2 to D6d in the classical cage isomer of C24 cluster is observed after encapsulation of a plutonium atom within it. This encapsulation leads to highly stable Pu@C24 cluster, which is well supported by the structural, energetic, and thermodynamic aspects. This study has been carried out with first five low-lying isomers of C24 fullerene, among which one is classical fullerene consisting of only five- and six-membered rings (MR) and remaining four isomers are nonclassical fullerene consisting of five and six MR along with varying number of four MR. The structural and stability aspects are investigated extensively for the Pu@C24 cluster. For the purpose of comparison we have also considered some other lanthanides/actinides with 8 valence electrons (Cm2+, Sm, and Gd2+) and investigated the encapsulation process into different C24 isomers. It has been found that the Pu@C24 cluster is the most stable one among all the metallofullerenes considered here. For Pu@C24, it has been observed that HOMO–LUMO gap is changed from 1.83 to 3.26 eV after encapsulation of a Pu atom into the bare classical C24 cage. It is interesting to note that the bare C24 nonclassical (C2 symmetry) cluster is the most stable one; however, after encapsulation, the classical isomer becomes the most stable with significant energy differences. The detail vibrational and electronic spectral studies have also been carried out for the classical Pu@C24 metallofullerene. High HOMO–LUMO gaps and positive binding energy values for the Pu@C24 clusters and negatives values of reaction enthalpy and free energy corresponding to the encapsulation process indicate toward possible formation of Pu@C24 and subsequent experimental detection. High stability of the Pu@C24 cluster can be rationalized through the fulfilment of 32 valence electron count corresponding to the fully occupied spdf shells for the central metal atom.

A computational study of the insertion of Li, Na, and Mg atoms into Si(111) nanosheets

Based on first principles calculations, we study the interaction of metal atoms (Li, Na, and Mg) with Si(111) nanosheets of different thicknesses. We show that the chemistry of the interactions is sensitive to both the nanosheet thickness and the dopant–surface distance. Both Li and Na atoms adsorb strongly on the nanosheet surface, accompanied by large charge transfers (∼0.9e) from the metal atoms to surrounding atoms. In contrast, Mg atoms have weak adsorption. Compared to bulk Si, we show that nanosheet Si is expected to improve the charge/discharge rate of Li/Na/Mg-ion batteries. Nevertheless, due to large insertion barriers (up to the prohibitive ∼2.1 and ∼3.1eV for Mg and Na, respectively) and significant energy differences between surface and sub-surface sites (∼1.0 and ∼1.9eV for Mg and Na, respectively), the theoretical capacities of Si for both Na-ion and Mg-ion batteries cannot be achieved at realistic charge/discharge rates.

Commercially prepared single serving meals as lunch meal replacements produce energy deficit and weight loss

Replacing conventional meals with portion‐controlled meals is an effective component of a weight loss program. However, little is known about the efficacy of meal replacements outside the context of a weight loss diet. The purpose of this study was to test the efficacy of replacing participants’ typical cafeteria or restaurant lunch with a prepared single serving meal, with no additional dietary intervention. Thirty five participants (ages 20–55 years, BMI 27–37) consumed their usual lunch at the cafeteria or restaurant. Energy composition of the lunch was determined using the duplicate plate method. For 30 days thereafter participants replaced their typical lunch with a frozen or shelf stable single serving meal. Compared to baseline, daily energy intake decreased by 374 kcal/d (2010 ± 550 vs. 1636 ± 463 kcal/d, p &lt; 0.01), with the decrease occurring primarily at lunch (−443 kcal, 766 ± 250 vs. 323 ± 69 kcal, p&lt;0.001). No significant (p &gt; 0.05) energy differences were observed at pre vs. post breakfast (−40 kcal, 286 ± 158 vs. 327 ± 183 kcal), dinner (+33 kcal, 704 ± 281 vs. 737 ± 338 kcal) and snacks (+30 kcal, 234 ± 246 vs. 264 ± 266 kcal). Resulting weight loss was 2.8 pounds (p&lt;0.01). This study demonstrates that lunch meal replacement with prepared single serving meals, not part of an overall weight loss program, is an effective method to produce energy deficit resulting in weight loss over 30 days.Supported by ConAgra Foods

On relativistic shifts of negative-ion resonances

Results from a Dirac approach to electron- (neutral) atom resonance calculations are compared with those from nonrelativistic ones. A recently developed amplitude-phase method for the Dirac equations that is valid also in the non-relativistic limit is applied. The main conclusion is that significant energy differences are expected for long-lived resonances.

Effect of epitaxial strain on the cation distribution in spinel ferrites CoFe2O4 and NiFe2O4: A density functional theory study

The effect of epitaxial strain on the cation distribution in spinel ferrites CoFe2O4 and NiFe2O4 is investigated by GGA+U total energy calculations. We obtain a very strong (moderate) tendency for cation inversion in NiFe2O4 (CoFe2O4), in agreement with experimental bulk studies. This preference for the inverse spinel structure is reduced by tensile epitaxial strain, which can lead to strong sensitivity of the cation distribution on specific growth conditions in thin films. Furthermore, we obtain significant energy differences between different cation arrangements with the same degree of inversion, providing further evidence for recently proposed short range B site order in NiFe2O4.

The crystal structure of an esterase from the hyperthermophilic microorganism Pyrobaculum calidifontis VA1 explains its enantioselectivity

The highly thermostable esterase from the hyperthermophilic archaeon Pyrobaculum calidifontis VA1 (PestE) shows high enantioselectivity (E > 100) in the kinetic resolution of racemic chiral carboxylic acids, but little selectivity towards acetates of tertiary alcohols (E = 2-4). To explain these unique properties, its crystal structure has been determined at 2.0 Å resolution. The enzyme is a member of the hormone-sensitive lipase group (group H) of the esterase/lipase superfamily on the basis of the amino acid sequence identity. The PestE structure shows a canonical α/β-hydrolase fold as core domain with a cap structure at the C-terminal end of the β-sheet. A tetramer in the crystal packing is formed of two dimers; the dimeric form is observed in solution. Conserved dimers and even tetramers are found in other group H proteins. The amino acid residues Ser157, His284, and Asp254 form the catalytic triad, which is typically found in α/β-hydrolases. The oxyanion hole is composed of Gly85 and Gly86 within the conserved sequence motif HGGG(M,F,W) (amino acid residues 83-87) and Ala158. With the elucidated structure, experimental results about enantioselectivity towards the two model substrate classes (as exemplified for 3-phenylbutanoic acid ethyl ester and 1,1,1-trifluoro-2-phenylbut-3-yn-2-yl acetate) could be explained by molecular modeling. For both enantiomers of the tertiary alcohol, orientations in two binding pockets were obtained without significant energy differences corresponding to the observed low enantioselectivity due to missing steric repulsions. In contrast, for the carboxylic acid ester, two different orientations with significant energy differences for each enantiomer were found matching the high E values.

Stability and Conformation of Polycopper−Thiolate Clusters Studied by Density Functional Approach

Quantum chemical studies of biologically relevant copper thiolate clusters can afford unique information about energetic principles of their formation and structure, which is important for understanding the basic principles of their formation and functioning in biological systems. In the current study, we used quantum chemical methods for the investigation of the structure and stability of Cu(x)S(y)-type clusters that serve as models for different copper thiolate clusters or for their intermediates in a variety of copper proteins. Density functional theory based modeling was performed including solvent effects for water and protein-like environments. Thermodynamic parameters (DeltaH, DeltaS, DeltaG) were calculated in order to assess the effect of thermal contributions to the formation energies of various copper thiolate clusters. The all-tricoordinated polycopper thiolate cluster [Cu4(SMe)6]2- turned out to be the most stable structure among the calculated ones. This result is in agreement with the prevalence of this type of clusters in various copper proteins with no sequence homology that contain six cysteine residues. The cooperativity of formation of [Cu4(SMe)6]2- can be inferred from the significant energy differences between intermediary clusters. Among tetrathiolate structures, [Cu2(SMe)4]2- was the most stable one. This cluster is also found in many copper proteins. Influence of slight structural perturbations on the energetics of copper thiolate clusters is also analyzed and discussed.

Collective motions in Glucosamine-6-phosphate Synthase: Influence of Ligand Binding and role in Ammonia Channelling and Opening of the Fructose-6-Phosphate Binding Site

The large protein motions of the bacterial enzyme glucosamine-6-phosphate synthase have been addressed using full atom normal modes analysis for the empty, the glucose-6-phosphate and the glucose-6-phosphate + glutamate bound proteins. The approach that was used involving energy minimizations along the normal modes coordinates identified functional motions of the protein, some of which were characterized earlier by X-ray diffraction studies. This method made it possible for the first time to highlight significant energy differences according to whether none, only one or both of the active sites of the protein were occupied. Our data favoured a specific motion of the glutamine binding domain following the fixation of fructose-6-phosphate and suggested a rigidified structure with both sites occupied. Here, we show that most of the collective large amplitude motions of glucosamine-6-phosphate synthase that are modulated by ligand binding are crucial for the enzyme catalytic cycle, as they strongly modify the geometry of both the ammonia channel and the C-tail, demonstrating their role in ammonia transfer and ligand binding.

Quantum chemical study of the intermediate complex required for iron-mediated reactivity and antimalarial activity of dispiro-1,2,4-trioxolanes

Quantum chemical methods were used to obtain a structure for the peroxide–iron intermediate complex required for the inner-sphere reduction of dispiro-1,2,4-trioxolane antimalarials. Investigation of this biologically important interaction with iron(II) allows further understanding of the mechanisms of action and clearance of this promising new class of fully synthetic peroxide antimalarials. UHF, B3LYP and B3LYP//MP2 calculations were undertaken to provide structural and energetic information about the coordination complex of iron(II) with five representative trioxolanes, ranging in both iron-mediated reactivity and antimalarial activity. Significant energy differences were observed between the conformational isomers of these trioxolanes, indicating the importance of steric interactions between the iron complex ligands and the trioxolane substituents. These calculations may explain the slower iron-mediated reaction rates of trioxolanes that preferentially adopt a conformation that sterically shields the peroxide bond. The relationship between antimalarial activity and accessibility of the peroxide bond to iron has also been demonstrated for these trioxolanes.

Steel heating in an arc smelting furnace and a ladle-furnace unit

Two-stage arc heating of ferrocarbon melts in smelting equipment and casting ladles is very widely used in ferrous metallurgy [1‐3]. The efficiency of steel smelting in this case may be judged from the reduced total power consumption when heating the melt in the arc smelting furnace and the ladle‐furnace unit. The energy-saving potential of the smelting technology depends significantly on the efficient integration of the operations within a steel-casting module that includes an arc furnace, a ladle‐furnace unit, and a high-speed continuous-casting machine [4, 5]. Obviously, the efficiency of two-stage melt heating by an electric arc largely depends on the harmonization of its parameters: the discharge temperature of the steel from the smelting unit, the duration and the initial and final temperatures of ladle treatment, and the temperature at which steel is supplied to the continuous-casting machine. To improve the production parameters, practically all electrosmelting shops, regardless of their development strategy, are equipped with ladle‐furnace units [6]. We also know that there are significant technological and energy differences between melt heating in an arc furnace and in a ladle‐furnace unit. This suggests the need for quantitative analysis of heating in each unit. In the present work, we investigate the heating rate of the metal, the thermal-energy consumption, and the efficiency of energy utilization from the electric arc and alternative sources in arc furnaces of classical and updated design and also in the ladle‐furnace unit. In experiments conducted in an arc furnace with a reduction period and in a casting ladle, the steel is reduced for at least 15‐20 min before the first measurement. The homogeneity of the refined slag and the operation of the injection nozzles are visually checked. In all the experiments, the transformer is switched off prior to the measurements, and the metal is held for 1.0‐1.5 min so as to average out the temperature. Then the steel temperature ( t 1 , ° C) is measured by an immersion thermocouple. Before switching the transformer on, the meter readings for the active electrical energy ( p 1 , kW-h) are recorded. Immediately after the first temperature measurement, the furnace transformer is turned on, and its operation is monitored in terms of the instrument readings. (In the heating period, no switching of the power stages, large jumps in the current, or changes in the conditions of inert-gas injection are permitted.) In addition, in the experiments, nothing is added to the melt bath. At the end of heating ( τ = 5‐ 15 min) and averaging of the temperature (1.0‐ 1.5 min), the steel temperature is measured again ( t 2 , ° C), and the readings of the electrical-energy meter are recorded ( p 2 , kW-h). The heating rate v ( ° C/min) and the power consumption ∆ p (kW-h/t ° C) are calculated from the formulas